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Strategic Experimentation with Poisson Bandits

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  • Keller, R 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 piecewise 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.

Suggested Citation

  • Keller, R Godfrey & Rady, Sven, 2009. "Strategic Experimentation with Poisson Bandits," CEPR Discussion Papers 7270, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:7270
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    References listed on IDEAS

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    1. Decamps, Jean-Paul & Mariotti, Thomas, 2004. "Investment timing and learning externalities," Journal of Economic Theory, Elsevier, vol. 118(1), pages 80-102, September.
    2. Nicolas Klein & Sven Rady, 2011. "Negatively Correlated Bandits," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 693-732.
    3. Nicolas Klein, 2009. "Free-Riding And Delegation In Research Teams," 2009 Meeting Papers 253, Society for Economic Dynamics.
    4. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    5. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    6. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    7. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers 1489, Cowles Foundation for Research in Economics, Yale University.
    8. Dirk Bergemann & Juuso Valimaki, 2006. "Bandit Problems," Cowles Foundation Discussion Papers 1551, Cowles Foundation for Research in Economics, Yale University.
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    More about this item

    Keywords

    Bayesian Learning; Differential-Difference Equation; Markov Perfect Equilibrium; Piecewise Deterministic Process; Poisson Process; Strategic Experimentation; Two-Armed Bandit;
    All these keywords.

    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; Information and Knowledge; Communication; Belief; Unawareness
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

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