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diff --git a/books/economics/game-theory-critical-introduction.md b/books/economics/game-theory-critical-introduction.md index 012c9ea..6b34244 100644 --- a/books/economics/game-theory-critical-introduction.md +++ b/books/economics/game-theory-critical-introduction.md @@ -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 |