Johanne Cohen

David Auger, Johanne Cohen, Antoine Lobstein

We introduce a game where players selfishly choose a resource and endure a cost depending on the number of players choosing nearby resources. We model the influences among resources by a weighted graph, directed or not. These games are generalizations of well-known games like Wardrop and congestion games. We study the conditions of equilibria existence and their efficiency if they exist. We conclude with studies of games whose influences among resources can be modelled by simple graphs.

Johanne Cohen, Amélie Héliou, Panayotis Mertikopoulos

Motivated by applications to data networks where fast convergence is essential, we analyze the problem of learning in generic N-person games that admit a Nash equilibrium in pure strategies. Specifically, we consider a scenario where players interact repeatedly and try to learn from past experience by small adjustments based on local - and possibly imperfect - payoff information. For concreteness, we focus on the so-called "hedge" variant of the exponential weights algorithm where players select an action with probability proportional to the exponential of the action's cumulative payoff over time. When players have perfect information on their mixed payoffs, the algorithm converges locally to a strict equilibrium and the rate of convergence is exponentially fast - of the order of $\mathcal{O}(\exp(-a\sum_{j=1}^{t}γ_{j}))$ where $a>0$ is a constant and $γ_{j}$ is the algorithm's step-size. In the presence of uncertainty, convergence requires a more conservative step-size policy, but with high probability, the algorithm remains locally convergent and achieves an exponential convergence rate.