Axiomatic Equilibrium Selection for Generic Two-Player Games

Axiomatic Equilibrium Selection for Generic Two-Player Games

By Srihari Govindan, Robert Wilson
2011Working Paper No. 2021

We impose three conditions on refinements of the Nash equilibria of finite games with perfect recall that select closed connected subsets, called solutions. <br> A. Each equilibrium in a solution uses undominated strategies; <br> B. Each solution contains a quasi-perfect equilibrium; <br> C. The solutions of a game map to the solutions of an embedded game, where a game is embedded if each players 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).