Dynamiques de Communication

Journal paper
Olivier Gossner, Penélope Hernández, Abraham Neyman
Revue Économique 55: 509-516
Publication year: 2004

Nous introduisons un modèle de communication avec état de la nature dynamique. En utilisant l’entropie comme mesure d’information, nous caractérisons les distributions empiriques espérées sur les actions qui sont réalisables. Nous présentons des applications aux jeux avec et sans intérêts communs.

Journal paper
Olivier Gossner, Nicolas Vieille
Games and Economic Behavior 42: 25-47
Publication year: 2003

This article studies situations in which agents do not initially know the effect of their decisions, but learn from experience the payoffs induced by their choices and their opponents’. We chararacterize equilibrium payoffs in terms of simple strategies in which an exploration phase is followed by a payoff acquisition phase.

Positive value of information in games

Journal paper
Bruno Bassan, Olivier Gossner, Marco Scarsini, Shmuel Zamir
International Journal of Game Theory 32: 17-31
Publication year: 2003

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments à la Blackwell. More specifically, we consider pairs consisting of a game with incomplete information G and an information structure S such that the extended game Gamma(G;S) has a unique Pareto payoff profile u. We prove that u is a Nash payoff profile of Gamma(G;S), and that for any information structure T that is coarser than S, all Nash payoff profiles of Gamma(G;T) are dominated by u.

We then prove that our condition is also necessary in the following sense: Given any convex compact polyhedron of payoff profiles, whose Pareto frontier is not a singleton, there exists an extended game Gamma(G;S) with that polyhedron as the convex hull of feasible payoffs, an information structure T coarser than S and a player i who strictly prefers a Nash equilibrium in Gamma(G;T) to any Nash equilibrium in Gamma(G;S).

On the complexity of coordination

Journal paper
Olivier Gossner, Penélope Hernández
Mathematics of Operations Research 28: 127-141
Publication year: 2003

Many results on repeated games played by finite automata rely on the complexity of the exact implementation of a coordinated play of length n. For a large proportion of sequences, this complexity appears to be no less than n. We study the complexity of a coordinated play when allowing for a few mismatches. We prove the existence of a constant C such that if (m ln(m))/n ≥ C, for almost any sequence of length n, there exists an automaton of size m that achieves a coordination ratio close to 1 with it. Moreover, we show that one can take any constant C such that C > e|X| ln(X), where |X| is the size of the alphabet from which the sequence is drawn. Our result contrasts with Neyman (1997) that shows that when (m ln(m))/n is close to 0, for almost no sequence of length n there exists an automaton of size m that achieves a coordination ratio significantly larger 1/|X| with it.

How to play with a biased coin?

Journal paper
Olivier Gossner, Nicolas Vieille
Games and Economic Behavior 41: 206-226
Publication year: 2002

We characterize the max min of repeated zero-sum games in which player one plays in pure strategies conditional on the private observation of a fixed sequence of random variables. Meanwhile we introduce a definition of a strategic distance between probability measures, and relate it to the standard Kullback distance.

Repeated communication through the `and' mechanism

Journal paper
Olivier Gossner, Nicolas Vieille
International Journal of Game Theory 30: 41-61
Publication year: 2001

We consider the “and” communication device that receives input from two players and outputs the public signal yes if both inputs are yes and outputs no otherwise. We prove that no correlation can securely be implemented through this device, even if an infinite number of communication rounds are allowed.

Comparison of information structures

Journal paper
Olivier Gossner
Games and Economic Behavior 30: 44-63
Publication year: 2000

We introduce the notion of an information structure I as being richer than another J when for every game G, all correlated equilibrium distributions of G induced by J are also induced by I. In particular, if I is richer than J then I can make all agents as well off as J in any game. We also define J to be faithfully reproducible from I when all the players can compute from their information in I “new information” that reproduces what they could have received from J. Our main result is that I is richer than J if and only if J is faithfully reproducible from I.

Repeated games with complete information

Book Chapter
Olivier Gossner, Tristan Tomala
in Meyers, Robert (Ed.) Encyclopedia of Complexity and Systems Science, Vol LXXX, Springer New York
Publication year: 1999

Secure protocols – or how communication generates correlation

Journal paper
Olivier Gossner
Journal of Economic Theory 83: 69-89
Publication year: 1998

Correlated equilibria and communication equilibria are useful notions to understand the strategic effects of information and communication. Between these two models, a protocol generates information through communication. We define a secure protocol
as a protocol from which no individual may have strategic incentives to deviate and characterize these protocols.

Protocoles de communication robustes

Journal paper
Olivier Gossner
Revue Économique 48: 685-695
Publication year: 1997

Lorsque des possibilités de communication existent, un protocole désigne un ensemble de règles utilisées par les agents pour échanger de l’information. Nous définissons un protocole robuste comme un protocole duquel aucun agent n’a intérêt à dévier, et caractérisons ces protocoles.

Overlapping generations games with mixed strategies

Journal paper
Olivier Gossner
Mathematics of Operations Research 21 : 477-486
Publication year: 1996

This paper proves a Folk Theorem for overlapping generations games in the case where the mixed strategies used by a player are not observable by the others, but only their realizations are public.

The folk theorem for finitely repeated games with mixed strategies

Journal paper
Olivier Gossner
International Journal of Game Theory 24 : 95-107
Publication year: 1995

This paper proves a Folk Theorem for finitely repeated games with mixed strategies. To obtain this result, we first show a similar property for finitely repeated games with terminal payoffs.