An Essay on Game Theory: Rationalizable Behavior under Coalitional Interactions

Abstract

We extend Ambrus’s [QJE, 2006] concept of “coalitional rationalizability (c-rationalizability)” to situations where, in seeking mutual beneficial interests, players in groups (i) make use of Bayes rule in expectation calculations and (ii) contemplate various deviations –i.e. the validity of deviation is checked against any arbitrary sets of strategies, not only against restricted subsets of strategies. In this paper we offer an alternative notion of c-rationalizability suitable for such complicated interactions. More specifically, following Bernheim’s [Econometrica 52(1984), 1007-1028] and Pearce’s[Econometrica 52(1984), 1029-1051] approach, we define c-rationalizability by the terminology “coalitional rationalizable set (CRS)”. Roughly speaking, a CRS is a product set of pure strategies from which no group of player(s) would like to deviate. We show that this notion of c-rationalizability possesses nice properties similar to those of conventional rationalizability. We also provide its epistemic foundation. JEL Classification: C70, C72, D81