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When Are Nonanonymous Players Negligible?

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Author Info

  • 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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Bibliographic Info

Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3203775.

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Date of creation: 1998
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Publication status: Published in Journal of Economic Theory
Handle: RePEc:hrv:faseco:3203775

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References

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  1. Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. 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.
  3. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-51, March.
  4. Dubey, Pradeep & Kaneko, Mamoru, 1984. "Information patterns and Nash equilibria in extensive games: 1," Mathematical Social Sciences, Elsevier, vol. 8(2), pages 111-139, October.
  5. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April.
  6. D. Fudenberg & David K. Levine, 1989. "Reputation and Equilibrium Selection in Games with a Patient Player," Levine's Working Paper Archive 508, David K. Levine.
  7. David K. Levine & Wolfgang Pesendorfer, 1995. "When Are Agents Negligible?," Levine's Working Paper Archive 96, David K. Levine.
  8. 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.
  9. Marco Celentani & Wolfgang Pesendorfer, 1992. "Reputation in Dynamic Games," Discussion Papers 1009, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. David Kreps & Robert Wilson, 1999. "Reputation and Imperfect Information," Levine's Working Paper Archive 238, David K. Levine.
  11. Marco Celentani, 1996. "Reputation with observed actions (*)," Economic Theory, Springer, vol. 7(3), pages 407-419.
  12. Fudenberg, Drew & Levine, David K., 1988. "Open-loop and closed-loop equilibria in dynamic games with many players," Journal of Economic Theory, Elsevier, vol. 44(1), pages 1-18, February.
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Citations

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Cited by:
  1. David K Levine & Salvatore Modica, 2013. "Peer Discipline and the Strength of Organizations," Levine's Bibliography 786969000000000713, UCLA Department of Economics.
  2. Aliprantis, C.D. & Camera, Gabriele & Puzzello, D., 2005. "Anonymous Markets and Monetary Trading," Purdue University Economics Working Papers 1179, Purdue University, Department of Economics.
  3. Marco Bassetto & Christopher Phelan, 2006. "Tax riots," Working Paper Series WP-06-04, Federal Reserve Bank of Chicago.
  4. 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.
  5. Bodoh-Creed, Aaron, 2013. "Efficiency and information aggregation in large uniform-price auctions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2436-2466.
  6. Marco Bassetto, 2000. "A Game-Theoretic View of the Fiscal Theory of the Price Level," Econometric Society World Congress 2000 Contributed Papers 1492, Econometric Society.
  7. 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.
  8. 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.
  9. 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.
  10. Gabriele Camera & Marco Casari, 2007. "Cooperation among strangers: an experiment with indefinite interaction," Purdue University Economics Working Papers 1201, Purdue University, Department of Economics.

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