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 two-player, zero-sum, dynamic game with incomplete information where one of the players is more informed than his opponent. We analyze the limit value as the players play more and more frequently. The more informed player observes the realization of a Markov process (X,Y) on which the payoffs depend, while the less informed player only observes Y and his opponent's actions. We show the existence of a limit value as the time span between two consecutive stages goes to zero. This value is characterized through an auxiliary optimization problem and as the unique viscosity solution of a second order Hamilton-Jacobi equation with convexity constraints.

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

Domaines: Optimisation et contrôle [math.OC]; Mathématiques [math]

Fabien Gensbittel. Continuous-time limit of dynamic games with incomplete information and a more informed player.. International Journal of Game Theory, 2016, 45 (1), pp.321-352. ⟨hal-00910970v3⟩