Possibilistic beliefs and higher-level rationality

Abstract

We consider rationality and rationalizability for normal-form games of incomplete information in which the players have possibilistic beliefs about their opponents. In this setting, we prove that the strategies compatible with the players being level-k rational coincide with the strategies surviving a natural k-step iterated elimination procedure. We view the latter strategies as the (level-k) rationalizable ones in our possibilistic setting. Rationalizability was defined by Pearce [23] and Bernheim [12] for complete-information settings. Our iterated elimination procedure is similar to that proposed by Dekel, Fuden- berg, and Morris [14] in a Bayesian setting. For other iterated elimination procedures and corresponding notions of rationalizability in Bayesian settings, see Brandenburger and Dekel [9], Tan and Werlang [24], Battigalli and Siniscalchi [8], Ely and Peski [15], Weinstein and Yildiz [25], and Halpern and Pass [19].