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Unformatted text preview: = 0. We say that player i maxminimizes if he chooses an action that is best for him on the assumption that whatever he does, player j will choose her action to hurt him as much as possible. We now show that for a strictly competitive game that possesses a Nash equilibrium, a pair of actions is a Nash equilibrium if and only if the action of each player is a maxminimizer. This result is striking because it provides a link between individual decision-making and the reasoning behind the notion of Nash equilibrium. In establishing the result we also prove the strong result that for strictly competitive games that possess Nash equilibria all equilibria yield the same payoffs. This property of Nash equilibria is rarely satisfied in games that are not strictly competitive. •Definition 21.2 Let be a strictly competitive strategic game. The action is a maxminimizer for player 1 if Similarly, the action is a maxminimizer for player 2 if...
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- Spring '10