gametheory3

# gametheory3 - Game Theoretic Solutions Def A strategy si 2...

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Game Theoretic Solutions Def: A strategy s i 2 S i is strictly dominated for player i if there exists another strategy, s 0 i 2 S i such that, for all s ¡ i 2 S ¡ i ,wehave ¼ i ( s 0 i ;s ¡ i ) i ( s i ¡ i ) : In this case, we say that s 0 i strictly dominates s i . Def: A strategy s i 2 S i is a strictly dominant strategy for player i if it strictly dominates every other strategy in S i . Note: A player has, at most, one strictly dominant strategy. When a player has a dominant strategy, that strategy is a compelling choice.

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Def: A (strict) dominant strategy equilibrium is a vector of strategies, s =( s 1 ;:::;s n ) 2 S , such that for each player i , s i is a strictly dominant strategy. Example: Prisoner's dilemma. (defect, defect) is a dominant strategy equilibrium. player 2 cooperate defect player 1 cooperate 3 ; 30 ; 4 defect 4 ; 01 ; 1
Def: A strategy s i 2 S i is weakly dominated for player i if there exists another strategy, s 0 i 2 S i such that, for all s ¡ i 2 S ¡ i ,wehave ¼ i ( s 0 i ;s ¡ i ) ¸ ¼ i ( s i ¡ i ) ; with strict inequality for some s ¡ i .I n t h i s c a s e , w e say that s 0 i weakly dominates s i . Def: A strategy s i 2 S i is a weakly dominant strategy for player i if it weakly dominates every other strategy in S i . Note: If you are unsure what your opponent will play, you should not play a weakly dominated strategy, but if you are sure, then playing a weakly dominated strategy can be rational.

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Example: For player 2, playing right is weakly domi- nated by left, but playing right is rational if she thinks that player 1 will play bottom.
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## This note was uploaded on 07/17/2008 for the course ECON 805 taught by Professor Peck during the Spring '08 term at Ohio State.

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gametheory3 - Game Theoretic Solutions Def A strategy si 2...

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