Trembles in the Bayesian foundations of solution concepts of games

The Bayesian approach to game theory is extended to a setting where players can believe that other players may tremble with infinitesimal probability. Here too, a player's type induces a probability distribution over Ether players' types. Two axioms of near rationality are introduced. Almost common knowledge of near rationality implies a strategy choice that survives one round of weak dominance followed by iterated strict dominance. Common knowledge of hierarchical rationality leads to iterated weak dominance. Perfect equilibria result from knowledge of near rationality and of other players' beliefs. To attain proper equilibria, a stronger hierarchical restriction on beliefs is necessary. (C) 1998 Academic Press.