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Economics 202: Intermediate Microeconomic Theory 1.HW #6 on website. Due Tuesday. 2.Second test covers up through today’s material, and will be “pseudo-cumulative” (to be explained).

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Game Theory “The Dating Game” –Multiple Nash equilibria –Nash equilibrium concept loses appeal “Copycat Game” –No Nash equilibrium –Players want to outguess the other –Introduce mixed strategies (in contrast to pure strategies) Timing Static Nash Equilibrium Information Dynamic CompleteIncomplete Mixed Strategy = a probability distribution over some or all of a player’s pure strategies Mixed strategies can add Nash equilbria Result: Any game with finite # players who have finite # pure strategies has a Nash equilibrium (possibly utilizing mixed strategies) Backward Induction Bayesian Nash Equilibrium Perfect Bayesian Equilibrium 2, 1 0, 0 1, 2 Chicken Steak RedWhite Pat Chris Jack Dating Game -1, 1 1, -1 -1, 1 Outside Inside Jill Inside Copycat Game

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Game Theory Dynamic, complete 2-player sequential move game Order of play –Player 1 chooses action a 1 –Player 2 observes a 1 and then chooses a 2 –Players receive their payoffs U 1 (a 1,a 2 ) & U 2 (a 1,a 2 ) Examples –Stackelberg-version of Cournot duopoly –Trust Game -- equilibrium? Timing Static Nash Equilibrium Information Dynamic CompleteIncomplete Dynamic, simultaneous move (or infinite horizon) games requires an extension of backward induction called subgame-perfect Nash equilibrium Backward Induction Bayesian Nash Equilibrium Perfect Bayesian Equilibrium 1, 1 -1, 2 0, 0 Not trust Trust HonorBetray Player 2 Player 1 Trust Game (normal form) Honor Not trust Betray Player 2 Trust 0,00,0 1,11,1-1, 2 Trust Game (extensive form)

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Game Theory “The Dormitory Game” –Write extensive form if simultaneous game –Write extensive & normal forms if A chooses first 6, 3 6, 4 5, 4 7, 5 Softly Loudly Softly B A

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Game Theory “Vote by Alternating Veto” –Player 1 prefers X to Y to X, Player 2 prefers Z to Y to X YXXYXYYZXYZYZXXZXYZZXZZY X0,2 1,1 Y0,2 2,0 0,2 2,0 Z1,12,01,12,01,12,01,12,0 Find Nash equilibria and subgame perfect Nash equilbria

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Extensive-form games. Extensive-form games with perfect information Player 1 Player 2 Player 1 2, 45, 33, 2 1, 00, 5 Players do not move simultaneously.

Extensive-form games. Extensive-form games with perfect information Player 1 Player 2 Player 1 2, 45, 33, 2 1, 00, 5 Players do not move simultaneously.

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