Proper rationalizability and backward induction

Abstract

This paper introduces a new normal form rationalizability concept, which in reduced normal form games corresponding to generic finite extensive games of perfect information yields the unique backward induction outcome. The basic assumption is that every player trembles “more or less rationally” as in the definition of a e-proper equilibrium by Myerson (1978). In the same way that proper equilibrium refines Nash and perfect equilibrium, our model strengthens the normal form rationalizability concepts by Bernheim (1984), Borgers (1994) and Pearce (1984). Common knowledge of trembling implies the iterated elimination of strategies that are strictly dominated at an information set. The elimination process starts at the end of the game tree and goes backwards to the beginning.