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Negatively Correlated Bandits

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  • Nicolas Klein
  • Sven Rady

Abstract

We analyse a two-player game of strategic experimentation with two-armed bandits. Either player has to decide in continuous time whether to use a safe arm with a known pay-off or a risky arm whose expected pay-off per unit of time is initially unknown. This pay-off can be high or low and is negatively correlated across players. We characterize the set of all Markov perfect equilibria in the benchmark case where the risky arms are known to be of opposite type and construct equilibria in cut-off strategies for arbitrary negative correlation. All strategies and pay-offs are in closed form. In marked contrast to the case where both risky arms are of the same type, there always exists an equilibrium in cut-off strategies, and there always exists an equilibrium exhibiting efficient long-run patterns of learning. These results extend to a three-player game with common knowledge that exactly one risky arm is of the high pay-off type. Copyright 2011, Oxford University Press.

Suggested Citation

  • Nicolas Klein & Sven Rady, 2011. "Negatively Correlated Bandits," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 693-732.
  • Handle: RePEc:oup:restud:v:78:y:2011:i:2:p:693-732
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    File URL: http://hdl.handle.net/10.1093/restud/rdq025
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    References listed on IDEAS

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    1. 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.
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    5. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    6. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
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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. Alessandro Bonatti & Johannes Horner, 2011. "Collaborating," American Economic Review, American Economic Association, vol. 101(2), pages 632-663, April.
    3. Ufuk Akcigit & Qingmin Liu, 2011. "The Role of Information in Competitive Experimentation," Levine's Working Paper Archive 786969000000000321, David K. Levine.
    4. Keller, Godfrey & Rady, Sven, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    5. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics, revised May 2014.
    6. Nicolas Klein & Tymofiy Mylovanov, 2011. "Should the Flatterers be Avoided?," 2011 Meeting Papers 1273, Society for Economic Dynamics.
    7. Anders Bredahl Kock & Martin Thyrsgaard, 2017. "Optimal sequential treatment allocation," Papers 1705.09952, arXiv.org, revised Jan 2018.
    8. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    9. Kaustav Das, 2013. "Strategic Experimentation with Heterogeneous Agents and Payoff Externalities," Discussion Papers 1315, Exeter University, Department of Economics.
    10. Yingni Guo, 2016. "Dynamic Delegation of Experimentation," American Economic Review, American Economic Association, vol. 106(8), pages 1969-2008, August.
    11. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
    12. Caroline D Thomas, 2010. "Strategic Experimentation with Congestion," Department of Economics Working Papers 130907, The University of Texas at Austin, Department of Economics, revised 04 Nov 2014.
    13. repec:eee:jcecon:v:45:y:2017:i:4:p:685-711 is not listed on IDEAS
    14. Besanko, David & Tong, Jian & Wu, Jianjun, 2016. "Subsidizing research programs with "if" and "when" uncertainty in the face of severe informational constraints," Discussion Paper Series In Economics And Econometrics 1605, Economics Division, School of Social Sciences, University of Southampton.
    15. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, Exeter University, Department of Economics.
    16. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    17. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    18. Sofia Moroni, 2016. "Experimentation in Organizations," Working Paper 5876, Department of Economics, University of Pittsburgh.
    19. Alós-Ferrer, Carlos & Kern, Johannes, 2015. "Repeated games in continuous time as extensive form games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 34-57.
    20. Mira Frick & Yuhta Ishii, 2015. "Innovation Adoption by Forward-Looking Social Learners," Cowles Foundation Discussion Papers 1877, Cowles Foundation for Research in Economics, Yale University.
    21. Cripps, Martin W., 2013. "Optimal learning of a set: Or how to edit a journal if you must," Economics Letters, Elsevier, vol. 120(3), pages 384-388.
    22. Roland G. Fryer, Jr. & Philipp Harms, 2013. "Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability," NBER Working Papers 19043, National Bureau of Economic Research, Inc.
    23. Külpmann, Philipp, 2015. "Procrastination and projects," Center for Mathematical Economics Working Papers 544, Center for Mathematical Economics, Bielefeld University.
    24. Alejandro Francetich, 2014. "Managing Multiple Research Projects," Working Papers 516, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

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