Abstract

Within a formal epistemic model for simultaneous-move games, we present the following conditions: belief in the opponents’ rationality, stating that a player believes that every opponent chooses an optimal strategy, self-referential beliefs, stating that a player believes that his opponents hold correct beliefs about his own beliefs, projective beliefs, stating that i believes that j’s belief about k’s choice is the same as i’s belief about k’s choice, and conditionally independent beliefs, stating that a player believes that opponents’ types choose their strategies independently. We show that, if a player satisfies BOR, SRB and CIB, and believes that every opponent satisfies BOR, SRB, PB and CIB, then he will choose a Nash strategy. We thus provide a sufficient collection of one-person conditions for Nash strategy choice. We also show that none of these seven conditions can be dropped