In Renegotiation in Repeated Games (1989), J. Farrell and E. Maskin present, among other results, sufficient conditions for payoffs to be “weakly renegotiation-proof”. We show that a step in the corresponding proof is not correct by giving a counterexample. We then provide a correct proof with slightly more demanding sufficient conditions.

We define feasible, posterior individually rational solutions for two-person Bayesian games with a single informed player. Such a solution can be achieved by direct signalling from the informed player and requires approval of both players after the signal has been sent. Without further assumptions on the Bayesian game, a solution does not necessarily exist. We show that, if the uninformed player has a "uniform punishment strategy" against the informed one, the existence of a solution follows from the existence of Nash equilibrium in infinitely repeated games with lack of information on one side. We also consider the extension of the result when both players have private information.

We consider two-person undiscounted and discounted infinitely repeated games in which every player privately knows his own payoffs (private values). Under a further assumption (existence of uniform punishment strategies), the Nash equilibria of the Bayesian infinitely repeated game without discounting are payoff-equivalent to tractable, completely revealing, equilibria. This characterization does not apply to discounted games with sufficiently patient players. We show that in a class of public good games, the set of Nash equilibrium payoffs of the undiscounted game can be empty, while limit (perfect Bayesian) Nash equilibrium payoffs of the discounted game, as players become increasingly patient, do exist. These equilibria share some features with the ones of two-sided reputation models.

Under appropriate assumptions (private values and uniform punishments), the Nash equilibria of a Bayesian repeated game without discounting are payoff-equivalent to tractable, completely revealing, equilibria and can be achieved as interim cooperative solutions of the initial Bayesian game. This characterization does not apply to discounted games with patient players. In a class of public good games, the set of Nash equilibrium payoffs of the undiscounted game can be empty, while limit (perfect Bayesian) Nash equilibrium payoffs of the discounted game, as players become infinitely patient, do exist. These equilibria share some features with the ones of multi-sided reputation models. JEL-Code: C730, C720, C710, D820, H410.

We consider Bayesian games, with independent private values, in which uniform punishment strategies are available. We establish that the Nash equilibria of the Bayesian infinitely repeated game without discounting are payoff equivalent to tractable separating (i.e., completely revealing) equilibria and can be achieved as interim cooperative solutions of the initial Bayesian game. We also show, on a public good example, that the set of Nash equilibrium payoffs of the undiscounted game can be empty, while limit Nash equilibrium payoffs of the discounted game, as players become infinitely patient, do exist.

We consider Bayesian games, with independent private values, in which uniform punishment strategies are available. We establish that the Nash equilibria of the Bayesian infinitely repeated game without discounting are payoff equivalent to tractable separating (i.e., completely revealing) equilibria and can be achieved as interim cooperative solutions of the initial Bayesian game. We also show, on a public good example, that the set of Nash equilibrium payoffs of the undiscounted game can be empty, while limit Nash equilibrium payoffs of the discounted game, as players become infinitely patient, do exist.