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Unformatted text preview: pairs of maxminimizers. • Proposition 22.2 Let be a strictly competitive strategic game . a. If ( x * , y * ) is a Nash equilibrium of G then x * is a maxminimizer for player 1 and y * is a maxminimizer for player 2 . b. If ( x * , y * ) is a Nash equilibrium of G then max x min y u 1 ( x, y ) = min y max x u 1 ( x, y ) = u 1 ( x * , y * ), and thus all Nash equilibria of G yield the same payoffs . c. If max x min y u 1 ( x, y ) = min y max x u 1 ( x, y ) (and thus, in particular, if G has a Nash equilibrium (see part b)), x * is a maxminimizer for player 1, and y * is a maxminimizer for player 2, then ( x * , y * ) is a Nash equilibrium of G . Proof. We first prove parts (a) and (b). Let ( x * , y * ) be a Nash equilibrium of G . Then for all or, since for all . Hence . Similarly,...
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This note was uploaded on 09/10/2011 for the course DEFR 090234589 taught by Professor Vinh during the Spring '10 term at Aarhus Universitet, Aarhus.
 Spring '10
 VINH

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