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Robust perfect equilibrium in large games

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  • Chen, Enxian
  • Qiao, Lei
  • Sun, Xiang
  • Sun, Yeneng

Abstract

This paper proposes a new equilibrium concept “robust perfect equilibrium” for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed strategies and also in pure strategies) and satisfy the important properties of admissibility, aggregate robustness, and ex post robust perfection. These properties strengthen relevant equilibrium results in an extensive literature on strategic interactions among a large number of agents. Illustrative applications to congestion games are presented. In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique symmetric robust perfect equilibrium.

Suggested Citation

  • Chen, Enxian & Qiao, Lei & Sun, Xiang & Sun, Yeneng, 2022. "Robust perfect equilibrium in large games," Journal of Economic Theory, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:jetheo:v:201:y:2022:i:c:s0022053122000230
    DOI: 10.1016/j.jet.2022.105433
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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. , & , P., 2014. "Refinements of Nash equilibrium in potential games," Theoretical Economics, Econometric Society, vol. 9(3), September.
    3. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    4. , & , P. & , & ,, 2015. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society, vol. 10(1), January.
    5. Darrell Duffie, 2012. "Over-The-Counter Markets," Introductory Chapters, in: Dark Markets: Asset Pricing and Information Transmission in Over-the-Counter Markets, Princeton University Press.
    6. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    7. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    8. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2007. "Dynamic Global Games of Regime Change: Learning, Multiplicity, and the Timing of Attacks," Econometrica, Econometric Society, vol. 75(3), pages 711-756, May.
    10. Michael Peters, 2010. "Noncontractible Heterogeneity in Directed Search," Econometrica, Econometric Society, vol. 78(4), pages 1173-1200, July.
    11. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
    12. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    13. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    14. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
    15. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    16. Carmona, Guilherme & Podczeck, Konrad, 2014. "Existence of Nash equilibrium in games with a measure space of players and discontinuous payoff functions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 130-178.
    17. Rath Kali P., 1994. "Some Refinements of Nash Equilibria of Large Games," Games and Economic Behavior, Elsevier, vol. 7(1), pages 92-103, July.
    18. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    19. F. H. Knight, 1924. "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(4), pages 582-606.
    20. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
    21. Igal Milchtaich, 2000. "Generic Uniqueness of Equilibrium in Large Crowding Games," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 349-364, August.
    22. Daron Acemoglu & Martin Kaae Jensen, 2015. "Robust Comparative Statics in Large Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 587-640.
    23. DavidP. Myatt & Chris Wallace, 2009. "Evolution, Teamwork and Collective Action: Production Targets in the Private Provision of Public Goods," Economic Journal, Royal Economic Society, vol. 119(534), pages 61-90, January.
    24. Kalai, Ehud & Shmaya, Eran, 2018. "Large strategic dynamic interactions," Journal of Economic Theory, Elsevier, vol. 178(C), pages 59-81.
    25. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
    26. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    27. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
    28. Armstrong, Mark & Vickers, John, 2001. "Competitive Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 579-605, Winter.
    29. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    30. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    31. Sun, Xiang & Zeng, Yishu, 2020. "Perfect and proper equilibria in large games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 288-308.
    32. Roger B. Myerson & Philip J. Reny, 2020. "Perfect Conditional ε‐Equilibria of Multi‐Stage Games With Infinite Sets of Signals and Actions," Econometrica, Econometric Society, vol. 88(2), pages 495-531, March.
    33. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    34. Rath, Kali P., 1998. "Perfect and Proper Equilibria of Large Games," Games and Economic Behavior, Elsevier, vol. 22(2), pages 331-342, February.
    35. Nicholas Yannelis, 2009. "Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 419-432, February.
    36. Cole, Harold L & Mailath, George J & Postlewaite, Andrew, 1992. "Social Norms, Savings Behavior, and Growth," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1092-1125, December.
    37. Carmona, Guilherme & Podczeck, Konrad, 2020. "Pure strategy Nash equilibria of large finite-player games and their relationship to non-atomic games," Journal of Economic Theory, Elsevier, vol. 187(C).
    38. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    39. Daron Acemoglu & Asuman Ozdaglar, 2007. "Competition and Efficiency in Congested Markets," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 1-31, February.
    40. Roughgarden, Tim & Tardos, Eva, 2004. "Bounding the inefficiency of equilibria in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 389-403, May.
    41. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    42. Riccardo Colini-Baldeschi & Roberto Cominetti & Panayotis Mertikopoulos & Marco Scarsini, 2020. "When Is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic," Operations Research, INFORMS, vol. 68(2), pages 411-434, March.
    43. Wei He & Nicholas C. Yannelis, 2016. "Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 497-513, March.
    44. Milchtaich, Igal, 2004. "Social optimality and cooperation in nonatomic congestion games," Journal of Economic Theory, Elsevier, vol. 114(1), pages 56-87, January.
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    More about this item

    Keywords

    Robust perfect equilibrium; Admissibility; Aggregate robustness; Ex post robust perfection; Large games; Congestion games;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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