A one-person doxastic characterization of Nash strategies

Within a formal epistemic model for simultaneous-move games, we present the following conditions: (1) belief in the opponents’ rationality (bor), stating that a player believes that every opponent chooses an optimal strategy, (2) self-referential beliefs (srb), stating that a player believes that his opponents hold correct beliefs about his own beliefs, (3) projective beliefs (pb), stating that i believes that j’s belief about k’s choice is the same as i’s belief about k’s choice, and (4) conditionally independent beliefs (cib), 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 (that is, a strategy that is optimal in some nash equilibrium). 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.