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When Are Non-Anonymous Players Negligible?

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  • Drew Fudenberg

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.

Suggested Citation

  • Drew Fudenberg, 1995. "When Are Non-Anonymous Players Negligible?," Discussion Papers 1114, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1114
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    References listed on IDEAS

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    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.
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    7. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
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    12. Drew Fudenberg & David K. Levine, 2008. "Open-Loop and Closed-Loop Equilibria in Dynamic Games with Many Players," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 3, pages 41-58, World Scientific Publishing Co. Pte. Ltd..
    13. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-351, March.
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