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Social Learning in One-Arm Bandit Problems

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  • Dinah Rosenberg
  • Eilon Solan
  • Nicolas Vieille

Abstract

We study a two-player one-arm bandit problem in discrete time, in which the risky arm can have two possible types, high and low, the decision to stop experimenting is irreversible, and players observe each other's actions but not each other's payoffs. We prove that all equilibria are in cutoff strategies and provide several qualitative results on the sequence of cutoffs. Copyright The Econometric Society 2007.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1396.

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Date of creation: Dec 2004
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Handle: RePEc:nwu:cmsems:1396

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
  2. Dirk Bergemann & Juuso Valimaki, 1999. "Experimentation in Markets," Cowles Foundation Discussion Papers 1214, Cowles Foundation for Research in Economics, Yale University.
  3. Cripps, Martin William & Keller, Godfrey & Rady, Sven, 2003. "Strategic Experimentation with Exponential Bandits," CEPR Discussion Papers 3814, C.E.P.R. Discussion Papers.
  4. Caplin, A. & Leahy, J., 1992. "Business as Usual, Market Crashes, and Wisdom after the Fact," Harvard Institute of Economic Research Working Papers 1594, Harvard - Institute of Economic Research.
  5. Chamley, Christophe & Gale, Douglas, 1994. "Information Revelation and Strategic Delay in a Model of Investment," Econometrica, Econometric Society, vol. 62(5), pages 1065-85, September.
  6. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
  7. Dirk Bergemann & Juuso Valimaki, 1996. "Market Diffusion with Two-Sided Learning," Cowles Foundation Discussion Papers 1138, Cowles Foundation for Research in Economics, Yale University.
  8. Keller, Godfrey & Rady, Sven, 1999. "Optimal Experimentation in a Changing Environment," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 475-507, July.
  9. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  10. Jeremy Bulow & Paul Klemperer, 1991. "Rational Frenzies and Crashes," NBER Technical Working Papers 0112, National Bureau of Economic Research, Inc.
  11. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  12. Chamley, Christophe, 2004. "Delays and equilibria with large and small information in social learning," European Economic Review, Elsevier, vol. 48(3), pages 477-501, June.
  13. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers 1489, Cowles Foundation for Research in Economics, Yale University.
  14. Martin W. Cripps & Godfrey Keller & Sven Rady, 2002. "Strategic Experimentation: The Case of Poisson Bandits," CESifo Working Paper Series 737, CESifo Group Munich.
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