From 23e5173f20deb87745f59e464d71189aa5494ae2 Mon Sep 17 00:00:00 2001 From: Silvio Rhatto Date: Fri, 10 Jan 2020 19:03:52 -0300 Subject: Updates books/economics/game-theory-critical-introduction --- .../economics/game-theory-critical-introduction.md | 78 ++++++++++++++++++++++ 1 file changed, 78 insertions(+) diff --git a/books/economics/game-theory-critical-introduction.md b/books/economics/game-theory-critical-introduction.md index 75260ae..901d32a 100644 --- a/books/economics/game-theory-critical-introduction.md +++ b/books/economics/game-theory-critical-introduction.md @@ -449,6 +449,22 @@ resolution would require a higher State in the next upper level of recursion: 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 @@ -488,3 +504,65 @@ Arguments against CAB: inclined to answer no, but why? And what is the difference as -- 57 + +Limits of reason conceptualized 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 -- cgit v1.2.3