Approximation results for discontinuous games with an application to equilibrium refinement

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may August 2011 AbstractWe provide approximation results for Nash equilibria in possibly discontinuous games when payoffs and strategy sets are perturbed, and compare these conditions to those considered in the related literature. We then prove existence results for a new "finitistic" infinite-game generalization of Selten's [17] notion of perfection, and study some of its properties. The existence results, which rely on the approximation theorems, relate existing notions of perfection to the new specification.

Perfect equilibria in games of incomplete information

“…In the special case of complete information games (i.e., when type spaces are singletons), this definition collapses to the notion of perfection considered in Al-Najjar [2], Carbonell-Nicolau [8,9,10,12], Carbonell-Nicolau and McLean [13,14,15], and the strong notion of perfection defined in Simon and Stinchcombe [24].…”

“…In normal-form games with complete information, Selten's [23] perfection refines the Nash equilibrium concept by requiring that equilibrium strategies be immune to slight trembles in the execution of the players' actions. The standard definition of perfect equilibrium for normal-form games with finite action spaces (see, e.g., van Damme [26]) can be extended to normal-form games with infinitely many actions, and these extensions have been studied by several authors (see, e.g., Al-Najjar [2], Simon and Stinchcombe [24], Carbonell-Nicolau [8,9,10,12], Carbonell-Nicolau and McLean [13,14,15], and Bajoori et al [4]).…”