042307 - Lecture Recall General comments criticisms...

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Lecture ??: 04/23/2007 Recall: General comments / criticisms about “classical” game theory. 1. Requires hyper-rational players (over the years, people have tried a variety of approaches to bounded probability . 2. Games can have multiple Nash equilibria—how to pick one (or a few) as “solution” to the game? Approach has been to refuse equilibria—identifying “sketchy” ones and throwing those out. Huge industry in game theory—just one example (of many)—R. Sellen’s trembling hand perfect equilibrium. Saw in this example: N Y P (2,0) (1,1) M (2,0) (-1,-1) Claim : (M,N) is “sketchy” –if column player were to play a mixed strategy (1- )N+ Y є є —where is small-then M is no longer a best reply for Player 1. є This equilibrium (ie. (M, N)) fails Selter’s criterion—not trembling-hand perfect. Other refinements: Proper equilibria (subset of tremblind hand perfect) (Myerism) In “dynamic games” (eg. repeated or extensive-form games) have sequential equilibria and subgame-perfect equilibria. 3. “Learning how to play” is not built in to classical game theory (cf. Nash’s thesis quote about populations—tatonnment process, etc.) Especially
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relevant for large games, wehre players need to learn not only how to play but what the structure of game.
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