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Backward Induction, Normal Form Perfection and Explicable Equilibria

Philip J. Reny

Abstract

A weakening of Kreps and Wilson's (1982) notion of sequential rationality for extensive form games is presented. The motivation behind this weakening stems from the difficulty in justifying sequentially rational behavior in subgames reachable only through a violation of sequential rationality. Although the notion of weak sequential rationality developed here is based upon extensive form considerations, it bears a close relation to Selten's (1975) normal form perfect equilibria. Also, a class of restrictions one might impose upon out of equilibrium beliefs is suggested. The weakest of these results from the assumption that deviators are expected utility maximizers. The strongest yields backward induction outcomes in generic games with perfect information. Lastly, it is argued, with the aid of an example having imperfect information, that sequential rationality is not the consequence of equilibrium play and the absence of incredible threats.