We characterize belief-free equilibria in inﬁnitely repeated games with incomplete information with N > 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoﬀs across players. The characterization is tight: we deﬁne a set of payoﬀs that contains all the belief-free equilibrium payoﬀs; conversely, any point in the interior of this set is a belief-free equilibrium payoﬀ vector when players are suﬀiciently patient. Further, we provide necessary conditions and suﬀicient conditions on the information structure for this set to be non-empty, both for the case of known-own payoﬀs, and for arbitrary payoﬀs.
Hörner, Johannes; Lovo, Stefano; and Tomala, Tristan, "Belief-free Equilibria in Games with Incomplete Information: Characterization and Existence" (2009). Cowles Foundation Discussion Papers. 2063.