A folk theorem for repeated games with unequal discounting

We introduce a “dynamic non-equivalent utilities” (DNEU) condition and the notion of dynamic player-specific punishments for a general repeated game with unequal discounting, both naturally generalizing the stationary counterparts in Abreu et al. (1994). We show that if the DNEU condition, i.e., no pair of players have equivalent utility functions in the repeated game, is satisfied, then any feasible and strictly sequentially individually rational payoff sequence allows dynamic player-specific punishments. Using this result, we prove a folk theorem for unequal discounting repeated games that satisfy the DNEU condition.