DOMINATED STRATEGIES AND COMMON KNOWLEDGE

This paper establishes five results. First, the common knowledge of admissibility is not equivalent to iterated admissibility. Second, there exist games in which the common knowledge of admissibility does not uniquely determine which strategies should be eliminated on admissibility grounds. Third, there exist games in which assuming that admissibility is common knowledge yields a contradiction. Fourth, admissibility can be common knowledge without the players knowing the choice sets implied by this knowledge. Finally, difficulties with the common knowledge of admissibility can arise even in games in which each player has a unique dominant strategy. © 1992.