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When are Non-Anonymous Players Negligible

Author

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  • Drew Fudenberg
  • David K. Levine
  • Wolfgang Pesendorfer

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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Suggested Citation

  • Drew Fudenberg & David K. Levine & Wolfgang Pesendorfer, 1996. "When are Non-Anonymous Players Negligible," Levine's Working Paper Archive 180, David K. Levine.
  • Handle: RePEc:cla:levarc:180
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    References listed on IDEAS

    as
    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.
    2. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
    3. Levine, David K & Pesendorfer, Wolfgang, 1995. "When Are Agents Negligible?," American Economic Review, American Economic Association, vol. 85(5), pages 1160-1170, December.
    4. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-351, March.
    5. 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..
    6. 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.
    7. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    8. repec:wsi:wschap:9789812818478_0003 is not listed on IDEAS
    9. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April.
    10. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    11. 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.
    12. 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.
    13. 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..
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    Citations

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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. David K Levine & Andrea Mattozzi & Salvatore Modica, 2018. "Trade Associations: Why Not Cartels?," Levine's Working Paper Archive 786969000000001489, David K. Levine.
    3. Rohan Dutta & David K Levine & Salvatore Modica, 2018. "Interventions when Social Norms are Endogenous: A Critique," Levine's Bibliography 786969000000001479, UCLA Department of Economics.
    4. 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.
    5. 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.
    6. Marco Bassetto & Christopher Phelan, 2008. "Tax Riots," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 649-669.
    7. Gabriele Camera & Marco Casari, 2007. "Cooperation among strangers: an experiment with indefinite interaction," Purdue University Economics Working Papers 1201, Purdue University, Department of Economics.
    8. 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.
    9. Bodoh-Creed, Aaron, 2013. "Efficiency and information aggregation in large uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2436-2466.
    10. 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.
    11. David K Levine & Salvatore Modica, 2013. "Peer Discipline and the Strength of Organizations," Levine's Bibliography 786969000000000713, UCLA Department of Economics.
    12. 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.
    13. 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.
    14. Aaron Bodoh-Creed & Brent Hickman, 2016. "College Assignment as a Large Contest," Working Papers 2016-27, Becker Friedman Institute for Research In Economics.
    15. 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.
    16. repec:eee:jetheo:v:175:y:2018:i:c:p:88-126 is not listed on IDEAS

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    JEL classification:

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

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