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...

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...