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+[[!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.
+
+# 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
+
+    [...]
+
+    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. In fact this need entail no more than a simple consistency of the
+
+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?).