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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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    References listed on IDEAS

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    Cited by:

    1. Nicolas Klein, 2009. "Free-Riding And Delegation In Research Teams," 2009 Meeting Papers 253, Society for Economic Dynamics.
    2. Bonatti, Alessandro & Hörner, Johannes, 2017. "Learning to disagree in a game of experimentation," Journal of Economic Theory, Elsevier, vol. 169(C), pages 234-269.
    3. Ufuk Akcigit & Qingmin Liu, 2011. "The Role of Information in Competitive Experimentation," Levine's Working Paper Archive 786969000000000321, David K. Levine.
    4. Takashi Kamihigashi & John Stachurski, 2014. "Partial Stochastic Dominance," Discussion Paper Series DP2014-23, Research Institute for Economics & Business Administration, Kobe University.
    5. Amador, Manuel & Weill, Pierre-Olivier, 2012. "Learning from private and public observations of othersʼ actions," Journal of Economic Theory, Elsevier, vol. 147(3), pages 910-940.
    6. Alessandro Bonatti & Johannes Horner, 2011. "Collaborating," American Economic Review, American Economic Association, vol. 101(2), pages 632-663, April.
    7. Mike Felgenhauer & Elisabeth Schulte, 2014. "Strategic Private Experimentation," American Economic Journal: Microeconomics, American Economic Association, vol. 6(4), pages 74-105, November.
    8. Yingni Guo, 2016. "Dynamic Delegation of Experimentation," American Economic Review, American Economic Association, vol. 106(8), pages 1969-2008, August.
    9. Nicolas Klein & Sven Rady, 2011. "Negatively Correlated Bandits," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 693-732.
    10. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    11. Wang, Tao, 2017. "Information revelation through bunching," Games and Economic Behavior, Elsevier, vol. 102(C), pages 568-582.
    12. Francis Bloch & Simona Fabrizi & Steffen Lippert, 2015. "Learning and collusion in new markets with uncertain entry costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 273-303, February.
    13. Caroline D. Thomas, 2010. "Strategic Experimentation with Congestion," Department of Economics Working Papers 130813, The University of Texas at Austin, Department of Economics, revised Aug 2013.
    14. Gensbittel, Fabien & Grün, Christine, 2017. "Zero-sum stopping games with asymmetric information," TSE Working Papers 17-859, Toulouse School of Economics (TSE).
    15. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    16. Wagner, Peter A., 2018. "Who goes first? Strategic delay under information asymmetry," Theoretical Economics, Econometric Society, vol. 13(1), January.
    17. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
    18. Keller, Godfrey & Rady, Sven, 2015. "Breakdowns," Theoretical Economics, Econometric Society, vol. 10(1), January.
    19. Nicolas Vieille & E. Solan & D. Rosenberg, 2006. "Informational Externalities and Convergence of Behavior," Post-Print halshs-00120992, HAL.
    20. Rosenberg, Dinah & Solan, Eilon & Vieille, Nicolas, 2010. "On the optimal amount of experimentation in sequential decision problems," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 381-385, March.
    21. Wagner, Peter, 2015. "Who goes first? Strategic Delay and Learning by Waiting," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 500, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    22. Tao Wang, 2011. "Dynamic Equilibrium Bunching," Working Papers 1291, Queen's University, Department of Economics.
    23. Rosenberg, Dinah & Solan, Eilon & Vieille, Nicolas, 2009. "Informational externalities and emergence of consensus," Games and Economic Behavior, Elsevier, vol. 66(2), pages 979-994, July.
    24. Camargo, Braz, 2014. "Learning in society," Games and Economic Behavior, Elsevier, vol. 87(C), pages 381-396.

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