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We establish the existence of pure strategy equilibria in games with discontinuous payoffs where the set of feasible actions of each player varies, also in a discontinuous fashion, as a function of the actions of the other players. Such games are used in modeling abstract economies and other...
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Perfect Bayesian equilibrium is not a subset of Nash equilibrium. Perfect Bayesian equilibrium requires players to have beliefs that are consistent with the equilibrium strategies of other players. Nash equilibrium does not explicitly specify the beliefs of the players. However, the default...
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In this paper, we fully characterize the Nash Equilibrium in the winner-take-all Bertrand Game, showing that a mixed strategy profile is a Nash Equilibrium, if and only if it is a zero operating profit one, and there exist at least two players whose bids are all unprofitable. Compared with...
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This chapter is devoted to the study of Nash equilibria, and correlated equilibria in both finite and infinite games. We restrict our discussions to only those properties that are somewhat special to the case of two-person games. Many of these properties fail to extend even to three-person...
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This chapter examines the conceptual foundations of the concept of strategic equilibrium and its various variants and refinements. The emphasis is very much on the underlying ideas rather than on any technical details.After an examination of some pre-equilibrium ideas, in particular the concept...
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This chapter of the Handbook of Game Theory (Vol. 3) provides an overview of the theory of Nash equilibrium and its …-enforcing theory of rational behavior in non-cooperative games. Given the assumption of independent behavior of the players, it follows … that a self-enforcing theory has to prescribe a Nash equilibrium, i.e., a strategy profile such that no player can gain by …
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