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Strategic experimentation with Poisson bandits

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  • ,

    (Department of Economics, University of Oxford)

  • ,

    (Department of Economics, University of Munich)

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 and show that all such equilibria exhibit an 'encouragement effect' relative to the single-agent optimum. There is no equilibrium in which all players use cut-off strategies. Owing to the encouragement effect, asymmetric equilibria in which players take turns playing the risky arm before all experimentation stops Pareto dominate the unique symmetric equilibrium. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce the intensity of experimentation at more optimistic beliefs. This suggests that there is no equilibrium that uniformly maximizes the players' average payoff.

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  • , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    • Handle: RePEc:the:publsh:595
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Strategic experimentation; two-armed bandit; Poisson process; Bayesian learning; piecewise deterministic process; Markov perfect equilibrium; differential-difference equation;
    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

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