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-rw-r--r--books/economics/game-theory-critical-introduction.md40
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@@ -448,3 +448,43 @@ resolution would require a higher State in the next upper level of recursion:
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?).
+
+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 agains 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