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Strategic Experimentation with Poisson Bandits

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Author Info
Godfrey Keller () (University of Oxford)
Sven Rady () (University of Munich)

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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 piecewise deterministic, payoff functions solve differential-difference equations. Here 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 suffciently 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 suffciently 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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Publisher Info
Paper provided by 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 of Munich in its series Discussion Papers 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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Related research
Keywords: Strategic Experimentation; Two-Armed Bandit; Poisson Process; Bayesian Learning; Piecewise Deterministic Process; Markov Perfect Equilibrium; Differential-Difference Equation.;

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Find related papers by JEL classification:
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
O32 - Economic Development, Technological Change, and Growth - - Technological Change - - - Management of Technological Innovation and R&D

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Decamps, Jean-Paul & Mariotti, Thomas, 2004. "Investment timing and learning externalities," Journal of Economic Theory, Elsevier, vol. 118(1), pages 80-102, September. [Downloadable!] (restricted)
  2. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, 01. [Downloadable!] (restricted)
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  3. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  4. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October. [Downloadable!] (restricted)
  5. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers 1489, Cowles Foundation, Yale University. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Klein, Nicolas & Rady, Sven, 2008. "Negatively Correlated Bandits," CEPR Discussion Papers 6983, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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