Markov Games with Frequent Actions and Incomplete Information—The Limit Case

References

• Abreu D, Milgrom P, Pearce D (1991) Information and timing in repeated partnerships. Econometrica 59:1713–1733.Crossref, Google Scholar
• Athey S, Bagwell K (2008) Collusion with persistent cost shocks. Econometrica 76(3):493–540.Crossref, Google Scholar
• Aumann RJ, Maschler MB (1995) Repeated Games with Incomplete Information (MIT Press, Cambridge, MA).Google Scholar
• Cardaliaguet P (2009) A double obstacle problem arising in differential game theory. J. Math. Anal. Appl. 360(1):95–107.Crossref, Google Scholar
• Cardaliaguet P, Rainer C (2009a) Stochastic differential games with asymmetric information. Appl. Math. Optim. 59:1–36.Crossref, Google Scholar
• Cardaliaguet P, Rainer C (2009b) On a continuous time game with incomplete information. Math. Oper. Res. 34(4):769–794.Link, Google Scholar
• Cardaliaguet P, Laraki R, Sorin S (2012) A continuous time approach for the asymptotic value in two-person zero-sum repeated games. SIAM J. Control Optim. 50(3):1573–1596.Crossref, Google Scholar
• Crandall MG, Ishii H, Lions P-L (1992) User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27(1):1–67.Crossref, Google Scholar
• de Meyer B (2010) Price dynamics on a stock market with asymmetric information. Games Econom. Behav. 69:42–71.Crossref, Google Scholar
• Escobar JF, Toikka J (2013) Efficiency in games with Markovian private information. Econometrica 81(5):1887–1934.Crossref, Google Scholar
• Evans LC, Souganidis PE (1984) Differential games and representation formulas for solutions of Hamilton-Jacobi equations. Indiana Univ. Math. J. 282:487–502.Google Scholar
• Fudenberg D, Levine DK (2007) Continuous time limits of repeated games with imperfect public monitoring. Rev. Econom. Dynam. 10:173–192.Crossref, Google Scholar
• Gensbittel F, Renault J (2015) The value of Markov Chain Games with incomplete information on both sides. Math. Oper. Res., ePub ahead of print January 27, http://dx.doi.org/10.1287/moor.2014.0697.Google Scholar
• Grün C (2012) A probabilistic numerical scheme for stochastic differential games with incomplete information. AMO 66:363–385.Google Scholar
• Hörner J, Rosenberg D, Solan E, Vieille N (2010) On a Markov game with one-sided incomplete information. Oper. Res. 58(4):1107–1115.Link, Google Scholar
• Hörner J, Sugaya T, Takahashi S, Vieille N (2011) Recursive methods in discounted stochastic games: An algorithm for δ → 1 and a Folk theorem. Econometrica 79:1277–1318.Crossref, Google Scholar
• Laraki R (2002) Repeated games with lack of information on one side: The dual differential approach. Math. Oper. Res. 27(2):419–440.Link, Google Scholar
• Lehrer E, Rosenberg D (2003) Information and its value in zero-sum repeated games. Mimeo.Google Scholar
• Lehrer E, Rosenberg D (2010) A note on the evaluation of information in zero-sum repeated games. J. Math. Econom. 46:393–399.Crossref, Google Scholar
• Mailath G, Samuelson L (2001) Who wants a good reputation? Rev. Econom. Stud. 68:415–441.Crossref, Google Scholar
• Mailath G, Samuelson L (2006) Repeated Games and Reputations: Long-Run Relationships (Oxford University Press, New York).Crossref, Google Scholar
• Mertens JF, Sorin S, Samir S (1994) Repeated Games. Reprinted in 2015. (Cambridge University Press, New York).Google Scholar
• Meyer P-A, Zheng WA (1984) Tightness criteria for laws of semimartingales. Ann. Inst. H. Poincaré Probab. Statist. 20(4):353–372.Google Scholar
• Neveu J (1970) Bases Mathématiques du Calcul des Probabilités (Masson, Paris).Google Scholar
• Neyman A (2008) Existence of optimal strategies in Markov games with incomplete information. Internat. J. Game Theory 37:518–596.Crossref, Google Scholar
• Pęski M, Wiseman T (2015) A folk theorem for stochastic games with infrequent state changes. Theory Econom. 10(1):131–173.Crossref, Google Scholar
• Phelan C (2006) Public trust and government betrayal. J. Econom. Theory 127(1):27–43.Crossref, Google Scholar
• Protter P (2005) Stochastic Integration and Differential Equations (Springer, Berlin).Crossref, Google Scholar
• Renault J (2006) The value of Markov chain games with lack of information on one side. Math. Oper. Res. 31(3):490–512.Link, Google Scholar
• Renault J, Solan E, Vieille N (2013) Dynamic sender-receiver games. J. Econom. Theory 148:502–534.Crossref, Google Scholar
• Sorin S (2002) A First Course on Zero-Sum Repeated Games (Springer, Berlin).Google Scholar
• Vieille N (1992) Weak approachability. Math. Oper. Res. 17(4):781–791.Link, Google Scholar
• Wiseman T (2008) Reputation and impermanent types. Games Econom. Behav. 62:190–210.Crossref, Google Scholar