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Negatively Correlated Bandits

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  • Klein, Nicolas
  • Rady, Sven

Abstract

We analyze a two-player game of strategic experimentation with two-armed bandits. Each player has to decide in continuous time whether to use a safe arm with a known payoff or a risky arm whose likelihood of delivering payoffs is initially unknown. The quality of the risky arms is perfectly negatively correlated between players. In marked contrast to the case where both risky arms are of the same type, we find that learning will be complete in any Markov perfect equilibrium if the stakes exceed a certain threshold, and that all equilibria are in cutoff strategies. For low stakes, the equilibrium is unique, symmetric, and coincides with the planner's solution. For high stakes, the equilibrium is unique, symmetric, and tantamount to myopic behavior. For intermediate stakes, there is a continuum of equilibria.

Suggested Citation

  • Klein, Nicolas & Rady, Sven, 2008. "Negatively Correlated Bandits," Discussion Papers in Economics 5332, University of Munich, Department of Economics.
  • Handle: RePEc:lmu:muenec:5332
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    References listed on IDEAS

    as
    1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
    2. 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.
    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. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    6. Bergin, James, 1992. "A model of strategic behaviour in repeated games," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 113-153.
    7. Rady, Sven & Keller, Godfrey, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    8. Kaylan Chatterjee & Robert Evans, 2004. "Rivals' Search for Buried Treasure: Competition and Duplication in R&D," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 160-183, Spring.
    9. Bergin, James & MacLeod, W Bentley, 1993. "Continuous Time Repeated Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
    10. Dirk Bergemann & Juuso Valimaki, 2006. "Bandit Problems," Cowles Foundation Discussion Papers 1551, Cowles Foundation for Research in Economics, Yale University.
    11. Camargo, Braz, 2007. "Good news and bad news in two-armed bandits," Journal of Economic Theory, Elsevier, vol. 135(1), pages 558-566, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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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. Ufuk Akcigit & Qingmin Liu, 2011. "The Role of Information in Competitive Experimentation," Levine's Working Paper Archive 786969000000000321, David K. Levine.
    3. Alessandro Bonatti & Johannes Horner, 2011. "Collaborating," American Economic Review, American Economic Association, vol. 101(2), pages 632-663, April.
    4. Yingni Guo, 2016. "Dynamic Delegation of Experimentation," American Economic Review, American Economic Association, vol. 106(8), pages 1969-2008, August.
    5. Rady, Sven & Keller, Godfrey, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    6. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    7. 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.
    8. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, Exeter University, Department of Economics.
    9. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    10. Sofia Moroni, 2016. "Experimentation in Organizations," Working Paper 5876, Department of Economics, University of Pittsburgh.
    11. 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.
    12. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
    13. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    14. 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.
    15. 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.
    16. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics, revised May 2014.
    17. Nicolas Klein & Tymofiy Mylovanov, 2011. "Should the Flatterers be Avoided?," 2011 Meeting Papers 1273, Society for Economic Dynamics.
    18. Anders Bredahl Kock & Martin Thyrsgaard, 2017. "Optimal sequential treatment allocation," Papers 1705.09952, arXiv.org, revised Jan 2018.
    19. Kaustav Das, 2013. "Strategic Experimentation with Heterogeneous Agents and Payoff Externalities," Discussion Papers 1315, Exeter University, Department of Economics.
    20. repec:eee:jcecon:v:45:y:2017:i:4:p:685-711 is not listed on IDEAS
    21. 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.
    22. 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.
    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

    Keywords

    Strategic Experimentation; Two-Armed Bandit; Exponential Distribution; Poisson Process; Bayesian Learning; Markov Perfect Equilibrium;

    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
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • 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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