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When Are Nonanonymous Players Negligible?

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

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 independently of the number of small players, then as the number of small players grows, the equilibrium set converges to that of the game where there is a continuum of small players. The 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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 79 (1998)
Issue (Month): 1 (March)
Pages: 46-71

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Handle: RePEc:eee:jetheo:v:79:y:1998:i:1:p:46-71
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. 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.
  2. David K. Levine & Wolfgang Pesendorfer, 1995. "When Are Agents Negligible?," Levine's Working Paper Archive 96, David K. Levine.
  3. 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.
  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. Marco Celentani, 1996. "Reputation with observed actions (*)," Economic Theory, Springer, vol. 7(3), pages 407-419.
  6. Paul Milgrom & John Roberts, 1997. "Predation, reputation , and entry deterrence," Levine's Working Paper Archive 1460, David K. Levine.
  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. 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.
  9. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  10. Marco Celentani & Wolfgang Pesendorfer, 1992. "Reputation in Dynamic Games," Discussion Papers 1009, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Schmidt, K.M., 1992. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Working papers 92-7, Massachusetts Institute of Technology (MIT), Department of Economics.
  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.
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