A_Course_in_Game_Theory_-_Martin_J._Osborne 39

A_Course_in_Game_Theory_-_Martin_J._Osborne 39 - Page 24...

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Page 24 player l's payoff is at most her equilibrium payoff. In a game that is not strictly competitive a player's equilibrium strategy does not in general have these properties (consider, for example, BoS (Figure 16.1)). • Exercise 24.1 Let G be a strictly competitive game that has a Nash equilibrium. a . Show that if some of player 1's payoffs in G are increased in such a way that the resulting game G' is strictly competitive then G' has no equilibrium in which player 1 is worse off than she was in an equilibrium of G . (Note that G ' may have no equilibrium at all.) b . Show that the game that results if player 1 is prohibited from using one of her actions in G does not have an equilibrium in which player l's payoff is higher than it is in an equilibrium of G . c .Give examples to show that neither of the above properties necessarily holds for a game that is not strictly competitive. 2.6 Bayesian Games: Strategic Games with Imperfect Information 2.6.1 Definitions
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