A canonical interpretation of an inﬁnitely repeated game is that of a “dynastic” repeated game: a stage game repeatedly played by successive generations of ﬁnitely-lived players with dynastic preferences. These two models are in fact equivalent when the past history of play is observable to all players. In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are suﬀiciently patient, all feasible payoﬀ vectors (including those below the minmax) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoﬀ set with a non-empty interior. Our results stem from the fact that, in equilibrium, a player may be unable to communicate eﬀectively relevant information to his successor in the same dynasty. This, in turn implies that following some histories of play the players’ equilibrium beliefs may violate “Inter-Generational Agreement.”
Anderlini, Luca; Gerardi, Dino; and Lagunoff, Roger, "The Folk Theorem in Dynastic Repeated Games" (2004). Cowles Foundation Discussion Papers. 1772.