Iterated Strict Dominance in General Games

We offer a definition of iterated elimination of strictly dominated strategies (IESDS∗) for games with (in)finite players, (non)compact strategy sets, and (dis)continuous payoff functions. IESDS∗ is always a well-defined order independent procedure that can be used to solve Nash equilibrium in dominance-solvable games. We characterize IESDS∗ by means of a “stability” criterion, and offer a sufficient and necessary epistemic condition for IESDS∗. We show by an example that IESDS∗ may generate spurious Nash equilibria in the class of Reny’s better-reply secure games. We provide sufficient/necessary conditions under which IESDS∗ preserves the set of Nash equilibria. JEL Classification: C70, C72.

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