Set Of Nash Equilibrium Payoffs Research Articles

Communication and cooperation in repeated games

We study the role of communication in repeated games with private monitoring. We first show that without communication, the set of Nash equilibrium payoffs in such games is a subset of the set ofε‐coarse correlated equilibrium payoffs (ε‐CCE) of the underlying one‐shot game. The value ofεdepends on the discount factor and the quality of monitoring. We then identify conditions under which there are equilibria with “cheap talk” that result in nearly efficient payoffs outside the setε‐CCE. Thus, in our model, communication is necessary for cooperation.

Bayesian repeated games and reputation

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.

Bayesian Repeated Games and Reputation

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.

Nash Equilibrium for Differential Games and Nonanticipative Strategies

AbstractIn this paper we introduce the definition of Nash equilibrium of two-person nonzero-sum differential in the class of nonanticipative strategies. It is assumed that both players play in nonanticipative strategies. We characterize the set of Nash equilibrium payoffs for this situation also.

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)].

An Approach to Communication Equilibria

The Nash equilibrium concept may be extended gradually when the rules of the game are interpreted in a wider and wider sense, so as to allow preplay or even intraplay communication. A well-known extension of the Nash equilibrium is Aumann's correlated equilibrium, which depends only on the normal form of the game. Two other solution concepts for multistage games are proposed here: the extensive form correlated equilibrium, where the players can observe private extraneous signals at every stage and the communication equilibrium, where the players are furthermore allowed to transmit inputs to an appropriate device at every stage. We show that the set of payoffs associated with each solution concept has a canonical representation (in the spirit of the revelation principle) and is a convex polyhedron. We also provide for each concept a super-canonical game such that the set of payoffs associated with the solution concept is precisely the set of Nash equilibrium payoffs of this game.

Asymptotic properties of a non-zero sum stochastic game

An example of a non-zero sum stochastic game is given where: i) the set of Nash Equilibrium Payoffs in the finitely repeated game and in the game with discount factor is reduced to the threat point; ii) the corresponding set for the infinitely repeated game is disjoint from this point and equals the set of feasible, individually rational and Pareto optimal payoffs.