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When Are Non-Anonymous Players Negligible?

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Author Info
Drew Fudenberg

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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 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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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1114.pdf
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1114.

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Date of creation: Jan 1995
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Handle: RePEc:nwu:cmsems:1114

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
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  2. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July. [Downloadable!] (restricted)
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  3. Wolfgang Pesendorfer & David Levine, 1992. "When are Agents Negligible?," Discussion Papers 1018, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  4. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  6. Fudenberg, Drew & Levine, David K, 1989. "Reputation and Equilibrium Selection in Games with a Patient Player," Econometrica, Econometric Society, vol. 57(4), pages 759-78, July. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
  8. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August. [Downloadable!] (restricted)
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  9. 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. [Downloadable!]
  10. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August. [Downloadable!] (restricted)
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  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. [Downloadable!]
  2. 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. [Downloadable!]
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  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. [Downloadable!]
  4. Gabriele Camera & Marco Casari, 2007. "Cooperation among strangers: an experiment with indefinite interaction," Purdue University Economics Working Papers 1201, Purdue University, Department of Economics. [Downloadable!]
  5. Marco Bassetto & Christopher Phelan, 2006. "Tax riots," Working Paper Series WP-06-04, Federal Reserve Bank of Chicago. [Downloadable!]
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