Strategic rationality orderings and the best rationalization principle

In a finite game fix a space of extended probabilities over strategies and a profile of best response correspondences. A profile of rationality orderings is then given by an ordered partition of the set of strategies of each player, representing different degrees of rationality, where at-least k + 1-rational strategies are best responses against extended probabilities reflecting at least k degrees of rationality. This solution can be constructed inductively, providing a Bayesian foundation for controversial deletion procedures such as extensive form rationalizability and iterated weak dominance. Focusing on extensive games, this approach formalizes the best rationalization principle. (C) 1996 Academic Press, Inc.