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When Are Nonanonymous Players Negligible?

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  • Pesendorfer, Wolfgang
  • Levine, David
  • Fudenberg, Drew

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.

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  • Pesendorfer, Wolfgang & Levine, David & Fudenberg, Drew, 1998. "When Are Nonanonymous Players Negligible?," Scholarly Articles 3203775, Harvard University Department of Economics.
  • Handle: RePEc:hrv:faseco:3203775
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    References listed on IDEAS

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    1. Dubey, Pradeep & Kaneko, Mamoru, 1985. "Information patterns and Nash equilibria in extensive games -- II," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 247-262, December.
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    3. repec:wsi:wschap:9789812818478_0007 is not listed on IDEAS
    4. Drew Fudenberg & David K. Levine, 1988. "Open and Closed-Loop Equilibria in Dynamic Games With Many Players," Levine's Working Paper Archive 221, David K. Levine.
    5. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
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    7. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April.
    8. Drew Fudenberg & David K. Levine, 2008. "Open-Loop and Closed-Loop Equilibria in Dynamic Games with Many Players," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 3, pages 41-58 World Scientific Publishing Co. Pte. Ltd..
    9. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    10. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    11. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142 World Scientific Publishing Co. Pte. Ltd..
    12. Sabourian, Hamid, 1990. "Anonymous repeated games with a large number of players and random outcomes," Journal of Economic Theory, Elsevier, vol. 51(1), pages 92-110, June.
    13. Celentani, Marco, 1996. "Reputation with Observed Actions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 407-419, April.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Marco Bassetto & Christopher Phelan, 2008. "Tax Riots," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 649-669.
    5. Gabriele Camera & Marco Casari, 2007. "Cooperation among strangers: an experiment with indefinite interaction," Purdue University Economics Working Papers 1201, Purdue University, Department of Economics.
    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. 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.
    8. David K Levine & Salvatore Modica, 2013. "Peer Discipline and the Strength of Organizations," Levine's Bibliography 786969000000000713, UCLA Department of Economics.
    9. 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.
    10. 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.
    11. Aaron Bodoh-Creed & Brent Hickman, 2016. "College Assignment as a Large Contest," Working Papers 2016-27, Becker Friedman Institute for Research In Economics.
    12. 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.

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

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