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When are Agents Negligible?

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  • Wolfgang Pesendorfer
  • David Levine

Abstract

We examine the following paradox: In a dynamic setting, an arbitrarily large finite number of agents adn a continuum of agents can lead to radically different equilibrium outcomes. We show that in a simple strategic setting this paradox is a general phenomenon. We also show that the paradox disappears when there is noisy observation of the players' actions: The aggregate level of noise must disappear as the number of players increases, but not too rapidly. We give several economic examples in which this paradox has recently received attention: the durable goods monopoly, corporate takeovers, and time consistency of optimal governmetn policy.

Suggested Citation

  • Wolfgang Pesendorfer & David Levine, 1992. "When are Agents Negligible?," Discussion Papers 1018, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1018
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    References listed on IDEAS

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    1. Bagwell, Kyle, 1995. "Commitment and observability in games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 271-280.
    2. Bagnoli, Mark & Salant, Stephen W & Swierzbinski, Joseph E, 1989. "Durable-Goods Monopoly with Discrete Demand," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1459-1478, December.
    3. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
    4. Chari, V V & Kehoe, Patrick J, 1990. "Sustainable Plans," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 783-802, August.
    5. Nabil Al-Najjar, 1992. "The Coase Conjecture in Markets with a Finite Number of Consumers," Cahiers de recherche du Département des sciences économiques, UQAM 9211, Université du Québec à Montréal, Département des sciences économiques.
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    Cited by:

    1. Ilya Segal, 1998. "Contracting with Externalities," Public Economics 9802002, EconWPA.
    2. Gabriele Camera & Marco Casari, 2009. "Cooperation among Strangers under the Shadow of the Future," American Economic Review, American Economic Association, vol. 99(3), pages 979-1005, June.
    3. 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.
    4. Frederico Finan & Laura Schechter, 2012. "Vote‐Buying and Reciprocity," Econometrica, Econometric Society, vol. 80(2), pages 863-881, March.
    5. Barlo, Mehmet & Carmona, Guilherme, 2015. "Strategic behavior in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 134-144.
    6. Drew Fudenberg & David Levine & Wolfgang Pesendorfer, 2008. "When Are Nonanonymous Players Negligible?," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 6, pages 95-120 World Scientific Publishing Co. Pte. Ltd..
    7. Giancarlo Corsetti & Amil Dasgupta & Stephen Morris & Hyun Song Shin, 2004. "Does One Soros Make a Difference? A Theory of Currency Crises with Large and Small Traders," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 87-113.
    8. Cellini, Roberto & Lambertini, Luca, 2007. "Time consistent fiscal policies in a Ramsey economy," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 296-313, May.
    9. Robert Zeithammer, 2009. "Commitment in sequential auctioning: advance listings and threshold prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 187-216, January.
    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.
    11. Marco Bassetto & Christopher Phelan, 2008. "Tax Riots," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 649-669.
    12. Gabriele Camera & Marco Casari, 2007. "Cooperation among strangers: an experiment with indefinite interaction," Purdue University Economics Working Papers 1201, Purdue University, Department of Economics.
    13. R. Preston Mcafee & Thomas Wiseman, 2008. "Capacity Choice Counters the Coase Conjecture," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 317-331.
    14. Karatzas, Ioannis & Shubik, Martin & Sudderth, William D., 1997. "A strategic market game with secured lending," Journal of Mathematical Economics, Elsevier, vol. 28(2), pages 207-247, September.
    15. Oliver Hart & John Moore, 1998. "Cooperatives vs. Outside Ownership," NBER Working Papers 6421, National Bureau of Economic Research, Inc.
    16. Hamilton, Jonathan & Slutsky, Steven, 2017. "Judicial review and the power of the executive and legislative branches," Research in Economics, Elsevier, vol. 71(1), pages 67-85.
    17. Bilancini, Ennio & Boncinelli, Leonardo, 2016. "Dynamic adverse selection and the supply size," European Economic Review, Elsevier, vol. 83(C), pages 233-242.
    18. Michael Waldman, 2004. "Antitrust Perspectives for Durable-Goods Markets," CESifo Working Paper Series 1306, CESifo Group Munich.
    19. Hamid Sabourian, 2000. "Bargaining and Markets: Complexity and the Walrasian Outcome," Cowles Foundation Discussion Papers 1249, Cowles Foundation for Research in Economics, Yale University.
    20. D. Aliprantis, C. & Camera, G. & Puzzello, D., 2007. "Anonymous markets and monetary trading," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1905-1928, October.
    21. Hamilton, Jonathan & Slutsky, Steven, 2004. "Nonlinear price discrimination with a finite number of consumers and constrained recontracting," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 737-757, June.
    22. Robert Zeithammer, 2007. "—Optimal Selling in Dynamic Auctions: Adaptation Versus Commitment," Marketing Science, INFORMS, vol. 26(6), pages 859-867, 11-12.
    23. Araujo, Luis & Camargo, Braz & Minetti, Raoul & Puzzello, Daniela, 2012. "The essentiality of money in environments with centralized trade," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 612-621.

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