Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information

The paper analyzes the Nash equilibria of two-person discounted repeated games with one-sided incomplete information and known own payo®s. If the informed player is arbitrarily patient relative to the uninformed player, then the characterization for the informed player's payoffs is essentially the same as that in the undiscounted case. This implies that even small amounts of incomplete information can lead to a discontinuous change in the equilibrium payoff set. For the case of equal discount factors, however, and under an assumption that strictly individually rational payoffs exist, a result akin to the Folk Theorem holds when a complete information game is perturbed by a small amount of incomplete information.Reputation, Folk Theorem, repeated games, incomplete information.

Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information

The paper analyzes the Nash equilibria of two-person discounted repeated games with one-sided incomplete information and known own payoffs. If the informed player is arbitrarily patient relative to the uninformed player, then the characterization for the informed player's payoffs is essentially the same as that in the undiscounted case. This implies that even small amounts of incomplete information can lead to a discontinuous change in the equilibrium payoff set. For the case of equal discount factors, however, and under an assumption that strictly individually rational payoffs exist, a result akin to the Folk Theorem holds when a complete information game is perturbed by a small amount of incomplete information.reputation, Folk Theorem, repeated games, incomplete information

Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture "Maxmin=lim⁡vn=lim⁡vλMaxmin=\lim v_n=\lim v_\lambda"

We study two-player zero-sum recursive games with a countable state space and finite action spaces at each state. When the family of $n$-stage values $\{v_n,n\geq 1\}$ is totally bounded for the uniform norm, we prove the existence of the uniform value. Together with a result in Rosenberg and Vieille (2000), we obtain a uniform Tauberian theorem for recursive games: $(v_n)$ converges uniformly if and only if $(v_\lambda)$ converges uniformly. We apply our main result to finite recursive games with signals (where players observe only signals on the state and on past actions). When the maximizer is more informed than the minimizer, we prove the Mertens conjecture $Maxmin=\lim_{n\to\infty} v_n=\lim_{\lambda\to 0}v_\lambda$. Finally, we deduce the existence of the uniform value in finite recursive game with symmetric information.Comment: 32 page

Belief-free equilibria in games with incomplete information

We de ne belief-free equilibria in two-player games with incomplete information as se- quential equilibria for which players' continuation strategies are best-replies, after every history, independently of their beliefs about the state of nature. We characterize a set of payos that includes all belief-free equilibrium payos. Conversely, any payo in the interior of this set is a belief-free equilibrium payorepeated game with incomplete information; Harsanyi doctrine; belief-free equilibria

Advances in Zero-Sum Dynamic Games

International audienceThe survey presents recent results in the theory of two-person zero-sum repeated games and their connections with differential and continuous-time games. The emphasis is made on the following(1) A general model allows to deal simultaneously with stochastic and informational aspects.(2) All evaluations of the stage payoffs can be covered in the same framework (and not only the usual Cesàro and Abel means).(3) The model in discrete time can be seen and analyzed as a discretization of a continuous time game. Moreover, tools and ideas from repeated games are very fruitful for continuous time games and vice versa.(4) Numerous important conjectures have been answered (some in the negative).(5) New tools and original models have been proposed. As a consequence, the field (discrete versus continuous time, stochastic versus incomplete information models) has a much more unified structure, and research is extremely active

Belief-free Equilibria in Games with Incomplete Information: Characterization and Existence

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs.Repeated games with incomplete information, Harsanyi doctrine, Belief-free equilibria

Belief-free Equilibria in games with incomplete information

In this paper, the authors define belief-free equilibria in two-player games with incomplete information as sequential equilibria for which players’ continuation strategies are best-replies, after every history, independently of their beliefs about the state of nature. They characterize a set of payoffs that includes all belief-free equilibrium payoffs. Conversely, any payoff in the interior of this set is a belief-free equilibrium payoff.game theory; equilibria; information

Stochastic Games : recent results

Nous présentons des résultats récents sur les jeux stochastiques finis. Ce texte est à paraître dans le Handbook of Game Theory, vol 3., eds. R.J. Aumann et S. HartJeux stochastiques