Duality and markovian strategies

Abstract. We introduce the dual of a stochastic game with incomplete information on one side, and we deduce some properties of optimal strategies of the uninformed player.

[1]  Bernard De Meyer,et al.  Repeated Games and Partial Differential Equations , 1996, Math. Oper. Res..

[2]  H. W. Kuhn,et al.  11. Extensive Games and the Problem of Information , 1953 .

[3]  Jean-François Mertens,et al.  The value of two-person zero-sum repeated games with lack of information on both sides , 1971 .

[4]  Jean-Pierre Ponssard,et al.  Optimal Behavioral Strategies In 0-Sum Games with Almost Perfect Information , 1982, Math. Oper. Res..

[5]  Martin Heuer,et al.  Optimal strategies for the uninformed player , 1991 .

[6]  Jean-François Mertens.  The speed of convergence in repeated games with incomplete information on one side , 1998, Int. J. Game Theory.

[7]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[8]  A. W. Tucker,et al.  Contributions to the Theory of Games, Vol. II , 1954 .

[9]  S. Zamir,et al.  "Big match" with lack of information on one side (Part II) , 1984 .

[10]  M. Heuer.  Asymptotically optimal strategies in repeated games with incomplete information , 1992 .

[11]  Ulrich Rieder,et al.  Markov games with incomplete information , 1997, Math. Methods Oper. Res..

[12]  S. Sorin.  “Big Match” with lack of information on one side (part i) , 1984 .

[13]  L. Shapley,et al.  Stochastic Games* , 1953, Proceedings of the National Academy of Sciences.

[14]  M. Sion.  On general minimax theorems , 1958 .

[15]  Robert J. Aumann,et al.  Repeated Games with Incomplete Information , 1995 .

[16]  Dinah Rosenberg,et al.  "Cav u" and the Dual Game , 1999, Math. Oper. Res..