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