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
     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