Continuous-time limit of dynamic games with incomplete information and a more informed player.

Fabien Gensbittel (1)

1 GREMAQ - Groupe de recherche en économie mathématique et quantitative

We study a model of two-player, zero-sum, dynamic game with incomplete information on one side in which the players receive exogenous information about the payoff-relevant state variable during the play. We assume that one of the players is always more informed than his opponent and that signals observed during the play correspond to the observation of some continuous-time Markov process at some fixed times on a finite grid. We show the existence of a limit value as the players play more and more frequently, and we provide two different characterizations for this value: through a stochastic optimization problem and through a variational inequality, related to some second-order Hamilton-Jacobi equation in some particular cases.

Mots clés: repeated games; incomplete information; zero-sum games; Hamilton-Jacobi equations

Domaines: Optimisation et contrôle [math.OC]

Fabien Gensbittel. Continuous-time limit of dynamic games with incomplete information and a more informed player.. 2013. ⟨hal-00910970v1⟩