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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.

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Bibliographic Info

Article provided by Oxford University Press in its journal The Review of Economic Studies.

Volume (Year): 78 (2011)
Issue (Month): 2 ()
Pages: 693-732

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Handle: RePEc:oup:restud:v:78:y:2011:i:2:p:693-732

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  1. Dirk Bergemann & Juuso Valimaki, 2006. "Bandit Problems," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1551, Cowles Foundation for Research in Economics, Yale University.
  2. Camargo, Braz, 2007. "Good news and bad news in two-armed bandits," Journal of Economic Theory, Elsevier, Elsevier, vol. 135(1), pages 558-566, July.
  3. Cripps, Martin & Keller, Godfrey & Rady, Sven, 2003. "Strategic Experimentation with Exponential Bandits," Discussion Papers in Economics, University of Munich, Department of Economics 4, University of Munich, Department of Economics.
  4. Keller, Godfrey & Rady, Sven, 2009. "Strategic Experimentation with Poisson Bandits," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University 260, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  5. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(2), pages 185-202, October.
  6. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
  7. James Bergin, 1989. "A Model of Strategic Behaviour in Repeated Games," Working Papers, Queen's University, Department of Economics 751, Queen's University, Department of Economics.
  8. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Social Learning in One-Arm Bandit Problems," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1396, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Kaylan Chatterjee & Robert Evans, 2004. "Rivals' Search for Buried Treasure: Competition and Duplication in R&D," RAND Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 35(1), pages 160-183, Spring.
  10. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, Econometric Society, vol. 67(2), pages 349-374, March.
  11. Rosenberg, Dinah & Solan, Eilon & Vieille, Nicolas, 2009. "Informational externalities and emergence of consensus," Games and Economic Behavior, Elsevier, Elsevier, vol. 66(2), pages 979-994, July.
  12. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1489, Cowles Foundation for Research in Economics, Yale University.
  13. Godfrey Keller & Sven Rady, 2005. "Strategic Experimentation with Undiscounted Bandits," 2005 Meeting Papers, Society for Economic Dynamics 473, Society for Economic Dynamics.
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Cited by:
  1. Jean Guillaume Forand, 2010. "Keeping Your Options Open," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 557, University of Rochester - Center for Economic Research (RCER).
  2. Cripps, Martin W., 2013. "Optimal learning of a set: Or how to edit a journal if you must," Economics Letters, Elsevier, Elsevier, vol. 120(3), pages 384-388.
  3. 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.
  4. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, Elsevier, vol. 82(C), pages 31-51.
  5. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, Elsevier, vol. 82(C), pages 636-657.
  6. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers, University of Sydney, School of Economics 2011-10, University of Sydney, School of Economics.
  7. repec:tex:wpaper:130907 is not listed on IDEAS
  8. Alejandro Francetich, 2014. "Managing Multiple Research Projects," Working Papers, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University 516, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  9. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers, Exeter University, Department of Economics 1404, Exeter University, Department of Economics.

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