Games with incomplete information in continuous time and for continuous types

Cardaliaguet, Pierre; Rainer, Catherine

Cardaliaguet, Pierre; Rainer, Catherine (2012), Games with incomplete information in continuous time and for continuous types, Dynamic Games and Applications, 2, 2, p. 206-227. http://dx.doi.org/10.1007/s13235-012-0043-x

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00672658

Date

2012

Journal name

Dynamic Games and Applications

Volume

Number

Publisher

Springer

Pages

206-227

Abstract (EN)

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.

Subjects / Keywords

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