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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.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6983.

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Date of creation: Oct 2008
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Handle: RePEc:cpr:ceprdp:6983

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Related research

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

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References

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  1. BERGIN, James, 1990. "A model of strategic behaviour in repeated games," CORE Discussion Papers 1990032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  3. 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.
  4. Rady, Sven & Keller, Godfrey, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
  5. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers 1489, Cowles Foundation for Research in Economics, Yale University.
  6. Cripps, Martin William & Keller, Godfrey & Rady, Sven, 2003. "Strategic Experimentation with Exponential Bandits," CEPR Discussion Papers 3814, C.E.P.R. Discussion Papers.
  7. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Social Learning in One-Arm Bandit Problems," Discussion Papers 1396, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Camargo, Braz, 2007. "Good news and bad news in two-armed bandits," Journal of Economic Theory, Elsevier, vol. 135(1), pages 558-566, July.
  9. Dirk Bergemann & Juuso Valimaki, 2006. "Bandit Problems," Cowles Foundation Discussion Papers 1551, Cowles Foundation for Research in Economics, Yale University.
  10. Godfrey Keller & Sven Rady, 2005. "Strategic Experimentation with Undiscounted Bandits," 2005 Meeting Papers 473, Society for Economic Dynamics.
  11. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  12. 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.
  13. 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.
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Citations

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Cited by:
  1. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics.
  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. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
  4. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
  5. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, Exeter University, Department of Economics.
  6. Jean Guillaume Forand, 2013. "Keeping Your options Open," Working Papers 1301, University of Waterloo, Department of Economics, revised Feb 2012.
  7. Alejandro Francetich, 2014. "Experimentation With Menus," Working Papers 516, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  8. repec:tex:wpaper:130907 is not listed on IDEAS
  9. 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.

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