Axiomatic Equilibrium Selection

We apply three axioms adapted from decision theory to refinements of the Nash equilibria of games with perfect recall that select connected closed subsets called solutions. Undominated Strategies : No player uses a weakly dominated strategy in an equilibrium in a solution. Backward Induction: Each solution contains a quasi-perfect equilibrium and thus a sequential equilibrium in strategies that provide conditionally admissible optimal continuations from information sets. Small Worlds: A refinement is immune to embedding a game in a larger game with additional players provided the original players’ strategies and payoffs are preserved, i.e. solutions of a game are the same as those induced by the solutions of any larger game in which it is embedded. For games with two players and generic payoffs, we prove that these axioms characterize each solution as an essential component of equilibria in undominated strategies, and thus a stable set as defined by Mertens (1989). Date: 23 April 2009.