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Strategic Experimentation with Poisson Bandits

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  • Keller, Godfrey
  • Rady, Sven

Abstract

We study a game of strategic experimentation with two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process. Its intensity is either high or low, and unknown to the players. We consider Markov perfect equilibria with beliefs as the state variable. As the belief process is piece-wise deterministic, payoff functions solve differential-difference equations. There is no equilibrium where all players use cut-off strategies, and all equilibria exhibit an ‘encouragement effect’ relative to the single-agent optimum. We construct asymmetric equilibria in which players have symmetric continuation values at sufficiently optimistic beliefs yet take turns playing the risky arm before all experimentation stops. Owing to the encouragement effect, these equilibria Pareto dominate the unique symmetric one for sufficiently frequent turns. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce average payoffs at more optimistic beliefs. Some equilibria exhibit an ‘anticipation effect’: as beliefs become more pessimistic, the continuation value of a single experimenter increases over some range because a lower belief means a shorter wait until another player takes over.

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Bibliographic Info

Paper provided by Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich in its series Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems with number 260.

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Date of creation: May 2009
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Handle: RePEc:trf:wpaper:260

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Keywords: Strategic Experimentation; Two-Armed Bandit; Poisson Process; Bayesian Learning; Piecewise Deterministic Process; Markov Perfect Equilibrium; Differential-Difference Equation;

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References

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  1. Cripps, Martin William & Keller, Godfrey & Rady, Sven, 2003. "Strategic Experimentation with Exponential Bandits," CEPR Discussion Papers 3814, C.E.P.R. Discussion Papers.
  2. Myles,Gareth D., 1995. "Public Economics," Cambridge Books, Cambridge University Press, number 9780521497695, November.
  3. Dirk Bergemann & Juuso Valimaki, 2006. "Bandit Problems," Cowles Foundation Discussion Papers 1551, Cowles Foundation for Research in Economics, Yale University.
  4. Decamps, Jean-Paul & Mariotti, Thomas, 2004. "Investment timing and learning externalities," Journal of Economic Theory, Elsevier, vol. 118(1), pages 80-102, September.
  5. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  6. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers 1489, Cowles Foundation for Research in Economics, Yale University.
  7. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
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Citations

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Cited by:
  1. Klein, Nicolas & Rady, Sven, 2008. "Negatively Correlated Bandits," CEPR Discussion Papers 6983, C.E.P.R. Discussion Papers.
  2. Johannes Horner & Larry Samuelson, 2009. "Incentives for Experimenting Agents," Cowles Foundation Discussion Papers 1726RR, Cowles Foundation for Research in Economics, Yale University, revised Mar 2013.
  3. Decamps, J.-P. & Mariotti, T., 2000. "Irreversible Investment and Learning Expternalities," Papers 00-534, Toulouse - GREMAQ.
  4. Jean Guillaume Forand, 2013. "Keeping Your options Open," Working Papers 1301, University of Waterloo, Department of Economics, revised Feb 2012.
  5. Nicolas Klein & Tymofiy Mylovanov, 2011. "Should the Flatterers be Avoided?," 2011 Meeting Papers 1273, Society for Economic Dynamics.
  6. Johannes Horner & Larry Samuelson, 2009. "Incentives for Experimenting Agents," Cowles Foundation Discussion Papers 1726RRR, Cowles Foundation for Research in Economics, Yale University, revised Jun 2013.
  7. Johannes Horner & Larry Samuelson, 2013. "Incentives for Experimenting Agents," Levine's Working Paper Archive 786969000000000671, David K. Levine.
  8. Koulovatianos, Christos & Wieland, Volker, 2011. "Asset Pricing under Rational Learning about Rare Disasters," CEPR Discussion Papers 8514, C.E.P.R. Discussion Papers.
  9. Klein, Nicolas & Rady, Sven, 2008. "Negatively Correlated Bandits," Discussion Papers in Economics 5332, University of Munich, Department of Economics.
  10. Kaustav Das, 2013. "Strategic Experimentation with Heterogeneous Agents and Payoff Externalities," Discussion Papers 1315, Exeter University, Department of Economics.
  11. Dinah Rosenberg & Antoine Salomon & Nicolas Vieille, 2010. "On Games of Strategic Experimentation," Working Papers hal-00579613, HAL.
  12. Matros, Alexander & Smirnov, Vladimir, 2011. "Treasure game," Working Papers 2011-10, University of Sydney, School of Economics.
  13. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, Exeter University, Department of Economics.
  14. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2012. "Strategic Experimentation with Private Payoffs," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 387, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  15. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
  16. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
  17. Nicolas Klein, 2009. "Free-Riding And Delegation In Research Teams," 2009 Meeting Papers 253, Society for Economic Dynamics.

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