Perfect Quasi-Perfect Equilibrium

Abstract

In strategic-form games Selten's (1975) perfect equilibria are admissible. This is not true for extensive-form perfection. Quasi-perfect equilibria solves this problem using Selten's (1975) trembles to introduce a refinement of Nash equilibrium wherein each player puts infinitesimal weight on other players's strategies, but not her own. One might be sure of oneself, while (infinitesimally) unsure of others. However, also quasi-perfection itself is not without problems, precisely because it ignores future infinitesimal uncertainties in one's own play. We introduce a refinement; perfect quasi-perfect equilibrium, to capture the best of both concepts. Our idea is to force each player to consider infinitesimal deviations in her own future play, but to make them so unlikely that they are infinitely less likely than the combined likelihood of deviations by all other players. Our refinement uses only strategies that are neither weakly dominated in the strategic form nor in the agent normal form.