Pairwise epistemic conditions for correlated rationalizability

We provide a foundation for correlated rationalizability by means of pairwise epistemic conditions imposed only on some pairs of players. Indeed, we show that pairwise mutual belief, for some pairs of players, of (i) the game payoffs, (ii) rationality, and (iii) deeming possible only strategy profiles that receive positive probability by the actual conjectures suffice for correlated rationalizability when there is a common prior. Moreover, we show that our epistemic conditions do not require nor imply mutual belief of rationality. Finally, we discuss the relationship between correlated rationalizability and Nash equilibrium on the basis of the respective pairwise epistemic conditions for each of the two concepts.