WEAK DOMINANCE AND APPROXIMATE COMMON KNOWLEDGE

Considering finite normal-form games, we assume that players maximise expected utility, that they hold beliefs with full support, and that these facts are ''approximate common knowledge'' among players. We show that players satisfy these assumptions if and only if they choose strategies that survive the following procedure: first, all weakly dominated strategies are eliminated, and then strongly dominated strategies are iteratively eliminated. This procedure is due to E. Dekel and D. Fudenberg [J. Econ. Theory 52 (1990), 243-267]. We compare our justification for this procedure to theirs.