Efficiency in Games with Markovian Private Information

We study repeated Bayesian n-player games in which the players' privately known types evolve according an irreducible Markov chain. Our main result shows that, with communication, any Pareto-efficient payoff vector above a stationary minmax value can be approximated arbitrarily closely in a perfect Bayesian equilibrium as the discount factor goes to one. As an intermediate step we construct a dynamic mechanism (without transfers) which is approximately efficient for patient players given a sufficiently long time horizon.

[1]  S. Athey,et al.  Collusion With Persistent Cost Shocks , 2008 .

[2]  Drew Fudenberg,et al.  The Folk Theorem in Repeated Games with Discounting or with Incomplete Information , 1986 .

[3]  Nicolas Vieille,et al.  Dynamic Sender-Receiver Games , 2012 .

[4]  Nicolas Vieille,et al.  On a Markov Game with One-Sided Incomplete Information , 2009 .

[5]  Johannes Hörner,et al.  Collusion with (almost) no information , 2008 .

[6]  M. Jackson,et al.  Overcoming Incentive Constraints by Linking Decisions , 2007 .

[7]  Cheng Wang.  Dynamic Insurance with Private Information and Balanced Budgets , 1995 .

[8]  Lones Smith,et al.  THE FOLK THEOREM FOR REPEATED GAMES: A NEU CONDITION' , 1994 .

[9]  B. Moldovanu,et al.  Efficient Design with Interdependent Valuations , 2001 .

[10]  Harold L. Cole,et al.  Dynamic Games with Hidden Actions and Hidden States , 2001, J. Econ. Theory.

[11]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[12]  Harold L. Cole,et al.  Default, Settlement, and Signalling: Lending Resumption in a Reputational Model of Sovereign Debt , 1995 .

[13]  D. Fudenberg,et al.  Learning from Private Information in Noisy Repeated Games , 2010, J. Econ. Theory.

[14]  D. Vere-Jones.  Markov Chains , 1972, Nature.

[15]  Christopher Phelan,et al.  Public trust and government betrayal , 2006, J. Econ. Theory.

[16]  Paul R. Milgrom,et al.  Predation, reputation, and entry deterrence☆ , 1982 .

[17]  Andrzej Skrzypacz,et al.  Tacit collusion in repeated auctions , 2001, J. Econ. Theory.

[18]  M. Morelli,et al.  Self Enforcing Voting in International Organizations , 2003 .

[19]  O. Gossner.  The Folk Theorem for finitely repeated games with mixed strategies , 1995 .

[20]  H. Varian.  Equity, Envy and Efficiency , 1974 .

[21]  Tristan Tomala,et al.  Belief-free equilibria in games with incomplete information: the N-player case , 2007 .

[22]  Larry Samuelson,et al.  Who Wants a Good Reputation , 2001 .

[23]  David M. Kreps,et al.  Reputation and imperfect information , 1982 .

[24]  Susan Athey,et al.  Collusion and Price Rigidity , 1998 .

[25]  R. Radner.  Monitoring Cooperative Agreements in a Repeated Principal-Agent Relationship , 1981 .

[26]  Johannes Hörner,et al.  Belief-Free Equilibria in Games with Incomplete Information: Characterization and Existence , 2009, J. Econ. Theory.

[27]  H. Rosenthal,et al.  Private incentives in social dilemmas: The effects of incomplete information and altruism , 1988 .

[28]  P. Billingsley,et al.  Statistical Methods in Markov Chains , 1961 .

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

[30]  D. Bergemann,et al.  The Dynamic Pivot Mechanism , 2008 .

[31]  Marcin Peski,et al.  Repeated games with incomplete information on one side , 2008 .

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

[33]  P. Massart.  The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality , 1990 .

[34]  Jonathan Levin.  Relational Incentive Contracts , 2003 .

[35]  D. Blackwell.  An analog of the minimax theorem for vector payoffs. , 1956 .

[36]  E. Stacchetti,et al.  Towards a Theory of Discounted Repeated Games with Imperfect Monitoring , 1990 .

[37]  D. Fudenberg,et al.  Efficiency and Observability with Long-Run and Short-Run Players , 1994 .

[38]  Drew Fudenberg,et al.  The Folk Theorem for Irreducible Stochastic Games with Imperfect Public Monitoring , 2010, J. Econ. Theory.

[39]  Johannes Horner,et al.  Recursive Methods in Discounted Stochastic Games: An Algorithm for δ → 1 and a Folk Theorem , 2010 .

[40]  P. Dutta.  A Folk Theorem for Stochastic Games , 1995 .

[41]  D. Fudenberg,et al.  Digitized by the Internet Archive in 2011 with Funding from Working Paper Department of Economics the Folk Theorem with Imperfect Public Information , 2022 .

[42]  Ilya Segal,et al.  An Efficient Dynamic Mechanism , 2013 .

[43]  Joel Watson,et al.  Starting Small and Commitment , 1999, Games Econ. Behav..

[44]  R. Townsend.  Optimal Multiperiod Contracts and the Gain from Enduring Relationships under Private Information , 1982, Journal of Political Economy.

[45]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[46]  Richard P. McLean,et al.  FULL EXTRACTION OF THE SURPLUS IN BAYESIAN AND DOMINANT STRATEGY AUCTIONS , 1988 .

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

[48]  D. Fudenberg,et al.  Subgame-perfect equilibria of finite- and infinite-horizon games , 1981 .