Axiomatic Equilibrium Selection for Generic two-player games

Abstract

We impose three axioms on refinements of the Nash equilibria of games with perfect recall that select connected closed nonempty subsets, called solutions. Undominated Strategies: Each equilibrium in a solution uses undominated strategies. Backward Induction: Each solution contains a quasi-perfect equilibrium. Small Worlds: The solutions of a game are induced by the solutions of any larger game in which it is embedded such that players' strategies and payoffs are preserved. For games with two players and generic payoffs these axioms 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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