Epistemic conditions for rationalizability

In this paper I show that, just as with Nash Equilibrium, there are sparse conditions, not involving common knowledge of rationality, that lead to (correlated) rationalizability. The basic observation is that, if the actual world belongs to a set of states where the set Z of action pro…les is played, each player knows her own payo¤, everyone is rational and it is mutual knowledge that the action pro…les played are in Z, then the actions played at the actual world are rationalizable actions. Alternatively, if at the actual world the support of the conjecture of player i is D, there is mutual knowledge of: (i) the game being played, (ii) that the players are rational, and (iii) that for every i the support of the conjecture of player i is contained in D, then every strategy in the support of the conjectures is rationalizable. The results do not require common knowledge of anything, are valid for games with any number of players, and extend to re…nements of rationalizability such as independent rationalizability and rationalizable conjectural equilibrium.