gametheory5 - Equilibrium in Dynamic Games In extensive...

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Equilibrium in Dynamic Games In extensive form games, a strategy is a speci¯cation of what action a player chooses at each information set he/she controls. A Nash equilibrium of an exten- sive form game is a pro¯le of strategies such that no player can receive a higher expected payo® with any other strategy, just as for normal form games. The set of N.E. of an extensive form game is always the same as for its corresponding normal form game. However, the explicit timing of play raises a new issue: when is a strategy credible? Consider the game ¡ 1 , which has the following normal form representation: player 2 left right player 1 top 2 ; 1 0 ; 0 bottom 1 ; 2 1 ; 2
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Check that (top, left) and (bottom, right) are both Nash equilibria for both the matrix and the game tree. For the matrix game, it is true that player 2 is playing a weakly dominated strategy in (bottom, right), but it is hard to argue that player 2's strategy is not rational.
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