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When are Non-Anonymous Players Negligible

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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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Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 180.

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Date of creation: 07 Dec 1996
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Handle: RePEc:cla:levarc:180

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Web page: http://www.dklevine.com/

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References

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  1. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
  2. Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Schmidt, Klaus M., 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Munich Reprints in Economics 3395, University of Munich, Department of Economics.
  4. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  5. 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.
  6. Drew Fudenberg & David K. Levine, 1995. "Reputation and Equilibrium Selection in Games with a Patient Player," Levine's Working Paper Archive 103, David K. Levine.
  7. David K. Levine & Wolfgang Pesendorfer, 1995. "When Are Agents Negligible?," Levine's Working Paper Archive 96, David K. Levine.
  8. 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.
  9. 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.
  10. Celentani, Marco, 1996. "Reputation with Observed Actions," Economic Theory, Springer, vol. 7(3), pages 407-19, April.
  11. 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.
  12. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April.
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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 & Salvatore Modica, 2013. "Peer Discipline and the Strength of Organizations," Levine's Bibliography 786969000000000713, UCLA Department of Economics.
  3. 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.
  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. 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.
  6. Christopher Phelan & Marco Bassetto, 2005. "Tax Riots," 2005 Meeting Papers 433, Society for Economic Dynamics.
  7. Aliprantis, C.D. & Camera, Gabriele & Puzzello, D., 2005. "Anonymous Markets and Monetary Trading," Purdue University Economics Working Papers 1179, Purdue University, Department of Economics.
  8. Gabriele Camera & Marco Casari, 2007. "Cooperation among strangers: an experiment with indefinite interaction," Purdue University Economics Working Papers 1201, Purdue University, Department of Economics.
  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. 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.

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