Hierarchies of compact beliefs and rationalizable behavior

Following Tan and Werlang [Journal of Economic Theory 45 (1988) 370], we consider games as collections of decision problems, in which the uncertainty facing any player is the strategy choice of the other players, their beliefs about the other players’ strategy choice, and so on. A distinctive feature of our approach is that we model players’ beliefs as infinite hierarchies of compact possibility sets, rather than probability measures as in the Bayesian setup. Within this framework, we derive an axiomatic foundation for the point-rationalizability concept proposed by Bernheim [Econometrica 52 (1984) 1007].