The article shows how Jean-Francois Mertens contributed to the development of game theory and microeconomics as we know them today. Along with about 80 articles, Mertens's topics go from the formulation of Bayesian decision making in games with incomplete information to the foundations of cost...

This paper is devoted to regret lower bounds in the classical model of stochastic multi-armed bandit. A well-known result of Lai and Robbins, which has then been extended by Burnetas and Katehakis, has established the presence of a logarithmic bound for all consistent policies. We relax the...

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform value, generalizing several results of the literature. A...

This paper studies the deviations of the regret in a stochastic multi-armed bandit problem. When the total number of plays n is known beforehand by the agent, Audibert et al. [2] exhibit a policy such that with probability at least 1−1/n, the regret of the policy is of order log n. They have...

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and...

We show on a 4x4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown-von Neumann-Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard...

This note establishes that in every 3-3 symmetric game, the replicator dynamics eliminates all strategies that are never used in correlated equilibrium. This extends to the best-response dynamics and to any convex monotonic dynamics. The proof is based on dual reduction.