The Local Best Response Criterion: A New Approach to Equilibrium Refinement Herbert Gintis ∗ November 29, 2006 Abstract The standard refinement criteria for extensive form games, including subgame perfection, perfection, sequentiality, and properness, are both too strong, since they reject important classes of acceptable Nash equilibria in finite extensive form games, and too weak, since they accept many unac- ceptable Nash equilibria. This paper develops a new refinement criterion, called the local best response (LBR) criterion, that more accurately and con- cisely captures the concept of a plausible Nash equilibrium. This criterion is also conceptually simpler than the standard refinement criteria, since it does not depend on out-of-equilibrium, counterfactual, or limit arguments, and it does not require the addition of a belief system to the usual assumptions of noncooperative game theory. 1 Introduction A Nash equilibrium refinement is a criterion that applies to all plausible Nash equi- libria of an extensive form game but fails to apply to implausible Nash equilibria. 1 A voluminous literature has developed in the past few decades in search of an acceptable equilibrium refinement criterion. While no single criterion has been ∗ Santa Fe Institute and Central European University. I would like to thank Jeffrey Ely, Larry Samuelson, and FernandoVega-Redondo for their help, and the John D. and Catherine T. MacArthur Foundation for financial support. 1 By plausibility I mean following logically and directly from the most basic principles of rational action. There is, of course, an ultimately unacceptable vagueness in this notion, but it will do until Section 9. 1