Games with incomplete information in continuous time and for continuous types.

Pierre Cardaliaguet (1) , Catherine Rainer (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LM - Laboratoire de mathématiques de Brest

We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an auxiliary optimization problem over a set of measure-valued processes. Then we use this equivalent formulation to characterize the value function as the viscosity solution of a special type of a Hamilton-Jacobi equation. This paper generalizes the results of a previous work of the authors , where only a finite number of possible payoffs is considered.

Mots clés: Continuous-time game; incomplete information; martingale measures; Hamilton-Jacobi equations

Domaines: Probabilités [math.PR]

Pierre Cardaliaguet, Catherine Rainer. Games with incomplete information in continuous time and for continuous types.. Dynamic Games and Applications, 2012, 2 (2), pp.206-227. ⟨hal-00672658⟩