the existence of perfect equilibrium in discontinuous games不连续的完美均衡的存在性游戏.pdf

Games 2011, 2, 235-256; doi:10.3390/g2030235 OPEN ACCESS games ISSN 2073-4336 /journal/games Article The Existence of Perfect Equilibrium in Discontinuous Games Oriol Carbonell-Nicolau Department of Economics, Rutgers University, 75 Hamilton Street, New Brunswick, NJ 08901, USA; E-Mail: carbonell@; Tel.: +1-732-932-7363; Fax: +1-732-932-7416 Received: 18 February 2011; in revised form: 27 April 2011 / Accepted: 27 June 2011 / Published: 15 July 2011 Abstract: We prove the existence of a trembling-hand perfect equilibrium within a class of compact, metric, and possibly discontinuous games. Our conditions for existence are easily verified in a variety of economic games. Keywords: trembling-hand perfect equilibrium; discontinuous game; infinite normal-form game; payoff security 1. Introduction A Nash equilibrium is trembling-hand perfect if it is robust to the players’ choice of unintended strategies through slight trembles. That is, in a world where agents make slight mistakes, trembling-hand perfection requires that there exist at least one perturbed model of low-probability errors with an equilibrium that is close to the original equilibrium, which is then thought of as an approximate description of “slightly constrained” rational behavior, or what could be observed if the players were to interact within the perturbed game. In this regard, a Nash equilibrium that is not trembling-hand perfect cannot be a good prediction of equilibrium behavior under any “conceivable” theory of (improbable, but