Rationalizability in large games

This paper characterizes both point-rationalizability and rationalizability in large games when societal responses are formulated as distributions or averages of individual actions. The sets of point-rationalizable and rationalizable societal responses are defined and shown to be convex, compact and equivalent to those outcomes that survive iterative elimination of never best responses, under point-beliefs and probabilistic beliefs, respectively. Given the introspection and mentalizing that rationalizability notions presuppose, one motivation behind the work is to examine their viability in situations where the terms rationality and full information can be given a more parsimonious, and thereby a more analytically viable, expression.