Nash Equilibrium as an Expression of Self-Referential Reasoning

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 should believe 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 equilibrium strategy (that is, a strategy that is optimal in some Nash equilibrium). We thus provide a set of sufficient conditions for Nash equilibrium strategy choice. We also show that none of these seven conditions can be dropped.