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diff --git a/books/economics/game-theory-critical-introduction.md b/books/economics/game-theory-critical-introduction.md new file mode 100644 index 0000000..462b4aa --- /dev/null +++ b/books/economics/game-theory-critical-introduction.md @@ -0,0 +1,2397 @@ +[[!meta title="Game Theory: a Critical Introduction"]] + +## Index + +* Difference between meteorological and traffic-jam-style predictions: 18. +* Frequent assumption (but not always) on game theory that individuals knows + the rules of the game; that they even known their inner motives: 28. +* Individualism, separation of structure and choice, 31. +* MAD, 86; 88. +* Elimination of non-credible threats, 88. + +# Excerpts + +## Intro + +What is game theory: + + In many respects this enthusiasm is not difficult to understand. Game theory + was probably born with the publication of The Theory of Games and Economic + Behaviour by John von Neumann and Oskar Morgenstern (first published in + 1944 with second and third editions in 1947 and 1953). They defined a game + as any interaction between agents that is governed by a set of rules + specifying the possible moves for each participant and a set of outcomes for + each possible combination of moves. + +How it can help: + + If game theory does make a further substantial contribution, then we + believe that it is a negative one. The contribution comes through + demonstrating the limits of a particular form of individualism in social + science: one based exclusively on the model of persons as preference satisfiers. + This model is often regarded as the direct heir of David Hume’s (the 18th + century philosopher) conceptualisation of human reasoning and motivation. It + is principally associated with what is known today as rational choice theory, or + with the (neoclassical) economic approach to social life (see Downs, 1957, and + Becker, 1976). Our main conclusion on this theme (which we will develop + through the book) can be rephrased accordingly: we believe that game theory + reveals the limits of ‘rational choice’ and of the (neoclassical) economic + approach to life. In other words, game theory does not actually deliver Jon + Elster’s ‘solid microfoundations’ for all social science; and this tells us + something about the inadequacy of its chosen ‘microfoundations’. + +Assumptions: + + three key assumptions: agents are instrumentally + rational (section 1.2.1); they have common knowledge of this rationality + (section 1.2.2); and they know the rules of the game (section 1.2.3). + These assumptions set out where game theory stands on the big questions of + the sort ‘who am I, what am I doing here and how can I know about either?’. + The first and third are ontological. 1 They establish what game theory takes as + the material of social science: in particular, what it takes to be the essence of + individuals and their relation in society. The second raises epistemological + issues 2 (and in some games it is not essential for the analysis). It is concerned + with what can be inferred about the beliefs which people will hold about how + games will be played when they have common knowledge of their rationality. + +Instrumental rationality (_Homo economicus_): + + We spend more time discussing these assumptions than is perhaps usual in + texts on game theory because we believe that the assumptions are both + controversial and problematic, in their own terms, when cast as general + propositions concerning interactions between individuals. This is one respect + in which this is a critical introduction. The discussions of instrumental + rationality and common knowledge of instrumental rationality (sections 1.2.1 + and 1.2.2), in particular, are indispensable for anyone interested in game + theory. In comparison section 1.2.3 will appeal more to those who are + concerned with where game theory fits in to the wider debates within social + + [...] + + Individuals who are instrumentally rational have preferences over various + ‘things’, e.g. bread over toast, toast and honey over bread and butter, rock + over classical music, etc., and they are deemed rational because they select + actions which will best satisfy those preferences. One of the virtues of this + model is that very little needs to be assumed about a person’s preferences. + Rationality is cast in a means-end framework with the task of selecting the + most appropriate means for achieving certain ends (i.e. preference + satisfaction); and for this purpose, preferences (or ‘ends’) must be coherent + in only a weak sense that we must be able to talk about satisfying them more + or less. Technically we must have a ‘preference ordering’ because it is only + when preferences are ordered that we will be able to begin to make + judgements about how different actions satisfy our preferences in different + degrees. + + [...] + + Thus it appears a promisingly general model of action. For instance, it could + apply to any type of player of games and not just individuals. So long as the + State or the working class or the police have a consistent set of objectives/ + preferences, then we could assume that it (or they) too act instrumentally so + as to achieve those ends. Likewise it does not matter what ends a person + pursues: they can be selfish, weird, altruistic or whatever; so long as they + consistently motivate then people can still act so as to satisfy them best. + +An agent is "rational" in this conext when they have preference ordering" and +if "they select the action that maximizes those preferences: + + Readers familiar with neoclassical Homo economicus will need no further + introduction. This is the model found in standard introductory texts, where + preferences are represented by indifference curves (or utility functions) and + agents are assumed rational because they select the action which attains the + highest feasible indifference curve (maximises utility). For readers who have + not come across these standard texts or who have forgotten them, it is worth + explaining that preferences are sometimes represented mathematically by a + utility function. As a result, acting instrumentally to satisfy best one’s + preferences becomes the equivalent of utility maximising behaviour. + +Reason and slavery: + + Even when we accept the Kantian argument, it is plain that reason’s + guidance is liable to depend on characteristics of time and place. For + example, consider the objective of ‘owning another person’. This obviously + does not pass the test of the categorical imperative since all persons could + not all own a person. Does this mean then we should reject slave-holding? At + first glance, the answer seems to be obvious: of course, it does! But notice it + will only do this if slaves are considered people. Of course we consider + slaves people and this is in part why we abhor slavery, but ancient Greece + did not consider slaves as people and so ancient Greeks would not have been + disturbed in their practice of slavery by an application of the categorical + imperative. + +Reason dependent on culture: + + Wittgenstein suggests that if you want to know why people act in the way that + they do, then ultimately you are often forced in a somewhat circular fashion to + say that such actions are part of the practices of the society in which those + persons find themselves. In other words, it is the fact that people behave in a + particular way in society which supplies the reason for the individual person to + act: or, if you like, actions often supply their own reasons. This is shorthand + description rather than explanation of Wittgenstein’s argument, but it serves to + make the connection to an influential body of psychological theory which + makes a rather similar point. + +Cognitive dissonance and free market proponents: + + Festinger’s (1957) cognitive dissonance theory proposes a model where + reason works to ‘rationalise’ action rather than guide it. The point is that we + often seem to have no reason for acting the way that we do. For instance, we + may recognise one reason for acting in a particular way, but we can equally + recognise the pull of a reason for acting in a contrary fashion. Alternatively, + we may simply see no reason for acting one way rather than another. In such + circumstances, Festinger suggests that we experience psychological distress. It + comes from the dissonance between our self-image as individuals who are + authors of our own action and our manifest lack of reason for acting. It is like + a crisis of self-respect and we seek to remove it by creating reasons. In short + we often rationalise our actions ex post rather than reason ex ante to take them + as the instrumental model suggests. + + [...] + + Research has shown that people seek out and read advertisements for + the brand of car they have just bought. Indeed, to return us to economics, it is + precisely this insight which has been at the heart of one of the Austrian and + other critiques of the central planning system when it is argued that planning + can never substitute for the market because it presupposes information + regarding preferences which is in part created in markets when consumers + choose. + +Infinite regress of the economics of information acquisiton (i.e learning, eg. +from a secret service): + + Actually most game theorists seem to agree on one aspect of the problem + of belief formation in the social world: how to update beliefs in the presence + of new information. They assume agents will use Bayes’s rule. This is explained + in Box 1.6. We note there some difficulties with transplanting a technique from + the natural sciences to the social world which are related to the observation we + have just made. We focus here on a slightly different problem. Bayes provides + a rule for updating, but where do the original (prior) expectations come from? + Or to put the question in a different way: in the absence of evidence, how do + agents form probability assessments governing events like the behaviour of + others? + + There are two approaches in the economics literature. One responds by + suggesting that people do not just passively have expectations. They do not + just wait for information to fall from trees. Instead they make a conscious + decision over how much information to look for. Of course, one must have + started from somewhere, but this is less important than the fact that the + acquisition of information will have transformed these original ‘prejudices’. + The crucial question, on this account, then becomes: what determines the + amount of effort agents put into looking for information? This is deceptively + easy to answer in a manner consistent with instrumental rationality. The + instrumentally rational agent will keep on acquiring information to the point + where the last bit of search effort costs her or him in utility terms the same + amount as the amount of utility he or she expects to get from the + information gained by this last bit of effort. The reason is simple. As long as + a little bit more effort is likely to give the agent more utility than it costs, + then it will be adding to the sum of utilities which the agent is seeking to + maximise. + + [...] + + This looks promising and entirely consistent with the definition of + instrumentally rational behaviour. But it begs the question of how the agent + knows how to evaluate the potential utility gains from a bit more information + _prior to gaining that information_. Perhaps he or she has formulated expectations of + the value of a little bit more information and can act on that. But then the + problem has been elevated to a higher level rather than solved. How did he or + she acquire that expectation about the value of information? ‘By acquiring + information about the value of information up to the point where the + marginal benefits of this (second-order) information were equal to the costs’, + is the obvious answer. But the moment it is offered, we have the beginnings of + an infinite regress as we ask the same question of how the agent knows the + value of this second-order information. To prevent this infinite regress, we + must be guided by something _in addition_ to instrumental calculation. But this + means that the paradigm of instrumentally rational choices is incomplete. The + only alternative would be to assume that the individual _knows_ the benefits that + he or she can expect on average from a little more search (i.e. the expected + marginal benefits) because he or she knows the full information set. But then + there is no problem of how much information to acquire because the person + knows everything! + +Infinite recursion of the common knowledge (CKR): + + If you want to form an expectation about what somebody does, what + could be more natural than to model what determines their behaviour and + then use the model to predict what they will do in the circumstances that + interest you? You could assume the person is an idiot or a robot or whatever, + but most of the time you will be playing games with people who are + instrumentally rational like yourself and so it will make sense to model your + opponent as instrumentally rational. This is the idea that is built into the + analysis of games to cover how players form expectations. We assume that + there is common knowledge of rationality held by the players. It is at once + both a simple and complex approach to the problem of expectation + formation. The complication arises because with common knowledge of + rationality I know that you are instrumentally rational and since you are + rational and know that I am rational you will also know that I know that you + are rational and since I know that you are rational and that you know that I + am rational I will also know that you know that I know that you are rational + and so on…. This is what common knowledge of rationality means. + + [...] + + It is difficult to pin down because common knowledge of X + (whatever X may be) cannot be converted into a finite phrase beginning with ‘I + know…’. The best one can do is to say that if Jack and Jill have common + knowledge of X then ‘Jack knows that Jill knows that Jack knows …that Jill + knows that Jack knows…X’—an infinite sentence. The idea reminds one of + what happens when a camera is pointing to a television screen that conveys the + image recorded by the very same camera: an infinite self-reflection. Put in this + way, what looked a promising assumption suddenly actually seems capable of + leading you anywhere. + + [...] + + The problem of expectation formation spins hopelessly out of control. + + Nevertheless game theorists typically assume CKR and many of them, and + certainly most people who apply game theory in economics and other + disciplines + +Uniformity: Consistent Alignment of Beliefs (CAB), another weak assumption +based on Harsanyi doctrine requiring equal information; followed by a +comparison with Socract dialectics: + + Put informally, the notion of _consistent alignment of beliefs_ (CAB) means that + no instrumentally rational person can expect another similarly rational + person who has the same infor mation to develop different thought + processes. Or, alternatively, that no rational person expects to be surprised + by another rational person. The point is that if the other person’s thought is + genuinely moving along rational lines, then since you know the person is + rational and you are also rational then your thoughts about what your + rational opponent might be doing will take you on the same lines as his or + her own thoughts. The same thing applies to others provided they respect + _your_ thoughts. So your beliefs about what your opponents will do are + consistently aligned in the sense that if you actually knew their plans, you + would not want to change your beliefs; and if they knew your plans they + would not want to change the beliefs they hold about you and which support + their own planned actions. + + Note that this does not mean that everything can be deterministically + predicted. + +Reason reflecting on itself: + + These observations are only designed to signal possible trouble ahead + and we shall examine this issue in greater detail in Chapters 2 and 3. We + conclude the discussion now with a pointer to wider philosophical currents. + Many decades before the appearance of game theor y, the Ger man + philosophers G.F.W.Hegel and Immanuel Kant had already considered the + notion of the self-conscious reflection of human reasoning on itself. Their + main question was: can our reasoning faculty turn on itself and, if it can, + what can it infer? Reason can certainly help persons develop ways of + cultivating the land and, therefore, escape the tyranny of hunger. But can it + understand how it, itself, works? In game theory we are not exactly + concerned with this issue but the question of what follows from common + knowledge of rationality has a similar sort of reflexive structure. When + reason knowingly encounters itself in a game, does this tell us anything + about what reason should expect of itself? + + What is revealing about the comparison between game theory and + thinkers like Kant and Hegel is that, unlike them, game theory offers + something settled in the form of CAB. What is a source of delight, + puzzlement and uncertainty for the German philosophers is treated as a + problem solved by game theory. For instance, Hegel sees reason reflecting + on reason as it reflects on itself as part of the restlessness which drives + human history. This means that for him there are no answers to the + question of what reason demands of reason in other people outside of + human history. Instead history offers a changing set of answers. Likewise + Kant supplies a weak answer to the question. Rather than giving substantial + advice, reason supplies a negative constraint which any principle of + knowledge must satisfy if it is to be shared by a community of rational + people: any rational principle of thought must be capable of being followed + by all. O’Neill (1989) puts the point in the following way: + + [Kant] denies not only that we have access to transcendent meta- + physical truths, such as the claims of rational theology, but also that + reason has intrinsic or transcendent vindication, or is given in + consciousness. He does not deify reason. The only route by which we + can vindicate certain ways of thinking and acting, and claim that those + ways have authority, is by considering how we must discipline our + thinking if we are to think or act at all. This disciplining leads us not to + algorithms of reason, but to certain constraints on all thinking, + communication and interaction among any plurality. In particular we are + led to the principle of rejecting thought, act or communication that is + guided by principles that others cannot adopt. + (O’Neill p. 27) + +Summary: + + To summarise, game theory is avowedly Humean in orientation. [...] + The second [aspect] is that game theorists seem to assume _too much_ on behalf + of reason [even more than Hume did]. + +Giddens, Wittgenstein language games and the "organic or holistic view of the relation between action and structure" (pages 30-31): + + The question is ontological and it connects directly with the earlier + discussion of instrumental rationality. Just as instrumental rationality is not + the only ontological view of what is the essence of human rationality, there is + more than one ontological view regarding the essence of social interaction. + Game theory works with one view of social interaction, which meshes well + with the instrumental account of human rationality; but equally there are + other views (inspired by Kant, Hegel, Marx, Wittgenstein) which in turn + require different models of (rational) action. + +State (pages 32-33): + + Perhaps the most famous example of this type of + institutional creation comes from the early English philosopher Thomas + Hobbes who suggested in Leviathan that, out of fear of each other, + individuals would contract with each other to form a State. In short, they + would accept the absolute power of a sovereign because the sovereign’s + ability to enforce contracts enables each individual to transcend the dog- + eat-dog world of the state of nature, where no one could trust anyone and + life was ‘short, nasty and brutish’. + + Thus, the key individualist move is to draw attention to the way that + structures not only constrain; they also enable (at least those who are in a + position to create them). It is the fact that they enable which persuades + individuals consciously (as in State formation) or unconsciously (in the case + of those which are generated spontaneously) to build them. To bring out + this point and see how it connects with the earlier discussion of the + relation between action and structure it may be helpful to contrast Hobbes + with Rousseau. Hobbes has the State emerging from a contract between + individuals because it serves the interests of those individuals. Rousseau + also talked of a social contract between individuals, but he did not speak + this individualist language. For him, the political (democratic) process was + not a mere means of ser ving persons’ interests by satisfying their + preferences. It was also a process which changed people’s preferences. People + were socialised, if you like, and democracy helped to create a new human + being, more tolerant, less selfish, better educated and capable of cherishing + the new values of the era of Enlightenment. By contrast, Hobbes’ men and + women were the same people before and after the contract which created + the State. 4 + +Game theory as justification of individualism (pages 32-33), which reminds the +discussion made by Dany-Robert Dufour in La Cite Perverse; it is also noted +that the State is considered a "collective action agency": + + Where do structures come from when they are separate from actions? An + ambitious response which distinguishes methodological individualists of all + types is that the structures are merely the deposits of previous interactions + (potentially understood, of course, as games). This answer may seem to threaten + an infinite regress in the sense that the structures of the previous + interaction must also be explained and so on. But, the individualist will want + to claim that ultimately all social str uctures spring from interactions + between some set of asocial individuals; this is why it is ‘individualist’. + + [...] + + Returning to game theory’s potential contribution, we can see that, in so + far as individuals are modelled as Humean agents, game theory is well placed + to help assess the claims of methodological individualists. After all, game + theory purports to analyse social interaction between individuals who, as + Hume argued, have passions and a reason to serve them. Thus game theory + should enable us to examine the claim that, beginning from a situation with + no institutions (or structures), the self-interested behaviour of these + instrumentally rational agents will either bring about institutions or fuel their + evolution. An examination of the explanatory power of game theory in such + settings is one way of testing the individualist claims. + In fact, as we shall see in subsequent chapters, the recurring difficulty + + [...] + + Suppose we take the methodological individualist route and see + institutions as the deposits of previous interactions between individuals. + Individualists are not bound to find that the institutions which emerge in + this way are fair or just. Indeed, in practice, many institutions reflect the + fact that they were created by one group of people and then imposed on + other groups. All that any methodological individualist is committed to is + being able to find the origin of institutions in the acts of individuals qua + individuals. The political theory of liberal individualism goes a stage + further and tries to pass judgement on the legitimacy of particular + institutions. Institutions in this view are to be regarded as legitimate in so + far as all individuals who are governed by them would have broadly + ‘agreed’ to their creation. + + Naturally, much will turn on how ‘agreement’ is to be judged because + people in desperate situations will often ‘agree’ to the most desperate of + outcomes. Thus there are disputes over what constitutes the appropriate + reference point (the equivalent to Hobbes’s state of nature) for judging + whether people would have agreed to such and such an arrangement. We set + aside a host of further problems which emerge the moment one steps outside + liberal individualist premises and casts doubt over whether people’s + preferences have been autonomously chosen. Game theory has little to + contribute to this aspect of the dispute. However, it does make two + significant contributions to the discussions in liberal individualism with + respect to how we might judge ‘agreement’. + +Prisioner's dilemma and the hobbesian argument for the creation of a State (pages 36-37): +resolution would require a higher State in the next upper level of recursion: + + Finally there is the prisoners’ dilemma game (to which we have dedicated the + whole of Chapter 5 and much of Chapter 6). Recall the time when there were + still two superpowers each of which would like to dominate the other, if + possible. They each faced a choice between arming and disarming. When both + arm or both disarm, neither is able to dominate the other. Since arming is + costly, when both decide to arm this is plainly worse than when both decide to + disarm. However, since we have assumed each would like to dominate the + other, it is possible that the best outcome for each party is when that party + arms and the other disarms since although this is costly it allows the arming + side to dominate the other. These preferences are reflected in the ‘arbitrary’ + utility pay-offs depicted in Figure 1.4. + + Game theory makes a rather stark prediction in this game: both players will + arm (the reasons will be given later). It is a paradoxical result because each + does what is in their own interest and yet their actions are collectively self- + defeating in the sense that mutual armament is plainly worse than the + alternative of mutual disarmament which was available to them (pay-off 1 for + utility pay-offs depicted in Figure 1.4. + + Game theory makes a rather stark prediction in this game: both players will + arm (the reasons will be given later). It is a paradoxical result because each + does what is in their own interest and yet their actions are collectively self- + defeating in the sense that mutual armament is plainly worse than the + alternative of mutual disarmament which was available to them (pay-off 1 for + each rather than 2). The existence of this type of interaction together with the + inference that both will arm has provided one of the strongest arguments for + the creation of a State. This is, in effect, Thomas Hobbes’s argument in + Leviathan. And since our players here are themselves States, both countries + should agree to submit to the authority of a higher State which will enforce an + agreement to disar m (an argument for a strong, independent, United + Nations?). + +Too much trust in that type of instrumental rationality might lead to lower +outcomes in some games: + + The term rationalisable has been used to describe such strategies because a + player can defend his or her choice (i.e. rationalise it) on the basis of beliefs + about the beliefs of the opponent which are not inconsistent with the game’s + data. However, to pull this off, we need ‘more’ commonly known rationality + than in the simpler games in Figures 2.1 and 2.3. Looking at Figure 2.4 we see + that outcome (100, 90) is much more inviting than the rationalisable outcome + (1, 1). It is the deepening confidence in each other’s instrumental rationality + (fifth-order CKR, to be precise) which leads our players to (1, 1). In summary + notation, the rationalisable strategies R2, C2 are supported by the following + train of thinking (which reflects the six steps described earlier): + + -- 48 + +Nash-equilibrium: self-confirming strategy: + + A set of rationalisable strategies (one for each player) are in a Nash + equilibrium if their implementation confirms the expectations of each player + about the other’s choice. Put differently, Nash strategies are the only + rationalisable ones which, if implemented, confirm the expectations on which + they were based. This is why they are often referred to as self-confirming + strategies or why it can be said that this equilibrium concept requires that + players’ beliefs are consistently aligned (CAB). + + -- 53 + +Arguments against CAB: + + In the same spirit, it is sometimes argued (borrowing a line from John von + Neumann and Oskar Morgenstern) that the objective of any analysis of games is + the equivalent of writing a book on how to play games; and the minimum + condition which any piece of advice on how to play a game must satisfy is + simple: the advice must remain good advice once the book has been published. + In other words, it could not really be good advice if people would not want to + follow it once the advice was widely known. On this test, only (R2, C2) pass, + since when the R player follows the book’s advice, the C player would want to + follow it as well, and vice versa. The same cannot be said of the other + rationalisable strategies. For instance, suppose (R1, C1) was recommended: then + R would not want to follow the advice when C is expected to follow it by + selecting C1 and likewise, if R was expected to follow the advice, C would not + want to. + + Both versions of the argument with respect to what mutual rationality entails + seem plausible. Yet, there is something odd here. Does respect for each other’s + rationality lead each person to believe that neither will make a mistake in a + game? Anyone who has talked to good chess players (perhaps the masters of + strategic thinking) will testify that rational persons pitted against equally + rational opponents (whose rationality they respect) do not immediately assume + that their opposition will never make errors. On the contrary, the point in + chess is to engender such errors! Are chess players irrational then? One is + inclined to answer no, but why? And what is the difference as + + -- 57 + +Limits conceptualizing reason as an algorithm ("Humean approach to reason +is algorithmic"): + + Harsanyi doctrine seems to depend on a powerfully algorithmic and controversial + view of reason. Reason on this account (at least in an important part) is akin + to a set of rules of inference which can be used in moving from evidence to + expectations. That is why people using reason (because they are using the same + algorithms) should come to the same conclusion. However, there is genuine + puzzlement over whether such an algorithmic view of reason can apply to all + circumstances. Can any finite set of rules contain rules for their own + application to all possible circumstances? The answer seems to be no, since + under some sufficiently detailed level of description there will be a question of + whether the rule applies to this event and so we shall need rules for applying + the rules for applying the rules. And as there is no limit to the detail of the + description of events, we shall need rules for applying the rules for applying + the rules, and so on to infinity. In other words, every set of rules will require + creative interpretation in some circumstances and so in these cases it is + perfectly possible for two individuals who share the same rules to hold + divergent expectations. + + This puts a familiar observation from John Maynard Keynes and Frank + Knight regarding genuine uncertainty in a slightly different way, but + nevertheless it yields the same conclusion. There will be circumstances under + which individuals are unable to decide rationally what probability assessment + to attach to events because the events are uncertain and so it should not be + surprising to find that they disagree. Likewise, the admiration for + entrepreneurship found among economists of the Austrian school depends on + the existence of uncertainty. Entrepreneurship is highly valued precisely + because, as a result of uncertainty, people can hold different expectations + regarding the future. In this context, the entrepreneurs are those who back + their judgement against that of others and succeed. In other words, there + would be no job for entrepreneurs if we all held common expectations in a + world ruled by CAB! + + A similar conclusion regarding ineliminable uncertainty is shared by social + theorists who have been influenced by the philosophy of Kant. They deny that + reason should be understood algorithmically or that it always supplies answers + as to what to do. For Kantians reason supplies a critique of itself which is the + source of negative restraints on what we can believe rather than positive + instructions as to what we should believe. Thus the categorical imperative (see + section 1.2.1), which according to Kant ought to determine many of our + significant choices, is a sieve for beliefs and it rarely singles out one belief. + Instead, there are often many which pass the test and so there is plenty of + room for disagreement over what beliefs to hold. + + Perhaps somewhat surprisingly though, a part of Kant’s argument might + lend support to the Nash equilibrium concept. In particular Kant thought that + rational agents should only hold beliefs which are capable of being + universalised. This idea, taken by itself, might prove a powerful ally of Nash. + [...] Of course, a full Kantian perspective is + likely to demand rather more than this and it is not typically adopted by game + theorists. Indeed such a defence of Nash would undo much of the + foundations of game theory: for the categorical imperative would even + recommend choosing dominated strategies if this is the type of behaviour that + each wished everyone adopted. Such thoughts sit uncomfortably with the + Humean foundations of game theory and we will not dwell on them for now. + Instead, since the spirit of the Humean approach to reason is algorithmic, we + shall continue discussing the difficulties with the Harsanyi—Aumann defence + of Nash. + + -- 58-60 + +"Irrational" plays which might intend to send a message to other players: + + Indeed why should one assume in this way that players cannot (or + should not) try to make statements about themselves through patterning + their ‘trembles? The question becomes particularly sharp once it is recalled + that, on the conventional account, players must expect that there is always + some chance of a tremble. Trembles in this sense are part of normal + behaviour, and the critics argue that agents may well attempt to use them + as a medium for signalling something to each other. Of course, players will + not do so if they believe that their chosen pattern is going to be ignored + by others. But that is the point: why assume that this is what they will + believe from the beginning, especially when agents can see that the + generally accepted use of trembles as signals might secure a better + outcome for both players [...]? + + Note that this is not an argument against backward induction per se: it is an + argument against assuming CKR while working out beliefs via backward + induction (i.e. a criticism of Nash backward induction). When agents consider + patterning their ‘trembles’, they project forward about future behaviour given + that there are trembles now or in the past. What makes it ambiguous whether + they should do this, or stick to Nash backward induction instead, is that there + is no uniquely rational way of playing games like Figures 3.5 or 3.6 (unlike the + race to 20 game in which there is). In this light, the subgame perfect Nash + equilibrium offers one of many possible scenarios of how rational agents will + behave. + + -- 93 + +Why not expand this affirmation so _any_ move to signal some intention? + +## Misc + +Page 101: + + Hence these refinements (e.g. proper equilibria), likethe Nash + equilibrium project itself, seem to have to appeal to somethingother + than the traditional assumptions of game theory regarding + rationalaction in a social context. + +Page 102: + + regarding the relation betweenconvention following and instrumental + rationality. The worry here takes usback to the discussion of section + 1.2.3 where for instance it was suggested thatconventions might best be + understood in the way suggested by Wittgenstein orHegel. In short, the + acceptance of convention may actually require a radicalreassessment of + the ontological foundations of game theory. + +Page 102: + + actually require a radicalreassessment of the ontological foundations + of game theory. + +Page 103: + + Why not give up on the Nash concept altogether? This ‘giving up’ might + takeon one of two forms. Firstly, game theory could appeal to the + concept ofrationalisable strategies (recall section 2.4 of Chapter 2) + which seemuncontentiously to flow from the assumptions of instrumental + rationalityand CKR. The difficulty with such a move is that it concedes + that gametheory is unable to say much about many games (e.g. Figures + 2.6, 2.12, etc.).Naturally, modesty of this sort might be entirely + appropriate for gametheory, although it will diminish its claims as a + solid foundation for socialscience. + +Page 104: + + Unlike the instrumentally rational model, for Hegelians and Marxists + actionbased on preferences feeds back to affect preferences, and so on, + in an everunfolding chain. (See Box 3.1 for a rather feeble attempt to + blend desires andbeliefs.) Likewise some social psychologists might + argue that the key to actionlies less with preferences and more with + the cognitive processes used bypeople; and consequently we should + address ourselves to understanding theseprocesses. + +Page 105: + + 105 + +Page 106: + + Quite simply, the significant social processes which write history + cannot beunderstood through the lens of instrumental rationality. This + destines gametheory to a footnote in some future text on the history of + social theory. Welet the reader decide.3 + +Page 108: + + Thirdly, the sociology of the discipline may provide further clues. + Twoconditions would seem to be essential for the modern development of + adiscipline within the academy. Firstly the discipline must be + intellectuallydistinguishable from other disciplines. Secondly, there + must be some barriersto the amateur pursuit of the discipline. (A third + condition which goes withoutsaying is that the discipline must be able + to claim that what it does ispotentially worth while.) The first + condition reduces the competition fromwithin the academy which might + come from other disciplines (to do thisworthwhile thing) and the second + ensures that there is no effectivecompetition from outside the academy. + In this context, the rational choicemodel has served economics very + well. It is the distinguishing intellectualfeature of economics as a + discipline and it is amenable to such formalisationthat it keeps most + amateurs well at bay. Thus it is plausible to argue that thesuccess of + economics as a discipline within the social sciences has been + closelyrelated to its championing of the rational choice model. + +Page 108: + + kind of amnesia or lobotomy which thediscipline seems to have suffered + regarding most things philosophical duringthe postwar period. + +Page 108: + + It isoften more plausible to think of the academy as a battleground + betweendisciplines rather than between ideas and the disciplines which + have goodsurvival features (like the barriers to entry identified + above) + +Page 109: + + explanations willonly prosper in so far as they are both superior and + they are not institutionallyundermined by the rise of neoclassical + economics and the demise ofsociology. It is not necessary to see these + things conspiratorially to see thepoint of this argument. All academics + have fought their corner in battles overresources and they always use + the special qualities of their discipline asammunition in one way or + another. Thus one might explain in functionalist termsthe mystifying + attachment of economics and game theory to Nash. + +Page 110: + + We have no special reason to prioritise one strand of our + proposedexplanation. Yet, there is more than a hint of irony in the + last suggestionbecause Jon Elster has often championed game theory and + its use of the Nashequilibrium concept as an alternative to functional + arguments in social science.Well, if the use of Nash by game theorists + is itself to be explainedfunctionally, then… + +Page 111: + + Liberal theorists often explain the State with reference to state of + nature. Forinstance, within the Hobbesian tradition there is a stark + choice between astate of nature in which a war of all against all + prevails and a peacefulsociety where the peace is enforced by a State + which acts in the interest ofall. The legitimacy of the State derives + from the fact that people who wouldotherwise live in Hobbes’s state of + nature (in which life is ‘brutish, nasty andshort’) can clearly see the + advantages of creating a State. Even if a State had + +Page 111: + + not surfaced historically for all sorts of other reasons, it would have + to beinvented.Such a hypothesised ‘invention’ would require a + cooperative act of comingtogether to create a State whose purpose will + be to secure rights over life andproperty. Nevertheless, even if all + this were common knowledge, it wouldnot guarantee that the State will + be created. There is a tricky further issuewhich must be resolved. The + people must agree to the precise property rightswhich the State will + defend and this is tricky because there are typically avariety of + possible property rights and the manner in which the benefits ofpeace + will be distributed depends on the precise property rights which + areselected (see Box 4.1).In other words, the common interest in peace + cannot be the onlyelement in the liberal explanation of the State, as + any well-defined andpoliced property rights will secure the peace. The + missing element is anaccount of how a particular set of property rights + are selected and thiswould seem to require an analysis of how people + resolve conflicts ofinterest. This is where bargaining theory promises + to make an importantcontribution to the liberal theory of the State + because it is concernedprecisely with interactions of this sort. + +Page 112: + + State creation in Hobbes’s world provides one example (which + especiallyinterests us because it suggests that bargaining theory may + throw light onsome of the claims of liberal political theory with + respect to the State), butthere are many others. + +Page 113: + + The creation of the institutions for enforcing agreements (like the + State)which are presumed by cooperative game theory requires as we have + seenthat agents first solve the bargaining problem non-cooperatively. + +Page 113: + + Indeed for this reason, and following thepractice of most game + theorists, we have so far discussed the non-cooperative play of games + ‘as if ’ there was no communication, therebyimplicitly treating any + communication which does take place in the absenceof an enforcement + agency as so much ‘cheap talk’ + +Page 113: + + In cooperative games agents cantalk to each other and make agreements + which are binding on later play. Innon-cooperative games, no agreements + are binding. Players can say whateverthey like, but there is no + external agency which will enforce that they dowhat they have said they + will do. + +Page 114: + + Thus it will have shown not just what sort of State rational agents + mightagree to create, but also how rational agents might solve a host + of bargainingproblems in social life. Unfortunately we have reasons to + doubt therobustness of this analysis and it is not difficult to see our + grounds forscepticism. If bargaining games resemble the hawk-dove game + and thediscussion in Chapter 2 is right to point to the existence of + multipleequilibria in this game under the standard assumptions of game + theory, thenhow does bargaining theory suddenly manage to generate a + uniqueequilibrium? + +Page 114: + + 114face value, the striking result of the non-cooperative analysis of + thebargaining problem is that it yields the same solution to the + bargainingproblem as the axiomatic approach. If this result is robust, + then it seems thatgame theory will have done an extraordinary service + by showing thatbargaining problems have unique solutions (whichever + route is preferred).Thus it will have shown not just what sort of State + rational agents mightagree to create, but also how rational agents + might solve a host of bargainingproblems in social life. Unfortunately + we have reasons to doubt therobustness of this analysis and it is not + difficult to see our grounds forscepticism. If bargaining games + resemble the hawk-dove game and thediscussion in Chapter 2 is right to + point to the existence of multipleequilibria in this game under the + standard assumptions of game theory, thenhow does bargaining theory + suddenly manage to generate a uniqueequilibrium? + +Page 116: + + A threat or promise which, if carried out, costs more tothe agent who + issued it than if it is not carried out, iscalled an incredible threat + or promise. + +Page 138: + + However, this failure topredict should be welcomed by John Rawls and + Robert Nozick as it providesan opening to their contrasting views of + what counts as justice betweenrational agents. + +Page 138: + + If the Nash solution were unique, then game theory would have + answeredan important question at the heart of liberal theory over the + type of Statewhich rational agents might agree to create. In addition, + it would have solveda question in moral philosophy over what justice + might demand in this and avariety of social interactions. After all, + how to divide the benefits from socialcooperation seems at first sight + to involve a tricky question in moralphilosophy concerning what is + just, but if rational agents will only ever agreeon the Nash division + then there is only one outcome for rational agents.Whether we want to + think of this as just seems optional. But if we do or ifwe think that + justice is involved, then we will know, and for onceunambiguously, what + justice apparently demands between instrumentallyrational + agents.Unfortunately, though, it seems we cannot draw these inferences + becausethe Nash solution is not the unique outcome. Accepting this + conclusion, weare concerned in this section with what bargaining theory + then contributes tothe liberal project of examining the State as if it + were the result of rational + +Page 140: + + behind the veil of ignorance. + +Page 142: + + Torture: Another example in moral philosophy is revealed by the problem + oftorture for utilitarians. For instance, a utilitarian calculation + focuses onoutcomes by summing the individual utilities found in + society. In so doing itdoes not enquire about the fairness or otherwise + of the processes responsiblefor generating those utilities with the + result that it could sanction torture whenthe utility gain of the + torturer exceeds the loss of the person being tortured.Yet most people + would feel uncomfortable with a society which sanctionedtorture on + these grounds because it unfairly transgresses the ‘rights’ of + thetortured. + +Page 143: + + Granted that society (andthe State) are not the result of some + living-room negotiation, what kind of“axioms” would have generated the + social outcomes which we observe in agiven society?’ That is, even if + we reject the preceding fictions (i.e. of the Stateas a massive + resolution of an n-person bargaining game, or of the veil ofignorance) + as theoretically and politically misleading, we may still + pinpointcertain axioms which would have generated the observed income + distributions(or distributions of opportunities, social roles, property + rights, etc.) as a resultof an (utterly) hypothetical bargaining game. + +Page 143: + + Roemer (1988) considers a problem faced by an international + agencycharged with distributing some resources with the aim of + improving health(say lowering infant mortality rates). How should the + authority distributethose resources? This is a particularly tricky + issue because different countriesin the world doubtless subscribe to + some very different principles which theywould regard as relevant to + this problem; and so agreement on a particularrule seems unlikely. + Nevertheless, he suggests that we approach the problemby considering + the following constraints (axioms) which we might want toapply to the + decision rule because they might be the object of significantagreement. + +Page 144: + + rule which allocates resources in such a way as to raise the country + with thelowest infant survival rate to that of the second lowest, and + then if the budgethas not been exhausted, it allocates resources to + these two countries until theyreach the survival rate of the third + lowest country, and so on until the budgetis exhausted. + +Page 147: + + It is tempting to think that the problem only arises here because + theprisoners cannot communicate with one another. If they could get + togetherthey would quickly see that the best for both comes from ‘not + confessing’.But as we saw in the previous chapter, communication is not + all that isneeded. Each still faces the choice of whether to hold to an + agreement that + +Page 148: + + The recognition ofthis predicament helps explain why individuals might + rationally submit to theauthority of a State, which can enforce an + agreement for ‘peace’. Theyvoluntarily relinquish some of their freedom + that they enjoy in the(hypothesised) state of nature to the State + because it unlocks the prisoners’dilemma. (It should be added perhaps + that this is not to be taken as a literalaccount of how all States or + enforcement agencies arise. The point of theargument is to demonstrate + the conditions under which a State or enforcementagency would enjoy + legitimacy among a population even though it restrictedindividual + freedoms.) + +Page 148: + + their normal business with the result that they prosper and enjoy a + more‘commodious’ living (as Hobbes phrased it), choosing strategy + ‘peace’ is like‘not confessing’ above; when everyone behaves in this + manner it is much betterthan when they all choose ‘war’ (’confess’). + However, and in spite of wideranging recognition that peace is better + than war, the same prisoners’ dilemmaproblem surfaces and leads to war. + +Page 148: + + While Hobbes thought that the authority of the State should be absolute + soas to discourage any cheating on ‘peace’, he also thought the scope + of itsinterventions in this regard would be quite minimal. In contrast + much of themodern fascination with the prisoners’ dilemma stems from + the fact that theprisoners’ dilemma seems to be a ubiquitous feature of + social life. Forinstance, it plausibly lies at the heart of many + problems which groups + +Page 148: + + they have struck over ‘not confessing’. Is it in the interest of either + party tokeep to such an agreement? No, a quick inspection reveals that + the bestaction in terms of pay-offs is still to ‘confess’. As Thomas + Hobbes remarkedin Leviathan when studying a similar problem, ‘covenants + struck without thesword are but words’. The prisoners may trumpet the + virtue of ‘notconfessing’ but if they are only motivated instrumentally + by the pay-offs,then it is only so much hot air because each will + ‘confess’ when the timecomes for a decision. + +Page 148: + + What seems to be required to avoid this outcome is a mechanism + whichallows for joint or collective decision making, thus ensuring that + both actuallydo ‘not confess’. In other words, there is a need for a + mechanism for enforcingan agreement—Hobbes’s ‘sword’, if you like. And + it is this recognition whichlies at the heart of a traditional liberal + argument dating back to Hobbes for thecreation of the State which is + seen as the ultimate enforcement agency.(Notice, however, that such an + argument applies equally to some otherinstitutions which have the + capacity to enforce agreements, for example theMafia.) In Hobbes’s + story, each individual in the state of nature can behavepeacefully or + in a war-like fashion. Since peace allows everyone to go about + +Page 149: + + it is notuncommon to find the dilemma treated as the essential model of + social life + +Page 149: + + The following four sectionsand the next chapter, on repeated games, + discuss some of the developmentsin the social science literature which + have been concerned with how thedilemma might be unlocked without the + services of the State. In otherwords, the later sections focus on the + question of whether the widespreadnature of this type of interaction + necessarily points to the (legitimate inliberal terms) creation of an + activist State. Are there other solutions whichcan be implemented + without involving the State or any public institution?Since the scope + of the State’s activities has become one of the mostcontested issues in + contemporary politics, it will come as no surprise todiscover that the + discussions around alternative solutions to the dilemmahave assumed a + central importance in recent political (and especially inliberal and + neoliberal) theory. + +Page 149: + + It arises as a problem of trust in every elemental economic + exchangebecause it is rare for the delivery of a good to be perfectly + synchronised withthe payment for it and this affords the opportunity to + cheat on the + +Page 150: + + These are two-person examples of the dilemma, but it is probably the + ‘n-person’ version of the dilemma (usually called the free rider + problem) which hasattracted most attention. It creates a collective + action problem among groupsof individuals. Again the examples are + legion. + +Page 151: + + The instrumentally rational individual will recognise that the best + action is‘do not attach’ (i.e. defection) whatever the others do. This + means that in apopulation of like-minded individuals, all will decide + similarly with the resultthat each individual gains 2 utils. This is + plainly an inferior outcome for allbecause everyone could have attached + the device and if they all had done soeach would have enjoyed 3 + utils.In these circumstances the individuals in this economy might + agree to theState enforcing attachment of the device. Alternatively, it + is easy to see howanother popular intervention by the State would also + do the trick. The Statecould tax each individual who did not attach the + device a sum equivalent to 2utils and this would turn ‘attach’ (C) into + the dominant strategy. + +Page 151: + + There is nothinglike the State which can enforce contracts within the + household to keep akitchen clean, but interestingly within a family + household one oftenobserves the exercise of patriarchal or paternal + power instead. Of course,the potential difficulty with such an + arrangement is that the patriarch mayrule in a partial manner with the + result that the kitchen is clean but with nohelp from the hands of the + patriarch! The role of the State has in suchcases been captured, so to + speak, by an interested party determined bygender. Then gender becomes + the determinant of who bears the burdenand who has the more privileged + role. Social power which ‘solves’prisoners’ dilemmas can be thus + exercised without the direct involvementof the State (even though the + State often enshrines such power in its owninstitutions). + +Page 152: + + Hence the prisoners’ dilemma/free rider might plausibly lie atthe + distinction which is widely attributed to Marx in the discussion of + classconsciousness between a class ‘of itself’ and ‘for itself’ (see + Elster, 1986b). Onsuch a view a class transforms itself into a ‘class + for itself’, or a society avoidsdeficient demand, by unlocking the + dilemma. + +Page 153: + + Adam Smith’s account of how the self-interest of sellers combines with + thepresence of many sellers to frustrate their designs and to keep + prices lowmight also fit this model of interaction. If you are the + seller choosing from thetwo row strategies C and D, then imagine that C + and D translate into ‘charge ahigh price’ and ‘charge a low price’ + respectively. Figure 5.2 could reflect yourpreference ordering as high + prices for all might be better than low prices forall and charging a + low price when all others charge a high might be the bestoption because + you scoop market share. Presumably the same applies to yourcompetitors. + Thus even though all sellers would be happier with a high level + ofprices, their joint interest is subverted because each acting + individually quiterationally charges a low price. It is as if an + invisible hand was at work onbehalf of the consumers. + +Page 155: + + This is perhaps the most radical departure from the + conventionalinstrumental understanding of what is entailed by + rationality because, whileaccepting the pay-offs, it suggests that + agents should act in a different wayupon them. The notion of + rationality is no longer understood in the means—end framework as the + selection of the means most likely to satisfy given ends. + +Page 155: + + thus enabling‘rationality’ to solve the problem when there are + sufficient numbers ofKantian agents. + +Page 155: + + For instance, we mighthave wrongly assumed earlier that there is no + honour among thieves becauseacting honourably could be connected to + acting rationally in some fullaccount of rationality in which case the + dilemma might be unlocked withoutthe intervention of the State (or some + such agency). This general idea oflinking a richer notion of rational + agency with the spontaneous solution ofthe dilemma has been variously + pursued in the social science literature andthis section and the + following three consider four of the more prominentsuggestions. + +Page 155: + + The first connects rationality with morality and Kant provides a + readyreference. His practical reason demands that we should undertake + thoseactions which when generalised yield the best outcomes. It does + not matterwhether others perform the same calculation and actually + undertake thesame action as you. The morality is deontological and it + is rational for theagent to be guided by a categorical imperative (see + Chapter 1). Consequently,in the free rider problem, the application of + the categorical imperative willinstruct Kantian agents to follow the + cooperative action + +Page 156: + + Similarly partisans in occupied Europe during the Second World War + riskedtheir lives even when it was not clear that it was instrumentally + rational toconfront the Nazis. In such cases, it seems people act on a + sense of what isright. + +Page 156: + + Likewise, Hardin (1982) suggests thatthe existence of environmental and + other voluntary organisations usuallyentails overcoming a free rider + problem and in the USA this may beexplained in part by an American + commitment to a form ofcontractarianism whereby ‘people play fair if + enough others do’ + +Page 156: + + Instead, rationality is conceived more as an expression of what is + possible: ithas become an end in its own right. This is not only + radical, it is alsocontroversial. Deontological moral philosophy is + controversial for the obviousreason that it is not concerned with the + actual consequences of an action, aswell as for the move to connect it + with rationality. (Nevertheless, O’Neill(1989) presents a recent + argument and provides an extended discussion of thismoral psychology + and how it might be applied.)Kant’s morality may seem rather demanding + for these reasons, but thereare weaker or vaguer types of moral + motivation which also seem capableof unlocking the prisoners’ dilemma. + For example, a general altruisticconcern for the welfare of others may + provide a sufficient reason forpeople not to defect on the cooperative + arrangement. + +Page 157: + + Another departure from the strict instrumental model of rational action + comeswhen individuals make decisions in a context of norms and these + norms arecapable of overriding considerations of what is instrumentally + rational. + +Page 157: + + On the other hand, given the well-known difficultiesassociated with any + coherent system of ethics (like utilitarianism), it seemsquite likely + that a person’s ethical concerns will not be captured by a well-behaved + set of preferences (see for instance Sen (1970) on the problems ofbeing + a Paretian Liberal). Indeed rational agents may well base their actions + onreasons which are external to their preferences. + +Page 157: + + Of course, there is a tricky issue concerning whether these rather + weaker orvaguer moral motivations (like altruism, acting on what is + fair or what is right)mark a deep breach with the instrumental model of + action. It might be arguedthat such ethical concerns can be represented + in this model by introducing theconcept of ethical preferences. Thus + the influence of ethical preferencestransforms the pay-offs in the + game. + +Page 158: + + Disputeswithin Aboriginal society are neither perceived as simply + between twoindividuals nor subject to some established community + tribunal. It is for thisreason that the resolution of a major conflict + will involve a significant amountof negotiation between the parties. + Yet the informal laws which govern thecontents of the negotiations are + well entrenched in the tribal culture. Forexample, it is not uncommon + for family members of the perpetrator to beasked to accept ‘punishment’ + if the individual offender is in prison andtherefore unavailable. + +Page 159: + + First World War. This was a war of unprecedentedcarnage both at the + beginning and the end. Yet during a middle period, non-aggression + between the two opposing trenches emerged spontaneously in theform of a + ‘live and let live’ norm. Christmas fraternisation is one + well-knownexample, but the ‘live and let live’ norm was applied much + more widely.Snipers would not shoot during meal times and so both sides + could go abouttheir business ‘talking and laughing’ at these hours. + Artillery was predictablyused both at certain times and at certain + locations. So both sides couldappear to demonstrate aggression by + venturing out at certain times and tocertain locations, knowing that + the shells would fall predictably close to, butnot on, their chosen + route. Likewise, it was not considered ‘etiquette’ to fireon working + parties who had been sent out to repair a position or collect thedead + and so on. + +Page 159: + + For instance, it is sometimes argued that thenorms of Confucian + societies enable those economies to solve the prisoners’dilemma/free + rider problems within companies without costly contracting + andmonitoring activity and that this explains, in part, the economic + success ofthose economies (see Hargreaves Heap, 1991, Casson, 1991, + North, 1991).Akerlof ’s (1983) discussion of loyalty filters, where he + explains the relativesuccess of Quaker groups in North America by their + respect for the norm ofhonesty, is another example— + +Page 160: + + Wittgenstein of Philosophical Investigations1 is an obvious source for + this viewbecause he would deny that the meaning of something like a + person’sinterests or desires can be divorced from a social setting; and + this is a usefulopportunity to take that argument further. The + attribution of meaningrequires language rules and it is impossible to + have a private language. Thereis a long argument around the possibility + or otherwise of private languagesand it may be worth pursuing the point + in a slightly different way by askinghow agents have knowledge of what + action will satisfy the condition ofbeing instrumentally rational. Any + claim to knowledge involves a firstunquestioned premise: I know this + because I accept x. Otherwise an infiniteregress is inevitable: I + accept x because I accept y and I accept ybecause…and so on. + Accordingly, if each person’s knowledge of what isrational is to be + accessible to one another, then they must share the samefirst premises. + It was Wittgenstein’s point that people must share somepractices if + they are to attach meaning to words and so avoid the problem ofinfinite + redescription which comes with any attempt to specify the rules + forapplying the rules of a language. + +Page 161: + + There is another similarity and difference which might also be + usefullymarked. To make it very crudely one might draw an analogy + between thedifficulty which Wittgenstein encounters over knowledge + claims and a similardifficulty which Simon (1982) addresses. (Herbert + Simon is well known ineconomics for his claim that agents are + procedurally rational, or boundedlyrational, because they do not have + the computing capacity to work out whatis the best to do in complex + settings.) To be sure, Wittgenstein finds theproblem in an infinite + regress of first principles while Simon finds thedifficulty in the + finite computing capacity of the brain. Nevertheless, both + +Page 161: + + discussion of the Harsanyi doctrine because a similar claim seems to + underpinthat doctrine. Namely that all rational individuals must come + to the sameconclusion when faced by the same evidence. Wittgenstein + would agree to theextent that some such shared basis of interpretation + must be present ifcommunication is to be possible. But he would deny + that all societies andpeoples will share the same basis for + interpretations. The source of the sharingfor Wittgenstein is not some + universal ‘rationality’, as it is for Harsanyi; ratherit is the + practices of the community in which the people live, and these willvary + considerably across time and space. + +Page 162: + + let us make the view inspired by Wittgensteinvery concrete. The + suggestion is that what is instrumentally rational is notwell defined + unless one appeals to the prevailing norms of behaviour. Thismay seem a + little strange in the context of a prisoners’ dilemma where thedemands + of instrumental rationality seem plain for all to see: defect! But,in + reply, those radically inspired by Wittgenstein would complain that + thenorms have already been at work in the definition of the matrix and + itspay-offs because it is rare for any social setting to throw up + unvarnishedpay-offs. A social setting requires interpretation before + the pay-offs can beassigned and norms are implicated in those + interpretations. (See forexample Polanyi (1945) who argues, in his + celebrated discussion of the riseof industrial society, that the + incentives of the market system are onlyeffective when the norms of + society place value on private materialadvance.) + +Page 162: + + The last reflection on rationality comes from David Gauthier. He + remainsfirmly in the instrumental camp and ambitiously argues that its + dictates havebeen wrongly understood in the prisoners’ dilemma game. + Instrumental rationalitydemands cooperation and not defection! To make + his argument he distinguishesbetween two sorts of maximisers: a + straightforward maximiser (SM) and aconstrained maximiser (CM). A + straightforward maximiser defects (D)following the same logic that we + have used so far. The constrained maximiseruses a conditional strategy + of cooperating (C) with fellow constrainedmaximisers and defecting with + straightforward maximisers. He then asks:which disposition + (straightforward or constrained) should an instrumentallyrational + person choose to have? (The decision can be usefully compared with + asimilar one confronting Ulysses in connection with listening to the + Sirens, + +Page 164: + + The point is that if instrumental rationality is what motivates the CM + inthe prisoners’ dilemma, then a CM must want to defect + +Page 164: + + In other words, being a CM may be better than beingan SM, but the best + strategy of all is to label yourself a CM and then cheaton the deal. + And, of course, when people do this, we are back in a worldwhere + everyone defects. + +Page 164: + + Surely, this line of argument goes,it pays not to ‘zap’ a fellow CM + because your reputation as a CM is therebypreserved and this enables + you to interact more fruitfully with fellow CMs inthe future. Should + you zap a fellow CM now, then everyone will know that youare a rogue + and so in your future interactions, you will be treated as an SM. + Inshort, in a repeated setting, it pays to forgo the short run gain + from defectingbecause this ensures the benefits of cooperation over the + long run. Thusinstrumental calculation can make true CM behaviour the + best course ofaction. + +Page 165: + + Moreover, it achieved aremarkable degree of cooperation. + +Page 165: + + each program.Tit-for-Tat, submitted by Anatol Rapoport, won the + tournament. Theprogram starts with a cooperative move and then does + whatever theopponent did on the previous move. It was, as Axelrod + points out, not onlythe simplest program, it was also the best! + +Page 165: + + dilemma can be defeated without the intervention of a collective agency + likethe State—that is, provided the interaction is repeated + sufficiently often tomake the long term benefits outweigh the short + gains. + +Page 166: + + ‘Is the Prisoners’ dilemma all of sociology?’Of course, it is not, he + answers. Nevertheless, it has fascinated social scientistsand proved + extremely difficult to unlock in one-shot plays of the game—atleast, + without the creation of a coercive agency like the State which is + capableof enforcing a collective action or without the introduction of + norms or somesuitable form of moral motivation on the part of the + individuals playing thegame. Of course, many interactions are repeated + and so this stark conclusionmay be modified by the discussion of the + next chapter. + +Page 167: + + Perhaps somewhat surprisingly, mutualdefection remains the only Nash + equilibrium. The following two sectionsdiscuss, respectively, + indefinitely repeated prisoners’ dilemma and therelated free rider + games. We show (section 6.4) that mutual cooperation isa possible Nash + equilibrium outcome in these games provided there is a‘sufficient’ + degree of uncertainty over when the repetition will cease.There are + some significant implications here both for liberal politicaltheory and + for the explanatory power of game theory. We notice that thisresult + means that mutual cooperation might be achieved without theintervention + of a collective agency like the State and/or withoutappealing to some + expanded notion of rational agency + +Page 168: + + the absence of a theory of equilibriumselection. + +Page 170: + + Firstly, it provides a theoretical warrant for the belief that + cooperation in theprisoners’ dilemma can be rationally sustained + without the intervention ofsome collective agency like the State, + provided there is sufficient (to be definedlater) doubt over when the + repeated game will end. Thus the presence of aprisoners’ dilemma + interaction does not necessarily entail either a poor socialoutcome or + the institutions of formal collective decision making. The + thirdalternative is for players to adopt a tit-for-tat strategy + rationally.1 If they adoptthis third alternative the socially inferior + outcome of mutual defection will beavoided without the interfering + presence of the State or some other formal(coercive) institution. + +Page 171: + + Equally, it is probable that both prisonersin the original example may + think twice about ‘confessing’ because each knowsthat they are likely + to encounter one another again (if not in prison, at leastoutside) and + so there are likely to be opportunities for exacting ‘punishment’ ata + later date. + +Page 171: + + Folk theorem + +Page 172: + + This is an extremely important result for the social sciences because + itmeans that there are always multiple Nash equilibria in such + indefinitelyrepeated games. Hence, even if Nash is accepted as the + appropriateequilibrium concept for games with individuals who are + instrumentally rationaland who have common knowledge of that + rationality, it will not explain howindividuals select their strategies + because there are many strategy pairs whichform Nash equilibria in + these repeated games. Of course, we have encounteredthis problem in + some one-shot games before, but the importance of this resultis that it + means the problem is always there in indefinitely repeated games.Even + worse, it is amplified by repetition. In other words, game theory needs + tobe supplemented by a theory of equilibrium selection if it is to + explain actionin these indefinitely repeated games, especially if it is + to explain howcooperation actually arises spontaneously in indefinitely + repeated prisoners’dilemma games. + +Page 175: + + Now consider a tit-for-tat strategy in this group which works in + thefollowing way. The strategy partitions the group into those who are + in ‘goodstanding’ and those who are in ‘no standing’ based on whether + the individualcontributed to the collective fund in the last time + period. Those in ‘goodstanding’ are eligible for the receipt of help + from the group if they fall ‘ill’ thistime period, whereas those who + are in ‘no standing’ are not eligible for help.Thus tit-for-tat + specifies cooperation and puts you in ‘good standing’ for thereceipt of + a benefit if you fall ‘ill’ (alternatively, to connect with the + earlierdiscussion, one might think of cooperating as securing a + ‘reputation’ whichputs one in ‘good standing’ + +Page 175: + + Notice your decision now will determine whether you are in ‘good + standing’from now until the next opportunity that you get to make this + decision (whichwill be the next period if you do not fall ‘ill’ or the + period after that if you fall‘ill’). So we focus on the returns from + your choice now until you next get theopportunity to choose. + +Page 176: + + Who needs the State? + +Page 176: + + Here we pick up threads of the Hobbesianargument for the State and see + what the result holds for this argument. At firstglance, the argument + for the State seems to be weakened because it appearsthat a group can + overcome the free rider problem without recourse to theState for + contract enforcement. So long as the group can punish free riders + byexcluding them from the benefits of cooperation (as for instance the + Pygmiespunished Cephu—see Chapter 5), then there is the possibility of + ‘spontaneous’public good provision through the generalisation of the + tit-for-tat strategy.Having noted this, nevertheless, the point seems + almost immediately to beblunted since the difference between a + Hobbesian State which enforcescollective agreements and the generalised + tit-for-tat arrangement is notaltogether clear and so in proving one we + are hardly undermining the other.After all, the State merely codifies + and implements the policies of‘punishment’ on behalf of others in a + very public way (with the rituals ofpolice stations, courts and the + like). But, is this any different from the golfclub which excludes a + member from the greens when the dues have not beenpaid or the Pygmies’ + behaviour towards Cephu? Or the gang which excludespeople who have not + contributed ‘booty’ to the common fund? + +Page 176: + + Box 6.2 + +Page 178: + + contract—that the creation of the State by the individual also helps + shape asuperior individual.) Hayek, however, prefers the ‘English + tradition’ because hedoubts (a) that the formation of the State is part + of a process which liberates(and moulds) the social agent and (b) that + there is the knowledge to informsome central design so that it can + perform the task of resolving free ridingbetter than spontaneously + generated solutions (like tit-for-tat). In other words,reason should + know its limits and this is what informs Hayek’s support forEnglish + pragmatism and its suspicion of the State.Of course there is a big ‘if + in Hayek’s argument. Although Beirut stillmanaged to function without a + grand design, most of its citizens prayed forone. In short, the + spontaneous solution is not always the best. Indeed, as wehave seen, + the cooperative solution is just one among many Nash equilibria + inrepeated games, so in the absence of some machinery of collective + decisionmaking, there seems no guarantee it will be selected. Against + this, however, itis sometimes argued that evolution will favour + practices which generate thecooperative outcome since societies that + achieve cooperation in these gameswill prosper as compared with those + which are locked in mutual defection.This is the cue for a discussion + of evolutionary game theory and we shall leavefurther discussion of the + State until we turn to evolutionary game theory + +Page 178: + + Instead the result seems important because it demythologises the + State.Firstly the State qua State (that is, the State with its police + force, its courts andthe like) is not required to intrude into every + social interaction which suffersfrom a free rider problem. There are + many practices and institutions which aresurrogates for the State in + this regard. Indeed, the Mafia has plausiblydisplaced the State in + certain areas precisely because it provides the services ofa State. + Likewise, during the long civil war years inhabitants of Beirutsomehow + still managed to maintain services which required the overcoming offree + rider problems.Secondly since something like the State as contract + enforcer might well arise‘spontaneously’ through the playing of free + rider games repeatedly, it need notrequire any grand design. There need + be no constitutional conventions. In thisway the result counts strongly + for what Hayek (1962) refers to as the Englishas opposed to the + European continental Enlightenment tradition. The latterstresses the + power of reason to construct institutions that overcome problemslike + those of the free rider. (It also often presupposes—recall Rousseau’s + social + +Page 178: + + different if you pay the State in the form of taxes or the Mafia in the + form oftribute? + +Page 185: + + example comes from strategicdecisions by the legislature when the + Executive is trying to push throughParliament a series of bills that + the latter is unsympathetic towards. + +Page 185: + + President proposes legislation. The Congress is notin sympathy with the + proposal and must decide whether to make amendments.If it decides to + make an amendment, then the President must decide whetherto fight the + amendment or acquiesce. Looking at the President’s pay-offs it + isobvious that, even though he or she prefers that the Congress does + not amendthe legislation, if it does, he or she would not want to fight + +Page 186: + + the Folk theorem ensures that aninfinity of war/acquiescence patterns + are compatible with instrumentalrationality. Nevertheless, the duration + of such games is usually finite andsometimes their length is + definite—e.g. US Presidents have a fixed term andincumbents have only a + fixed number of local markets that they wish todefend. What happens + then? Would it make sense for the President or theincumbent to put on a + show of strength early on (e.g. by fighting the Congressor unleashing a + price war) in order to create a reputation for belligerence thatwould + make the Congress and the entrant think that, in future rounds, + theywill end up with pay-off -1/2 if they dare them? + +Page 186: + + In the finitely repeated version of the game Nash backward + inductionargues against this conclusion. Just as in the case of the + prisoners’ dilemmain the previous subsection, it suggests that, since + there will be no fighting atthe last play of the game, the reputation + of the President/incumbent willunravel to the first stage and no + fighting will occur (rationally). Theconclusion changes again once we + drop CKR (or allow for different types ofplayers). + +Page 190: + + Of course, there may be actions that can be takenoutside the game and + which have a similar effect on the beliefs of others. Such‘signalling’ + behaviour is considered briefly in this section to round out + thediscussion of reputations. It is of potential relevance not only to + repeated, butalso to one-shot games. + +Page 192: + + when the game isrepeated and there is a unique Nash equilibrium things + change. The Nashequilibrium is attractive because as time goes by and + agents adjust theirexpectations of what others will do in the light of + experience, then they willseem naturally drawn to the Nash equilibrium + because it is the only restingplace for beliefs. Any other set of + beliefs will upset itself. + +Page 192: + + Nevertheless, there is still no guarantee that a Nash equilibrium + willsurface even if it exists and it is unique. + +Page 193: + + The strength of the Nash equilibrium is that forward looking agents + mayrealise that (R2, C2) is the only outcome that does not engender + such thoughts.We just saw that adaptive (or backward looking) + expectations will not do thetrick. If, however, after having been + around the pay-off matrix a few timesplayers ask themselves the + question ‘How can we reach a stable outcome?’,they may very well + conclude that the only such outcome is the Nashequilibrium (R2, C2).But + why would they want to ask such a question? What is so wrong + withinstability (and disequilibrium) after all? Indeed in the case of + Figure 2.6 ourplayers have an incentive to avoid a stable outcome + (observe that on averagethe cycle which takes them from one extremity + of the pay-off matrix toanother yields a much higher pay-off than the + Nash equilibrium result). If, onthe other hand, pay-offs were as in + Figure 6.4 below, they would be stronglymotivated to reach the Nash + equilibrium. + +Page 193: + + It is easy to see that this type of adaptivelearning will never lead + the players to the Nash equilibrium outcome (R2, C2).Instead, they will + be oscillating between outcomes (R1, C1), (R1, C3), (R3, C1)and (R3, + C3).Can they break away from this never ending cycle and hit the + Nashequilibrium? They can provided they converge onto a common + forwardlooking train of thought. For + +Page 194: + + Thus we conclude that whether repetition makes the Nashequilibrium more + or less likely when it is unique must depend on thecontingencies of how + people learn and the precise pay-offs from non-Nashbehaviour. + +Page 194: + + Broadly put, this is one and the same problem. It is a problem + withspecifying how agents come to hold beliefs which are extraneous to + the game(in the sense that they cannot be generated endogenously + through theapplication of the assumptions of instrumental rationality + and commonknowledge of instrumental rationality) + +Page 195: + + the insights of evolutionary game theory arecrucial material for many + political and philosophical debates, especially thosearound the State. + +Page 195: + + The argument for suchan agency turns on the general problem of + equilibrium selection and on theparticular difficulty of overcoming the + prisoners’ dilemma. When there aremultiple equilibria, the State can, + through suitable action on its own part, guidethe outcomes towards one + equilibrium rather than another. Thus the problemof equilibrium + selection is solved by bringing it within the ambit of + consciouspolitical decision making. Likewise, with the prisoners’ + dilemma/ free riderproblem, the State can provide the services of + enforcement. Alternativelywhen the game is repeated sufficiently and + the issue again becomes one ofequilibrium selection, then the State can + guide the outcomes towards thecooperative Nash equilibrium. + +Page 195: + + intransigent Right’ + +Page 196: + + —that is, the idea that you can turn social outcomes intomatters of + social choice through the intervention of a collective action + agencylike the State. The positive argument against ‘political + rationalism’, as the quoteabove suggests, turns on the idea that these + interventions are not evennecessary. The failure to intervene does not + spell chaos, chronic indecision,fluctuations and outcomes in which + everyone is worse off than they couldhave been. Instead, a ‘spontaneous + order’ will be thrown up as a result ofevolutionary processes. + +Page 196: + + Likewise, there are problems of ‘political failure’ that subvert the + ideal ofdemocratic decision making and which can match the market + failures that theState is attempting to rectify. For example, Buchanan + and Wagner (1977) andTullock (1965) argue that special interests are + bound to skew ‘democraticdecisions’ towards excessively large + bureaucracies and high governmentexpenditures. Furthermore there are + difficulties, especially after the Arrowimpossibility theorem, with + making sense of the very idea of something likethe ‘will of the people’ + in whose name the State might be acting (see Arrow,1951, Riker, 1982, + Hayek, 1962, and Buchanan, 1954).1These, so to speak, are a shorthand + list of the negative arguments comingfrom the political right against + ‘political rationalism’ or ‘socialconstructivism’ + +Page 196: + + Forinstance, there are problems of inadequate knowledge which can mean + thateven the best intentioned and executed political decision generates + unintendedand undesirable consequences. Indeed this has always been an + importanttheme in Austrian economics, featuring strongly in the 1920s + debate over thepossibility of socialist planning as well as + contemporary doubts over thewisdom of more minor forms of State + intervention. + +Page 196: + + Hayek (1962) himself tracesthe battlelines in the dispute back to the + beginning of Enlightenmentthinking:Hayek distinguished two intellectual + lines of thought about freedom, ofradically opposite upshot. The first + was an empiricist, essentially Britishtradition descending from Hume, + Smith and Ferguson, and seconded byBurke and Tucker, which understood + political development as aninvoluntary process of gradual institutional + improvement, comparable tothe workings of a market economy or the + evolution of common law. Thesecond was a rationalist, typically French + lineage descending fromDescartes through Condorcet to Comte, with a + horde of modernsuccessors, which saw social institutions as fit for + premeditatedconstruction, in the spirit of polytechnic engineering. The + former lineled to real liberty; the latter inevitably destroyed it. + +Page 197: + + evolutionary stable strategies + +Page 197: + + In particular, wesuggest that the evolutionary approach can help + elucidate the idea that poweris mobilised through institutions and + conventions. We conclude the chapterwith a summing-up of where the + issue of equilibrium selection and the debateover the State stands + after the contribution of the evolutionary approach. + +Page 197: + + The basic idea behind this equilibrium concept is that an ESS is a + strategywhich when used among some population cannot be ‘invaded’ by + anotherstrategy because it cannot be bested. So when a population uses + a strategy I,‘mutants’ using any other strategy J cannot get a toehold + and expand amongthat population. + +Page 197: + + This is why evolutionary game theory assumes significance in the + debateover an active State. It should help assess the claims of + ‘spontaneous order’made by those in the British corner and so advance + one of the central debatesin Enlightenment political thinking. + +Page 198: + + This is, if youlike, a version of Hobbes’s nightmare where there are no + property rightsand everyone you come across will potentially claim your + goods. + +Page 202: + + Secondly, and more specifically, there is the result that although the + symmetricalplay of this game yields a unique equilibrium, it becomes + unstable the momentrole playing begins and some players start to + recognise asymmetry. Sincecreative agents seem likely to experiment + with different ways of playing thegame, it would be surprising if there + was never some deviation based on anasymmetry. Indeed it would be more + than surprising because there is muchevidence to support the idea that + people look for ‘extraneous’ reasons whichmight explain what are in + fact purely random types of behaviour (see theadjacent box on winning + streaks).Formally, this leaves us with the old problem of how the + solution to thegame comes about. However, evolutionary game theory does + at least point usin the direction of an answer. The phase diagram in + Figure 7.2 reveals that theselection of an equilibrium depends + critically on the initial set of beliefs + +Page 202: + + once animperfect form of rationality is posited. In other words, it is + not beingdeduced as an implication of the common knowledge of + rationalityassumption which has been the traditional approach of + mainstream gametheory. + +Page 203: + + Thirdly, it can be noted that the selection of one ESS rather than + anotherembodies a convention + +Page 203: + + To put these observationsrather less blandly, since rationality on this + account is only responsible for thegeneral impulse towards mimicking + profitable behaviour, the history of thegame depends in part on what + are the idiosyncratic and unpredictable (non-rational, one might say, + as opposed to irrational) features of individual beliefsand learning. + +Page 204: + + Fourthly, the selection of one equilibrium rather than another + potentiallymatters rather deeply. In effect in the hawk—dove game over + contestedproperty, what happens in the course of moving to one of the + ESSs is theestablishment of a form of property rights. Either those + playing role R get theproperty and role C players concede this right, + or those playing role C get theproperty and role R players concede this + right. This is interesting not onlybecause it contains the kernel of a + possible explanation of property rights (onwhich we shall say more + later) but also because the probability of playing roleR or role C is + unlikely to be distributed uniformly over the population. Indeed,this + distribution will depend on whatever is the source of the distinction + usedto assign people to roles. + +Page 204: + + The question, then, of how a source of differentiation gets + establishedbecomes rather important. + +Page 204: + + Thus the behaviour at one of theseESSs is conventionally determined + and, to repeat the earlier point, we can plotthe emergence of a + particular convention with the use of this phase diagram.It will depend + both on the presumption that agents learn from experience(the rational + component of the explanation) and on the particularidiosyncratic (and + non-rational) features of initial beliefs and precise learningrules. + +Page 206: + + After all, perhaps the presence of these conventions can only + beaccounted for by a move towards a Wittgensteinian ontology, in which + casemainstream game theory’s foundations look decidedly wobbly. To + prevent thisdrift a more robust response is required.The alternative + response is to deny that the appeal to shared prominenceor salience + involves either an infinite regress or an acknowledgement + thatindividuals are necessarily ontologically social + +Page 206: + + There is a further and deeper problem with the concept of salience + basedon analogy because the attribution of terms like ‘possession’ + plainly begs thequestion by presupposing the existence of some sort of + property rights in thepast. In other words, people already share a + convention in the past and this isbeing used to explain a closely + related convention in the present. Thus we havenot got to the bottom of + the question concerning how people come to holdconventions in the first + place.3 + +Page 206: + + So, of course, we cannot hope to explainhow they actually achieve a new + coordination without appealing to thosebackground conventions. In this + sense, it would be foolish for socialscientists (and game theorists, in + particular) to ignore the social context inwhich individuals play new + games. + +Page 208: + + This conclusion reinforces the earlier result that the course of + historydepends in part on what seem from the instrumental account of + rationalbehaviour to be non-rational (and perhaps idiosyncratic) and + thereforefeatures of human beliefs and action which are difficult to + predict + +Page 209: + + mechanically. One can interpret this in the spirit of + methodologicalindividualism at the expense of conceding that + individuals are, in this regard,importantly unpredictable. On the one + hand, this does not look good for theexplanatory claims of the theory. + On the other hand, to render theindividuals predictable, it seems that + they must be given a shared history andthis will only raise the + methodological concern again of whether we canaccount for this sharing + satisfactorily without a changed ontology. Insummary, if individuals + are afforded a shared history, then social context is‘behind’ no one + and ‘in’ everyone and then the question is whether it is agood idea to + analyse behaviour by assuming (as methodological individualistsdo) the + separability of context and action.4 + +Page 213: + + The underlying point here is that discrimination may be + evolutionarystable if the dominated cannot find ways of challenging the + social conventionthat supports their subjugation. This conclusion is + not necessarily rightbecause there are other potential sources of + change. The insight that we preferto draw is that individual attempts + to buck an established convention areunlikely to succeed, whereas the + same is not true when individuals takecollective action. + +Page 213: + + Stasis, status quo: Thus the introduction of a convention will benefit + the average person, butif you happen to be so placed with respect to + the convention that you onlyplay the dominant role with a probability + of less than 1/3, then you would bebetter off without the convention. + This result may seem puzzling at first: whydo the people who play a + dominant role less than 1/3 of the time not revert tothe symmetric play + of the game and so undermine the convention? The answeris that even + though the individual would be better off if everyone quit + theconvention, it does not make sense to do so individually. After all, + aconvention will tell your opponent to play either H or D, and then + instruct youto play D or H respectively; and you can do no better than + follow thisconvention since the best reply to H remains D and likewise + the best reply toD is H. It is just tough luck if you happen to get the + D instruction all thetime!We take the force of this individual + calculation to be a powerful contributorto the status quo and it might + seem to reveal that evolutionary processes yieldto stasis. + +Page 213: + + Conventions, inequality and revolt + +Page 214: + + To summarise, we should expect a convention to emerge even though itmay + not suit everyone, or indeed even if it short-changes the majority. It + maybe discriminatory, inequitable, non-rational, indeed thoroughly + disagreeable, yetsome such convention is likely to arise whenever a + social interaction like hawk-dove is repeated. Which convention emerges + will depend on the sharedsalience of extraneous features of the + interaction, initial beliefs and the waythat people learn. + +Page 214: + + Standstill: A potential weakness of evolutionary game theory has just + becomeapparent. Once the bandwagon has come to a standstill, and one + conventionhas been selected, the theory cannot account for a potential + subversion of theestablished convention. Such an account would require, + as we argued in theprevious paragraph, an understanding of political + (that is, collective) actionbased on a more active form of human agency + than the one provided byinstrumental rationality. Can evolutionary game + theory go as far? + +Page 219: + + Recall the idea of a trembling hand in section 2.7.1 and suppose + thatplayers make mistakes sometimes. In particular, when they intend + tocooperate they occasionally execute the decision wrongly and they + defect. Inthese circumstances, playing t punishes you for the mistake + endlessly becauseit means that your opponent defects next round in + response to your mistakendefection. If in the next period you + cooperate, you are bound to get zapped.If you follow your t-strategy + next time, then you will be defecting while youropponent will be + cooperating and a frustrating sequence of alternatingdefections and + cooperations will ensue. One way out of this bind is toamend t to t’ + whereby, if you defect by mistake, then you cooperate twiceafterwards: + the first time as a gesture of acknowledging your mistake and thesecond + in order to coordinate your cooperative behaviour with that of + youropponent. In other words, the amended tit-for-tat instructs you to + cooperatein response to a defection which has been provoked by an + earlier mistakendefection on your part. + +Page 219: + + Eventhough strategy C would do equally well as a reply to t’, if your + opponentmade the mistake (last period) then you know that your opponent + willcooperate in the next two rounds no matter what you do this period. + Thusyour best response in this round is to defect + +Page 221: + + Conventions as covert social power + +Page 221: + + even more covert power that comes from being able to mould the + preferencesand the beliefs of others so that a conflict of interest is + not even latentlypresent. + +Page 221: + + with the interests of another.It is common in discussions of power to + distinguish between the overt andthe covert exercise of power. Thus, + for instance, Lukes (1974) distinguishesthree dimensions of power. + There is the power that is exercised in the politicalor the economic + arena where individuals, or firms, institutions, etc., are able + tosecure decisions which favour their interests over others quite + overtly. This isthe overt exercise of power along the first dimension. + In addition, there is themore covert power that comes from keeping + certain items off the politicalagenda. Some things simply do not get + discussed in the political arena and inthis way the status quo + persists. Yet the status quo advantages some rather thanothers and so + this privileging of the status quo by keeping certain issues offthe + political agenda is the second dimension of power. Finally, there is + the + +Page 222: + + The figure of Spartacus captured imaginations over theages, not so much + because of his military antics, but because he personifiedthe + possibility of liberating the slaves from the beliefs which sustained + theirsubjugation. + +Page 222: + + this is the power which works through the mind and which dependsfor its + influence on the involvement or agreement of large numbers of + thepopulation (again connecting with the earlier observation about the + force ofcollective action). + +Page 222: + + State were consciously to select a convention in these circumstances + thenwe might observe the kind of political haggling associated with the + overtexercise of power. Naturally when a convention emerges + spontaneously, we donot observe this because there is no arena for the + haggling to occur, yet theemergence of a convention is no less decisive + than a conscious politicalresolution in resolving the conflict of + interest.6Evolutionary game theory also helps reveal the part played by + beliefs,especially the beliefs of the subordinate group, in securing + the power of thedominant group (a point, for example, which is central + to Gramsci’s notion ofhegemony and Hart’s contention that the power of + the law requires voluntarycooperation). + +Page 224: + + Theannexing of virtue can happen as a result of well-recognised + patterns ofcognition. + +Page 224: + + Of course, like all theories of cognitive dissonance removal,this story + begs the question of whether the adjustment of beliefs can do thetrick + once one knows that the beliefs have been adjusted for the + purpose.Nevertheless, there seem to be plenty of examples of dissonance + removal + +Page 225: + + Our final illustration of how evolutionary game theory might help + sharpenour understanding of debates around power in the social sciences + relates tothe question of how gender and race power distributions are + constitutedand persist. The persistence of these power imbalances is a + puzzle to some. + +Page 227: + + Once a convention isestablished in this game, a set of property + relations are also established.Hence the convention could encode a set + of class relations for this gamebecause it will, in effect, indicate + who owns what and some may end upowning rather a lot when others own + scarcely anything. However, as wehave seen a convention of this sort + will only emerge once the game isplayed asymmetrically and this + requires an appeal to some piece ofextraneous information like sex or + age or race, etc. In short, the creationof private property relations + from the repeated play of these gamesdepends on the use of some other + asymmetry and so it is actuallyimpossible to imagine a situation of + pure class relations, as they couldnever emerge from an evolutionary + historical process. Or to put thisslightly differently: asymmetries + always go in twos!This understanding of the relation has further + interesting implications.For instance, an attack on gender + stratification is in part an attack on classstratification and vice + versa. + +Page 227: + + Likewise, however, it would be wrong toimagine that the attack on + either if successful would spell the end of theother. + +Page 227: + + On this account of powerthrough the working of convention, the + ideological battle aimed atpersuading people not to think of themselves + as subordinate is half thebattle because these beliefs are part of the + way that power is mobilised. + +Page 228: + + . The feedback mechanism, however, ispresent in this analysis and it + arises because there is ‘learning’. It is theassumption that people + shift towards practices which secure better outcomes(without knowing + quite why the practice works for the best) which is thefeedback + mechanism responsible for selecting the practices. Thus in the + debateover functional explanation, the analysis of evolutionary games + lends supportto van Parijs’s (1982) argument that ‘learning’ might + supply the generalfeedback mechanism for the social sciences which will + license functionalexplanations in exactly the same way as natural + selection does in the biologicalsciences. + +Page 228: + + effect, the explanation of gender and racial inequalities using + thisevolutionary model is an example of functional argument. + +Page 228: + + The differencebetween men and women or between whites and blacks has no + merit inthe sense that it does not explain why the differentiation + persists. Thedifferentiation has the unintended consequence of helping + the populationto coordinate its decision making in settings where there + are benefitsfrom coordination. It is this function of helping the + population to selectan equilibrium in a situation which would otherwise + suffer from theconfusion of multiple equilibria which explains the + persistence of thedifferentiation. + +Page 229: + + So far, however, the difference between the two camps (H&EVGT andMarx) + is purely based on value judgements: one argues that illusory moralsare + good for all, the other that they are not. In this sense, both + canprofitably make use of the analysis in evolutionary game theory. + Indeed, aswe have already implied in section 7.3.4, a radical political + project grounded + +Page 229: + + On the side of H&EVGT, Hume thinks that suchillusions play a positive + role (in providing the ‘cement’ which keeps societytogether) in + relation to the common good. So do neo-Humeans (like Sugden)who are, of + course, less confident that invocation of the ‘common good’ is agood + idea (as we mentioned in section 7.6.2) but who are still happy to + seeconventions (because of the order they bring) become entrenched in + sociallife even if this is achieved with the help of a few moral + ‘illusions’. On theother side, however, Marx insists that moral + illusions are never a good idea(indeed he dislikes all illusions). + Especially since, as he sees it, their socialfunction is to help some + dreadful conventions survive (recall how in section7.3.4 we showed that + disagreeable conventions may become stable even ifthey are detrimental + to the majority). Marx believed that we can + +Page 229: + + which sound quite like observations that Marxists might make: + theimportance of taking collective action if one wants to change a + convention;how power can be covertly exercised; how beliefs + (particularly moral beliefs)may become endogenous to the conventions we + follow; how propertyrelations might develop functionally; and so on. + +Page 229: + + Indeedmost of the ideas developed on the basis of H&EVGT in the + precedingpages would find Marx in agreement. + +Page 229: + + People may think that their beliefson such matters go beyond material + values (i.e. self-interest, which in ourcontext means pay-offs); that + they respond to certain universal ideals aboutwhat is ‘good’ and + ‘right’, when all along their moral beliefs are a direct(even if + unpredictable) repercussion of material conditions and interests. + +Page 230: + + An analysis of hawk—dove games, along the lines of H&EVGT, helpsexplain + the evolution of property rights in primitive societies. Once + theserights are in place and social production is under way, each group + in society(e.g. the owners of productive means, or those who do not own + tools, land,machines, etc.) develops its own interest. And since (as + H&EVGT concurs)conventions evolve in response to such interests, it is + not surprising thatdifferent conventions are generated within different + social groups in responseto the different interests. The result is + conflicting sets of conventions which + +Page 230: + + Finally, the established (stable) conventions acquire moral weight and + even leadpeople to believe in something called the common good—which is + most likelyanother illusion + +Page 230: + + In summary, H&EVGTbegins with a behavioural theory based on the + individual interest and eventuallylands on its agreeable by-product: + the species interest. There is nothing inbetween the two types of + interest. By contrast, Marx posits another type ofinterest in between: + class interest.Marx’s argument is that humans are very different from + other speciesbecause we produce commodities in an organised way before + distributingthem. Whereas other species share the fruits of nature + (hawk—dove games aretherefore ‘naturally’ pertinent in their state of + nature), humans have developedcomplex social mechanisms for producing + goods. Naturally, the norms ofdistribution come to depend on the + structure of these productive mechanisms.They involve a division of + labour and lead to social divisions (classes). Whichclass a person + belongs to depends on his or her location (relative to others)within + the process of production. The moment collective production (as in + thecase of Cephu and his tribe in Chapter 5) gave its place to a + separationbetween those who owned the tools of production and those who + workedthose tools, then groups with significantly different (and often + contradictory)interests developed. + +Page 230: + + in collective action is as compatible with evolutionary game theory as + is theneo-Humeanism of Sugden (1986, 1989). But is there something more + inMarx than a left wing interpretation of evolutionary game theory? We + thinkthere is. + +Page 231: + + lead to conflicting morals. Each set of morals becomes an ideology.9 + Which setof morals (or ideology) prevails at any given time? Marx + thinks that, inevitably,the social class which is dominant in the + sphere of production and distributionwill also be the one whose set of + conventions and morals (i.e. whose ideology)will come to dominate over + society as a whole.To sum up Marx’s argument so far, prevailing moral + beliefs are illusoryproducts of a social selection process where the + driving force is not somesubjective individual interest but objective + class interest rooted in thetechnology and relations of production. + Although there are many conflictingnorms and morals, at any particular + time the morality of the ruling class isuniquely evolutionary stable. + The mélange of legislation, moral codes, norms,etc., reflects this + dominant ideology.But is there a fundamental difference between the + method of H&EVGTand Marx? Or is it just a matter of introducing classes + in the analysiswithout changing the method? + +Page 231: + + So, how would Marx respond to evolutionary game theory if he werearound + today? He would, we think, be very interested in some of the + radicalconclusions in this chapter. However, he would also speak + derisively of thematerialism of H&EVGT Marx habitually poured scorn on + those (e.g.Spinoza and Feuerbach) who transplanted models from the + natural sciencesto the social sciences with little or no modification + to allow for the fact thathuman beings are very different to atoms, + planets and molecules.12 Wemention this because at the heart of H&EVGT + lies a simple Darwinianmechanism (witness that there is no analytical + difference between the modelsin the biology of John Maynard Smith and + the models in this chapter). Marxwould probably claim that the theory + is not sufficiently evolutionary because(a) its mechanism comes to a + standstill once a stable convention has evolved,and (b) of its reliance + on instrumental rationality which reduces humanactions to passive + reflex responses to some (meta-physical) self-interest. + +Page 232: + + Especially in hisphilosophical (as opposed to economic) works, Marx + argued strongly for anevolutionary (or more precisely historical) + theory of society with a modelof human agency which retains human + activity as a positive (creative) forceat its core. In addition, Marx + often spoke out against mechanism; againstmodels borrowed directly from + the natural sciences (astronomy andbiology are two examples that he + warned against). It is helpful to preservesuch an aversion since humans + are ontologically different to atoms andgenes. Of course Marx himself + has been accused of mechanism and,indeed, in the modern (primarily + Anglo-Saxon) social theory literature he istaken to be an exemplar of + 19th century mechanism. Nevertheless hewould deny this, pointing to the + dialectical method he borrowed fromHegel and which (he would claim) + allowed him to have a scientific, yetnon-mechanistic, outlook. Do we + believe him? As authors we disagree here.SHH does not, while YV does. + +Page 232: + + Of course there is always the answer that self-interest feeds into + moral beliefsand then moral beliefs feed back into self-interest and + alter people’s desires.And so on. But that would be too circular for + Marx. It would not explainwhere the process started and where it is + going. By contrast, his version ofmaterialism (which he labelled + historical materialism) starts from thetechnology of production and the + corresponding social organisation. Thelatter entails social classes + which in turn imbue people with interests; peopleact on those interests + and, mostly without knowing it, they shape theconventions of social + life which then give rise to morals. The process,however, is grounded + on the technology of production at the beginning of thechain. And as + this changes (through technological innovations) it provides theimpetus + for the destabilisation of the (temporarily) evolutionary + stableconventions at the other end of the chain. + +Page 232: + + Ifmorals are socially manufactured, then so is self-interest. + +Page 233: + + Perhaps our disagreement needs to be understood in terms of thelack of + a shared history in relation to these debates—one of us embarkingfrom + an Anglo-Saxon, the other from a (south) European, tradition. It + was,after all, one of our important points in earlier chapters that + game theoristsshould not expect a convergence of beliefs unless agents + have a sharedhistory! + +Page 234: + + most of the population. This would seem to provide ammunition for the + socialconstructivists, but of course it depends on them believing that + collectiveaction agencies like the State will have sufficient + information to distinguish thesuperior outcomes. Perhaps all that can + be said on this matter is that, if youreally believe that evolutionary + forces will do the best that is possible, then it isbeyond dispute that + these forces have thrown up people who are predisposedto take + collective action. Thus it might be argued that our + evolutionarysuperiority as a species derives in part precisely from the + fact that we are pro-active through collective action agencies rather + than reactive as we would beunder a simple evolutionary scheme. + +Page 234: + + Turning to another dispute, that between social constructivism and + spontaneousorder within liberal political theory, two clarifications + have occurred. The first isthat there can be no presumption that a + spontaneous order will deliveroutcomes which make everyone better off, + or even outcomes which favour + +Page 234: + + Thesetheoretical moves will threaten to dissolve the distinction + between action andstructure which lies at the heart of the game + theoretical depiction of social lifebecause it will mean that the + structure begins to supply reasons for action andnot just constraints + upon action. On the optimistic side, this might be seen asjust another + example of how discussions around game theory help to dissolvesome of + the binary oppositions which have plagued some debates in + socialscience—just as it helped dissolve the opposition between gender + and classearlier in this chapter. However, our concern here is not to + point to requiredchanges in ontology of a particular sort. The point is + that some change isnecessary, and that it is likely to threaten the + basic approach of game theory tosocial life. + +Page 234: + + Secondly, on the difficult cases where equilibrium selection + involveschoices over whose interests are to be favoured (i.e. it is not + a matter ofselecting the equilibrium which is better for everyone), + then it is notobvious that a collective action agency like the State is + any better placed tomake this decision than a process of spontaneous + order. This may come asa surprise, since we have spent most of our time + here focusing on theindeterminacy of evolutionary games when agents are + only weaklyinstrumentally rational. + +Page 235: + + In other words the very debate within liberal political theory over + socialconstructivism versus spontaneous order is itself unable to come + to aresolution precisely because its shared ontological foundations are + inadequatefor the task of social explanation. In short, we conclude + that not only willgame theory have to embrace some expanded form of + individual agency, if itis to be capable of explaining many social + interactions, but also that this isnecessary if it is to be useful to + the liberal debate over the scope of theState. + +Page 237: + + sabotage + +Page 238: + + What it does mean is thatour interpretation of results must be cautious + and that, ultimately,laboratory experiments may only be telling us how + people behave inlaboratories. + +Page 241: + + becausethere are some players who are unconditionally cooperative or + ‘altruistic’ in theway that they play this game and, secondly, because + whether someone iscooperative or not seems to be determined by one’s + background, rather thanby how clever (or rational) he or she is (see + adjacent box on the curse ofeconomics). In this sense, the evidence + seems to point to a falsification of theassumption of instrumentally + rational action based on the pay-offs + +Page 242: + + divisions of an army are stationed on two hill-tops overlooking a + valley inwhich an enemy division can be clearly seen. It is known that + if both divisionsattack simultaneously they will capture the enemy with + none, or very little, lossof life. However, there were no prior plans + to launch such an attack, as it wasnot anticipated that the enemy would + be spotted in that location. How will thetwo divisions coordinate their + attack (we assume that they must maintain visualand radio silence)? + Neither commanding officer will launch an attack unless heis sure that + the other will attack at the same time. Thus a classic + coordinationproblem emerges.Imagine now that a messenger can be sent + but that it will take him about anhour to convey the message. However, + it is also possible that he will be caughtby the enemy in the meantime. + If everything goes smoothly and the messengergets safely from one + hill-top to another, is this enough for a coordinated attackto be + launched? Suppose the message sent by the first commanding officer + tothe second read: ‘Let’s attack at dawn!’ Will the second officer + attack at dawn?No, unless he is confident that the first commanding + officer (who sent the + +Page 242: + + message) knows that the message has been received. So, the + secondcommanding officer sends the messenger back to the first with the + message:‘Message received. Dawn it is!’ Will the second officer attack + now? Not untilhe knows that the messenger has delivered his message. + Paradoxically, noamount of messages will do the trick since + confirmation of receipt of the lastmessage will be necessary regardless + of how many messages have been alreadyreceived. + +Page 242: + + We see that in a coordination game like the above, even a very + highdegree of common knowledge of the plan to attack at dawn is not + enough toguarantee coordination (see Box 8.3 for an example of how + different degreesof common knowledge can be engendered in the + laboratory). What is needed(at least in theory) is a consistent + alignment of beliefs (CAB) about the plan.1And yet this does not + exclude the possibility that the two commandingofficers will both + attack at dawn with very high probability. How successfullythey + coordinate will, however, depend on more than a high degree ofcommon + knowledge. Indeed the latter may even be un-necessary providedthe time + of the attack is carefully chosen. The classic early experiments + byThomas Schelling on behaviour in coordination games have confirmed + this— + +Page 246: + + Thus in experiments, Pareto superiority does not seem to be a + generalcriterion which players use to select between Nash equilibria + (see also Chapter7). In conclusion, so far it seems that the way people + actually play these gamesis neither directly controlled by the + strategic aspects of the game (i.e. thelocation of the best response + marks (+) and (-) in the matrix) nor by the size ofthe return from + coordinating on non-Nash outcomes such as (R3, C3): it is + aso-far-unexplained mixture of the two factors that decides. + +Page 251: + + To phrase this conclusion slightly differently, but in a way which + connectswith the results in the next section, bargaining is a ‘complex + socialphenomenon’ where people take cues from aspects of their social + life whichgame theory typically overlooks. Thus players seem to base + their behaviouron aspects of the social interaction which game theory + typically treats asextraneous; and when players share these extraneous + reference points such + +Page 258: + + What we have here is an evolution ofsocial roles. Players with the R + label develop a different attitude towardsreflective cooperation to + those players with the C role in spite of the fact that theRs and the + Cs are the same people. In other words, the signal which causes + theobserved pattern of cooperation seems to be emitted by the label R + or C. Thisreminds us of the discussion in Chapter 7 about the capacity + of sex, race andother extraneous features to pin down a convention on + which the structure ofdiscrimination is grounded. + +Page 258: + + Experimentation with game theory is good, clean fun. Can it be more + thanthat? Can it offer a way out of the obtuse debates on CKR, CAB, + NEMS,Nash backward induction, out-of-equilibrium behaviour, etc.? The + answerdepends on how we interpret the results. And as interpretation + leaves plentyof room for controversy, we should not expect the data + from the laboratoryunequivocally to settle any disputes. Our suspicion + is that experiments are togame theory what the latter is to liberal + individualism: a brilliant means ofcodifying its problems and of + creating a taxonomy of time-honoureddebates.There are, however, + important benefits from experimenting. Watchingpeople play games + reminds us of their inherent unpredictability, their sense offairness, + their complex motivation—of all those things that we tend to forgetwhen + we model humans as bundles of preferences moving around some pay- + +Page 258: + + radical breakwith the exclusive reliance of instrumental rationality is + also necessary. + +Page 260: + + At root we suspect that the major problem is the one that the + experimentsin the last chapter isolate: namely, that people appear to + be more complexlymotivated than game theory’s instrumental model allows + and that a part ofthat greater complexity comes from their social + location.We do not regard this as a negative conclusion. Quite the + contrary, it standsas a challenge to the type of methodological + individualism which has had afree rein in the development of game + theory. + +Page 260: + + Along the way to this conclusion, we hope also that you have had + fun.Prisoners’ dilemmas and centipedes are great party tricks. They are + easy todemonstrate and they are amenable to solutions which are + paradoxical enoughto stimulate controversy and, with one leap of the + liberal imagination, theaudience can be astounded by the thought that + the fabric of society (even theexistence of the State) reduces to these + seemingly trivial games—Fun andGames, as the title of Binmore’s (1992) + text on game theory neatly puts it. Butthere is a serious side to all + this. Game theory is, indeed, well placed toexamine the arguments in + liberal political theory over the origin and the scopeof agencies for + social choice like the State. In this context, the problems whichwe + have identified with game theory resurface as timely warnings of + thedifficulties any society is liable to face if it thinks of itself + only in terms ofliberal individualism. + +Page 260: + + The ambitious claim that game theory will provide a unified foundation + for allsocial science seems misplaced to |