p.889

Justifiable Beliefs in Sequential Equilibrium

Andrew McLennan

Abstract

An action in an extensive game that has a suboptimal payoff in every sequential equilibrium is said to be useless. There are sequential equilibria in which beliefs at each information set assign positive probability only to those nodes reached by the fewest useless actions. An action is second order useless if it is not useless but is strictly suboptimal in every equilibrium satisfying this condition on beliefs, and there exist sequential equilibria in which beliefs assign positive probability only to those nodes reached by the fewest useless actions, and, in this set, only those nodes requiring the fewest second order useless actions. Higher order uselessness is defined inductively, and beliefs satisfying the associated sequence of conditions are said to be justifiable. The existence of sequential equilibria with justifiable beliefs is demonstrated.