A folk theorem for dynamic games

This paper focuses on infinite horizon dynamic games satisfying the monotonicity property: the objective function of every player is increasing (decreasing) in the strategy of the other players. We prove that, when closed-loop strategies are allowed, the set of Nash equilibrium payoffs coincides with the set of individually rational feasible payoffs in the game which allows only open-loop strategies. The significance of this general result is demonstrated by illustrating its applicability to the study of dynamic duopolistic competition [Fershtman and Kamien (1987), Reynolds (1987)], dynamic voluntary provision of public goods [Fershtman and Nitzan (1991)] and competitive arms race [Van der Ploeg and De Zeeuw (1990)].