Axiomatic Equilibrium Selection for Generic Two-Player Games
60 Pages Posted: 12 Jun 2009 Last revised: 27 May 2011
Date Written: May 24, 2011
We impose three conditions on refinements of the Nash equilibria of finite games with perfect recall that select closed connected subsets, called solutions. A. Each equilibrium in a solution uses undominated strategies; B. Each solution contains a quasi-perfect equilibrium; C. The solutions of a game map to the solutions of an embedded game, where a game is embedded if each player’s feasible strategies and payoffs are preserved by a multilinear map. We prove for games with two players and generic payoffs that these conditions characterize each solution as an essential component of equilibria in undominated strategies, and thus a stable set as defined by Mertens (1989).
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