Solving two-state Markov games with incomplete information on one side

We study the optimal use of information in Markov games with incomplete information on one side and two states. We provide a finite-stage algorithm for calculating the limit value as the gap between stages goes to 0, and an optimal strategy for the informed player in the limiting game in continuous time. This limiting strategy induces an-optimal strategy for the informed player, provided the gap between stages is small. Our results demonstrate when the informed player should use his information and how.

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

[2]  Nicolas Vieille,et al.  Optimal dynamic information provision , 2014, Games Econ. Behav..

[3]  Abraham Neyman Existence of optimal strategies in Markov games with incomplete information , 2008, Int. J. Game Theory.

[4]  Nicolas Vieille,et al.  On a Markov Game with One-Sided Information , 2010, Oper. Res..

[5]  M. Coste AN INTRODUCTION TO O-MINIMAL GEOMETRY , 2002 .

[6]  Catherine Rainer,et al.  On a Continuous-Time Game with Incomplete Information , 2008, Math. Oper. Res..

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

[8]  Nicolas Vieille,et al.  Markov Games with Frequent Actions and Incomplete Information - The Limit Case , 2013, Math. Oper. Res..

[9]  Christine Grun,et al.  A BSDE approach to stochastic differential games with incomplete information , 2011, 1106.2629.

[10]  Jérôme Renault,et al.  The Value of Markov Chain Games with Lack of Information on One Side , 2006, Math. Oper. Res..

[11]  Fabien Gensbittel Continuous-time limit of dynamic games with incomplete information and a more informed player , 2016, Int. J. Game Theory.

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

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

[14]  Fabien Gensbittel,et al.  Continuous-Time Markov Games with Asymmetric Information , 2018, Dyn. Games Appl..

[15]  Miquel Oliu-Barton,et al.  Differential Games with Asymmetric and Correlated Information , 2014, Dynamic Games and Applications.

[16]  Shmuel Zamir,et al.  Repeated games of incomplete information: Zero-sum , 1992 .

[17]  Stéphane Gaubert,et al.  Definable Zero-Sum Stochastic Games , 2013, Math. Oper. Res..

[18]  Nicolas Vieille,et al.  Markov Games with Frequent Actions and Incomplete Information , 2013, 1307.3365.

[19]  P. Cardaliaguet Numerical Approximation and Optimal Strategies for Differential Games with Lack of Information on One Side , 2007 .

[20]  Jérôme Renault,et al.  The Value of Repeated Games with an Informed Controller , 2008, Math. Oper. Res..

[21]  Christine Grün,et al.  A Probabilistic-Numerical Approximation for an Obstacle Problem Arising in Game Theory , 2011, ArXiv.

[22]  J. Harsanyi Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[23]  Fabien Gensbittel,et al.  The Value of Markov Chain Games with Incomplete Information on Both Sides , 2012, Math. Oper. Res..

[24]  Fabien Gensbittel,et al.  Zero-Sum Stopping Games with Asymmetric Information , 2014, Math. Oper. Res..

[25]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..