On a Continuous-Time Game with Incomplete Information

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, the authors show that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some martingale measures. The authors also characterize the optimal martingale measures and compute them explicitly in several examples.

[1]  Pierre Cardaliaguet,et al.  Differential Games with Asymmetric Information , 2007, SIAM J. Control. Optim..

[2]  A. Souquière.  Approximation and representation of the value for some differential games with imperfect information , 2008 .

[3]  Anne Souquière,et al.  Approximation and representation of the value for some differential games with asymmetric information , 2010, Int. J. Game Theory.

[4]  Pierre Cardaliaguet,et al.  A double obstacle problem arising in differential game theory , 2009 .

[5]  S. Sorin.  A First Course on Zero Sum Repeated Games , 2002 .

[6]  P. Souganidis,et al.  Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations. , 1983 .

[7]  H. Soner,et al.  Dynamic programming for stochastic target problems and geometric flows , 2002 .

[8]  Bernard De Meyer,et al.  Price dynamics on a stock market with asymmetric information , 2007, Games Econ. Behav..

[9]  Jérôme Renault,et al.  Repeated Games with Incomplete Information , 2009, Encyclopedia of Complexity and Systems Science.

[10]  Marc Quincampoix,et al.  A Representation Formula for the Mean Curvature Motion , 2001, SIAM J. Math. Anal..

[11]  M. Émery,et al.  On the Azéma martingales , 1989 .

[12]  P. Cardaliaguet,et al.  Stochastic Differential Games with Asymmetric Information , 2007, math/0703155.

[13]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[14]  H. Ishii,et al.  Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains , 1991 .