On the existence of pure-strategy perfect equilibrium in discontinuous games

Oriol Carbonell-Nicolau

Games and Economic Behavior, 2011, vol. 71, issue 1, 23-48

Abstract: We provide sufficient conditions for a (possibly) discontinuous normal-form game to possess a pure-strategy trembling-hand perfect equilibrium. We first show that compactness, continuity, and quasiconcavity of a game are too weak to warrant the existence of a pure-strategy perfect equilibrium. We then identify two classes of games for which the existence of a pure-strategy perfect equilibrium can be established: (1) the class of compact, metric, concave games satisfying upper semicontinuity of the sum of payoffs and a strengthening of payoff security; and (2) the class of compact, metric games satisfying upper semicontinuity of the sum of payoffs, strengthenings of payoff security and quasiconcavity, and a notion of local concavity and boundedness of payoff differences on certain subdomains of a player's payoff function. Various economic games illustrate our results.

Keywords: Pure-strategy; trembling-hand; perfect; equilibrium; Infinite; normal-form; game; Selten; perturbation; Discontinuous; game; Quasiconcave; game; Payoff; security (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (32)

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