Common belief in rationality in psychological games: Belief-dependent utility and the limits of strategic reasoning

Abstract

Psychological games enable us to study diverse motivations like anger, guilt, and intention-based reciprocity using models of rational strategic choice based on common belief in rationality (aka correlated rationalizability). This is achieved by letting utility depend not only on outcomes and beliefs about others’ behavior but also on higher-order beliefs. It is an open question whether such belief-dependent utilities can be made consistent with common belief in rationality in all empirically relevant cases. In this paper, we use a novel existence condition to show that common belief in rationality is possible for any empirically relevant case of belief-dependent utility. In addition, we present a recursive elimination procedure that characterizes common belief in rationality under minimal assumptions on belief-dependent utility functions.