Advanced Search
Article Contents
Article Contents

Pure and Random strategies in differential game with incomplete informations

Abstract Related Papers Cited by
  • We investigate a two players zero sum differential game with incomplete information on the initial state: The first player has a private information on the initial state while the second player knows only a probability distribution on the initial state. This could be view as a generalization to differential games of the famous Aumann-Maschler framework for repeated games. In an article of the first author, the existence of the value in random strategies was obtained for a finite number of initial conditions (the probability distribution is a finite combination of Dirac measures). The main novelty of the present work consists in : first extending the result on the existence of a value in random strategies for infinite number of initial conditions and second - and mainly - proving the existence of a value in pure strategies when the initial probability distribution is regular enough (without atoms).
    Mathematics Subject Classification: Primary: 49N70; Secondary: 91A05.


    \begin{equation} \\ \end{equation}
  • [1]

    L. Ambrosio, Lecture Notes on Optimal Transport Problems, Mathematical Aspects of Evolving Interfaces, CIME Summer School in Madeira, Vol. 1812, Springer, 2003.doi: 10.1007/978-3-540-39189-0_1.


    R. J. Aumann, Mixed and behavior strategies in infinite extensive games, in Advances in Game Theory, Princeton Univ. Press, Princeton, N.J., 1964, 627-650.


    R. J. Aumann and M. B. Maschler, Repeated Games with Incomplete Information, MIT Press, Cambridge, MA, 1995.


    R. Buckdahn, P. Cardaliaguet and M. Quincampoix, Some recent aspects of differential game theory, Dynamic Games Applications, 1 (2011), 74-114.doi: 10.1007/s13235-010-0005-0.


    R. Buckdahn, J. Li and M. Quincampoix, Value function of differential games without isaacs conditions. An approach with non-anticipative mixed strategies, Internat. J. of Game Theory, 42 (2013), 989-1020.doi: 10.1007/s00182-012-0351-9.


    P. Cardaliaguet, Differential games with asymmetric information, SIAM J. Control Optim., 46 (2007), 816-838.doi: 10.1137/060654396.


    P. Cardaliaguet and M. Quincampoix, Deterministic differential games under probability knowledge of initial condition, Int. Game Theory Rev., 10 (2008), 1-16.doi: 10.1142/S021919890800173X.


    P. Cardaliaguet and C. Rainer, Stochastic differential games with assymetric information, Appl. Math. Optim., 59 (2009), 1-36.doi: 10.1007/s00245-008-9042-0.


    P. Cardaliaguet and C. Rainer, Games with incomplete information in continuous time and for continuous types, Dyn. Games Appl., 2 (2012), 206-227.doi: 10.1007/s13235-012-0043-x.


    C. Dellacherie and P. A. Meyer, Probabilities and Potential, North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam, 1978.


    J. F. Mertens, S. Sorin and S. Zamir, Repeated Games, CORE Discussion Papers 9420, 9421, 9422, 1994.doi: 10.1057/9780230226203.3424.


    A. Pratelli, On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation, Ann. Inst. H. Poincaré Probab. Statist., 43 (2007), 1-13.doi: 10.1016/j.anihpb.2005.12.001.


    D. Schmeidler, Equilibrium points of nonatomic games, Journal of Statistical Physics, 7 (1973), 295-300.doi: 10.1007/BF01014905.


    C. Villani, Topics in Optimal Transportation, Graduate studies in Mathematics, Vol. 58, AMS, 2003.doi: 10.1007/b12016.

  • 加载中

Article Metrics

HTML views() PDF downloads(170) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint