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Efficiency in Games with Markovian Private Information

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  • Juan F. Escobar
  • Juuso Toikka

Abstract

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.

Suggested Citation

  • Juan F. Escobar & Juuso Toikka, 2012. "Efficiency in Games with Markovian Private Information," Documentos de Trabajo 289, Centro de Economía Aplicada, Universidad de Chile.
  • Handle: RePEc:edj:ceauch:289
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    References listed on IDEAS

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    1. Eduardo Engel & Ronald Fischer & Alexander Galetovic & Manuel Hermosilla, 2009. "Renegociación de concesiones en Chile," Documentos de Trabajo 262, Centro de Economía Aplicada, Universidad de Chile.
    2. Francisco Henríquez & Alejandra Mizala & Andrea Repetto, 2009. "Effective Schools for Low Income Children: a Study of Chile’s Sociedad de Instrucción Primaria," Documentos de Trabajo 258, Centro de Economía Aplicada, Universidad de Chile.
    3. Alejandra Mizala & Pilar Romaguera & Sebastian Gallegos, 2010. "Public-Private Wage Gap In Latin America (1999-2007): A Matching Approach," Documentos de Trabajo 268, Centro de Economía Aplicada, Universidad de Chile.
    4. Bernardo Lara & Alejandra Mizala & Andrea Repetto, 2009. "The Effectiveness of Private Voucher Education: Evidence from Structural School Switches," Documentos de Trabajo 263, Centro de Economía Aplicada, Universidad de Chile.
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    Cited by:

    1. Yu Awaya & Vijay Krishna, 2016. "On Communication and Collusion," American Economic Review, American Economic Association, vol. 106(2), pages 285-315, February.
    2. Romans Pancs, 2015. "Efficient dark markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(3), pages 605-624, August.
    3. Aristotelis Boukouras & Kostas Koufopoulos, 2017. "Efficient allocations in economies with asymmetric information when the realized frequency of types is common knowledge," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 75-98, June.
    4. Daniel Monte & Ideen Riahi & Nikolaus Robalino, 2019. "Collusion and turnover in experience goods markets," Review of Economic Design, Springer;Society for Economic Design, vol. 23(3), pages 91-111, December.
    5. Pablo Hernandez-Lagos & Dylan Minor & Dana Sisak, 2017. "Do people who care about others cooperate more? Experimental evidence from relative incentive pay," Experimental Economics, Springer;Economic Science Association, vol. 20(4), pages 809-835, December.
    6. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    7. Andrzej Skrzypacz & Juuso Toikka, 2015. "Mechanisms for Repeated Trade," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 252-293, November.
    8. Renou, Ludovic & Tomala, Tristan, 2015. "Approximate implementation in Markovian environments," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 401-442.
    9. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    10. Margaria, Chiara & Smolin, Alex, 2018. "Dynamic communication with biased senders," Games and Economic Behavior, Elsevier, vol. 110(C), pages 330-339.
    11. Aristotelis Boukouras & Kostas Koufopoulos, 2015. "Efficient Allocations in Economies with Asymmetric Information when the Realized Frequency of Types is Common Knowledge," Discussion Papers in Economics 15/04, Division of Economics, School of Business, University of Leicester.
    12. Escobar, Juan F. & Llanes, Gastón, 2018. "Cooperation dynamics in repeated games of adverse selection," Journal of Economic Theory, Elsevier, vol. 176(C), pages 408-443.
    13. Chan, Jimmy & Zhang, Wenzhang, 2015. "Collusion enforcement with private information and private monitoring," Journal of Economic Theory, Elsevier, vol. 157(C), pages 188-211.
    14. Suehyun Kwon, 2019. "Informed-Principal Problem in Mechanisms with Limited Commitment," CESifo Working Paper Series 7513, CESifo.
    15. Renault, Jérôme & Solan, Eilon & Vieille, Nicolas, 2017. "Optimal dynamic information provision," Games and Economic Behavior, Elsevier, vol. 104(C), pages 329-349.
    16. Fudenberg, Drew & Ishii, Yuhta & Kominers, Scott Duke, 2014. "Delayed-response strategies in repeated games with observation lags," Journal of Economic Theory, Elsevier, vol. 150(C), pages 487-514.
    17. James Best & Daniel Quigley, 2016. "Persuasion for the Long-Run," Economics Papers 2016-W12, Economics Group, Nuffield College, University of Oxford.
    18. Frankel, Alexander, 2016. "Discounted quotas," Journal of Economic Theory, Elsevier, vol. 166(C), pages 396-444.
    19. Suehyun Kwon, 2016. "Relational contracts in a persistent environment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 183-205, January.

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