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The dynamic cost of ex post incentive compatibility in repeated games of private information

Author

Listed:
  • David A. Miller

    (UCSD)

Abstract
In a repeated game with private information, a perfect public equilibrium (PPE) can break down if communication is not necessarily simultaneous or if players can “spy” on each others’ information. An ex post perfect public equilibrium (EPPPE) is a PPE that is ex post incentive compatible in each stage game; unlike PPE, EPPPE is robust under to any communication protocol, and to spying. However, robustness comes at a cost to the players: in many games, efficient payoffs in the corresponding static mechanism design problem cannot be supported as average payoffs in an EPPPE, even when players are patient. In two- player repeated allocation games, an optimal EPPPE never employs a (static) efficient outcome function in any stage game. Instead, the players always prefer to give up some static efficiency by sometimes allocating to the player with the lower valuation. Under independent valuations, optimal equilibria are often stationary, but when valuations are globally interdependent, optimal equilibria are never stationary. Applied to the problem of collusion with hidden costs, these results yield new insights into the phenomenon of price wars in collusive equilibria.

Suggested Citation

  • David A. Miller, 2005. "The dynamic cost of ex post incentive compatibility in repeated games of private information," Game Theory and Information 0510002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0510002
    Note: Type of Document - pdf; pages: 55
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0510/0510002.pdf
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    References listed on IDEAS

    as
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    Cited by:

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    2. Rohit Lamba, 2022. "Efficiency with(out) intermediation in repeated bilateral trade," Papers 2202.04201, arXiv.org.
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    4. Moritz Drexl & Andreas Kleiner, 2018. "Why Voting? A Welfare Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 253-271, August.
    5. Chan, Jimmy & Zhang, Wenzhang, 2015. "Collusion enforcement with private information and private monitoring," Journal of Economic Theory, Elsevier, vol. 157(C), pages 188-211.
    6. Andreas Blume & April Mitchell Franco & Paul Heidhues, 2021. "Dynamic coordination via organizational routines," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1001-1047, November.
    7. Lin William Cong & Zhiguo He, 2019. "Blockchain Disruption and Smart Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 32(5), pages 1754-1797.
    8. Susan Athey & Ilya Segal, 2013. "An Efficient Dynamic Mechanism," Econometrica, Econometric Society, vol. 81(6), pages 2463-2485, November.
    9. Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December.
    10. Martin, Alberto & Vergote, Wouter, 2008. "On the role of retaliation in trade agreements," Journal of International Economics, Elsevier, vol. 76(1), pages 61-77, September.
    11. Yuichi Yamamoto, 2012. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 12-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Shao, Ran & Zhou, Lin, 2016. "Optimal allocation of an indivisible good," Games and Economic Behavior, Elsevier, vol. 100(C), pages 95-112.
    13. Andrzej Skrzypacz & Juuso Toikka, 2015. "Mechanisms for Repeated Trade," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 252-293, November.
    14. Vinicius Carrasco & Gustavo Manso, 2006. "Syndication and Robust Collusion in Financial Markets," Textos para discussão 522, Department of Economics PUC-Rio (Brazil).
    15. Drexl, Moritz & Kleiner, Andreas, 2015. "Optimal private good allocation: The case for a balanced budget," Games and Economic Behavior, Elsevier, vol. 94(C), pages 169-181.
    16. Joao Correia-da-Silva, 2013. "Impossibility of market division with two-sided private information about production costs," FEP Working Papers 490, Universidade do Porto, Faculdade de Economia do Porto.
    17. Palsule-Desai, Omkar D., 2021. "Multi-product supply networks: Implications of intermediaries," European Journal of Operational Research, Elsevier, vol. 292(3), pages 909-929.
    18. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    19. Takuo Sugaya & Yuichi Yamamoto, 2019. "Common Learning and Cooperation in Repeated Games," PIER Working Paper Archive 19-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    20. Leo, Greg, 2017. "Taking turns," Games and Economic Behavior, Elsevier, vol. 102(C), pages 525-547.
    21. Martin, Alberto & Vergote, Wouter, 2004. "Antidumping: Welfare Enhancing Retaliation?," MPRA Paper 5416, University Library of Munich, Germany.

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    More about this item

    Keywords

    repeated games; private information; ex post incentive compatibility; price wars;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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