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Negatively Correlated Bandits

  • Klein, Nicolas
  • Rady, Sven

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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File URL: http://epub.ub.uni-muenchen.de/5332/1/Klein_Rady_2008_Munich_Econ_DP.pdf
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Paper provided by University of Munich, Department of Economics in its series Discussion Papers in Economics with number 5332.

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Date of creation: 01 Aug 2008
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Handle: RePEc:lmu:muenec:5332
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  1. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  2. Keller, R Godfrey & Rady, Sven, 2009. "Strategic Experimentation with Poisson Bandits," CEPR Discussion Papers 7270, C.E.P.R. Discussion Papers.
  3. 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.
  4. Godfrey Keller & Sven Rady, 2005. "Strategic Experimentation with Undiscounted Bandits," 2005 Meeting Papers 473, Society for Economic Dynamics.
  5. Bergin, James, 1992. "A model of strategic behaviour in repeated games," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 113-153.
  6. Camargo, Braz, 2007. "Good news and bad news in two-armed bandits," Journal of Economic Theory, Elsevier, vol. 135(1), pages 558-566, July.
  7. 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.
  8. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
  9. 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.
  10. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  11. Dirk Bergemann & Juuso Valimaki, 2006. "Bandit Problems," Cowles Foundation Discussion Papers 1551, Cowles Foundation for Research in Economics, Yale University.
  12. Cripps, Martin William & Keller, R Godfrey & Rady, Sven, 2003. "Strategic Experimentation with Exponential Bandits," CEPR Discussion Papers 3814, C.E.P.R. Discussion Papers.
  13. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers 1489, Cowles Foundation for Research in Economics, Yale University.
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