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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.

Suggested Citation

  • Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
  • Handle: RePEc:ecm:emetrp:v:75:y:2007:i:6:p:1591-1611
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2007.00807.x
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    1. Decamps, Jean-Paul & Mariotti, Thomas, 2004. "Investment timing and learning externalities," Journal of Economic Theory, Elsevier, vol. 118(1), pages 80-102, September.
    2. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 475-507.
    3. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    4. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    5. 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.
    6. Dirk Bergemann & Juuso Valimaki, 1997. "Market Diffusion with Two-Sided Learning," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 773-795, Winter.
    7. Dirk Bergemann & Juuso Välimäki, 2000. "Experimentation in Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 213-234.
    8. Martin Cripps & Godfrey Keller & Sven Rady, 2000. "Strategic Experimentation: The Case of the Poisson Bandits," Econometric Society World Congress 2000 Contributed Papers 0878, Econometric Society.
    9. Bulow, Jeremy & Klemperer, Paul, 1994. "Rational Frenzies and Crashes," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 1-23, February.
    10. 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.
    11. Caplin, Andrew & Leahy, John, 1994. "Business as Usual, Market Crashes, and Wisdom after the Fact," American Economic Review, American Economic Association, vol. 84(3), pages 548-565, June.
    12. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    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. Chamley, Christophe & Gale, Douglas, 1994. "Information Revelation and Strategic Delay in a Model of Investment," Econometrica, Econometric Society, vol. 62(5), pages 1065-1085, September.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
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