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Negatively Correlated Bandits

Author

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  • Nicolas Klein
  • Sven Rady

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

  • Nicolas Klein & Sven Rady, 2008. "Negatively Correlated Bandits," Working Papers 040, Bavarian Graduate Program in Economics (BGPE).
  • Handle: RePEc:bav:wpaper:040_klein_rady
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    File URL: http://www.bgpe.de/texte/DP/040_klein_rady.pdf
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    References listed on IDEAS

    as
    1. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    2. Bergin, James, 1992. "A model of strategic behaviour in repeated games," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 113-153.
    3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
    4. Dirk Bergemann & Juuso Valimaki, 2006. "Bandit Problems," Cowles Foundation Discussion Papers 1551, Cowles Foundation for Research in Economics, Yale University.
    5. 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.
    6. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    7. Rady, Sven & Keller, Godfrey, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    8. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    9. 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.
    10. Camargo, Braz, 2007. "Good news and bad news in two-armed bandits," Journal of Economic Theory, Elsevier, vol. 135(1), pages 558-566, July.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ufuk Akcigit & Qingmin Liu, 2011. "The Role of Information in Competitive Experimentation," PIER Working Paper Archive 11-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    2. 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.
    3. Külpmann, Philipp, 2015. "Procrastination and projects," Center for Mathematical Economics Working Papers 544, Center for Mathematical Economics, Bielefeld University.
    4. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    5. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    6. Alejandro Francetich, 2014. "Managing Multiple Research Projects," Working Papers 516, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Rady, Sven & Keller, Godfrey, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    8. Alessandro Bonatti & Johannes Horner, 2011. "Collaborating," American Economic Review, American Economic Association, vol. 101(2), pages 632-663, April.
    9. 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.
    10. Nicolas Klein & Tymofiy Mylovanov, 2011. "Should the Flatterers be Avoided?," 2011 Meeting Papers 1273, Society for Economic Dynamics.
    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. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    13. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, Exeter University, Department of Economics.
    14. Sofia Moroni, 2016. "Experimentation in Organizations," Working Paper 5876, Department of Economics, University of Pittsburgh.
    15. Anders Bredahl Kock & Martin Thyrsgaard, 2017. "Optimal sequential treatment allocation," Papers 1705.09952, arXiv.org, revised Jan 2018.
    16. Nicolas Klein, 2009. "Free-Riding And Delegation In Research Teams," 2009 Meeting Papers 253, Society for Economic Dynamics.
    17. 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.
    18. 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.
    19. Yingni Guo, 2016. "Dynamic Delegation of Experimentation," American Economic Review, American Economic Association, vol. 106(8), pages 1969-2008, August.
    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. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics, revised May 2014.
    23. Kaustav Das, 2013. "Strategic Experimentation with Heterogeneous Agents and Payoff Externalities," Discussion Papers 1315, Exeter University, Department of Economics.
    24. 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.

    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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