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When Are Nonanonymous Players Negligible?

In: A Long-Run Collaboration On Long-Run Games

Author

Listed:
  • Drew Fudenberg

    (Department of Economics, Harvard University, Cambridge, Massachusetts 02138, USA)

  • David Levine

    (Department of Economics, University of California, Los Angeles, Los Angeles, California 90024, USA)

  • Wolfgang Pesendorfer

    (Department of Economics, Princeton University, Princeton, New Jersey 08544-5264, USA)

Abstract

We examine games played by a single large player and a large number of opponents who are small, but not anonymous. If the play of the small players is observed with noise, and if the number of actions the large player controls is bounded as the number of small players grows, the equilibrium set converges to that of the game where there is a continuum of small players. This paper extends previous work on the negligibility of small players by dropping the assumption that small players' actions are “anonymous.” That is, we allow each small player's actions to be observed separately, instead of supposing that the small players' actions are only observed through their effect on an aggregate statistic.

Suggested Citation

  • Drew Fudenberg & David Levine & Wolfgang Pesendorfer, 2008. "When Are Nonanonymous Players Negligible?," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 6, pages 95-120, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812818478_0006
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    2. David K. Levine & Andrea Mattozzi & Salvatore Modica, 2021. "Trade Associations: Why Not Cartels?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(1), pages 47-64, February.
    3. Marco Bassetto, 2002. "A Game-Theoretic View of the Fiscal Theory of the Price Level," Econometrica, Econometric Society, vol. 70(6), pages 2167-2195, November.
    4. Gabriele Camera & Marco Casari, 2007. "Cooperation among strangers: an experiment with indefinite interaction," Purdue University Economics Working Papers 1201, Purdue University, Department of Economics.
    5. Ronen Gradwohl & Omer Reingold & Ariel Yadin & Amir Yehudayoff, 2009. "Players' Effects Under Limited Independence," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 971-980, November.
    6. Bodoh-Creed, Aaron, 2013. "Efficiency and information aggregation in large uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2436-2466.
    7. Alessandro Marchesiani, 2024. "The essentiality of money in a trading post economy with random matching," Oxford Economic Papers, Oxford University Press, vol. 76(3), pages 823-836.
    8. David K Levine & Salvatore Modica, 2013. "Peer Discipline and the Strength of Organizations," Levine's Bibliography 786969000000000713, UCLA Department of Economics.
    9. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2000. "Pivotal Players and the Characterization of Influence," Journal of Economic Theory, Elsevier, vol. 92(2), pages 318-342, June.
    10. Aaron Bodoh-Creed & Brent Hickman, 2016. "College Assignment as a Large Contest," Working Papers 2016-27, Becker Friedman Institute for Research In Economics.
    11. Eric J. Friedman* & Paul Resnick, 2001. "The Social Cost of Cheap Pseudonyms," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 10(2), pages 173-199, June.
    12. Bodoh-Creed, Aaron L. & Hickman, Brent R., 2018. "College assignment as a large contest," Journal of Economic Theory, Elsevier, vol. 175(C), pages 88-126.
    13. David K. Levine, 2021. "Fine cartels," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 155-166, October.
    14. Nabil I. Al-Najjar & Rann Smorodinsky, 1998. "Large Non-Anonymous Repeated Games," Discussion Papers 1250, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Rohan Dutta & David K Levine & Salvatore Modica, 2018. "Interventions when Social Norms are Endogenous: A Critique," Levine's Bibliography 786969000000001479, UCLA Department of Economics.
    16. Kalai, Ehud & Shmaya, Eran, 2018. "Large strategic dynamic interactions," Journal of Economic Theory, Elsevier, vol. 178(C), pages 59-81.
    17. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Markov Perfect Industry Dynamics with Many Firms," Research Papers 1919r, Stanford University, Graduate School of Business.
    18. Marco Bassetto & Christopher Phelan, 2008. "Tax Riots," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 649-669.
    19. Alessandro Marchesiani, 2022. "The Essentiality of Money in a Trading Post Economy with Random Matching," Working Papers 202223, University of Liverpool, Department of Economics.
    20. D. Aliprantis, C. & Camera, G. & Puzzello, D., 2007. "Anonymous markets and monetary trading," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1905-1928, October.
    21. Smorodinsky, Rann & Tennenholtz, Moshe, 2006. "Overcoming free riding in multi-party computations--The anonymous case," Games and Economic Behavior, Elsevier, vol. 55(2), pages 385-406, May.
    22. Iijima, Ryota & Oyama, Daisuke, 2025. "Mean-field approximation of forward-looking population dynamics," Journal of Economic Theory, Elsevier, vol. 230(C).
    23. Rohan Dutta & David K. Levine & Salvatore Modica, 2021. "The whip and the Bible: Punishment versus internalization," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(5), pages 858-894, October.
    24. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2007. "The efficiency of competitive mechanisms under private information," Journal of Economic Theory, Elsevier, vol. 137(1), pages 383-403, November.
    25. Drew Fudenberg & David K Levine, 2016. "Whither Game Theory?," Levine's Working Paper Archive 786969000000001307, David K. Levine.

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    • I10 - Health, Education, and Welfare - - Health - - - General

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