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authorSilvio Rhatto <rhatto@riseup.net>2020-01-10 19:03:52 -0300
committerSilvio Rhatto <rhatto@riseup.net>2020-01-10 19:03:52 -0300
commit23e5173f20deb87745f59e464d71189aa5494ae2 (patch)
parent19c91f1ad39b5642fc577bbdcdd4ed2e70fb9872 (diff)
Updates books/economics/game-theory-critical-introduction
1 files changed, 78 insertions, 0 deletions
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
+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