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Strategic Experimentation with Exponential Bandits

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  • Godfrey Keller
  • Sven Rady
  • Martin Cripps

Abstract

We analyze a game of strategic experimentation with two-armed bandits whose risky arm might yield payoffs after exponentially distributed random times. Free-riding causes an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with beliefs as the state variable. We construct the unique symmetric Markovian equilibrium of the game, followed by various asymmetric ones. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between experimenting and free-riding all yield a similar pattern of information acquisition, greater efficiency being achieved when the players share the burden of experimentation more equitably. When players switch roles infinitely often, they can acquire an approximately efficient amount of information, but still at an inefficient rate. In terms of aggregate payoffs, all these asymmetric equilibria dominate the symmetric one wherever the latter prescribes simultaneous use of both arms. Copyright The Econometric Society 2005.

Suggested Citation

  • Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
  • Handle: RePEc:ecm:emetrp:v:73:y:2005:i:1:p:39-68
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00564.x
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    References listed on IDEAS

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    1. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 327-358.
    2. Bergemann, Dirk & Hege, Ulrich, 1998. "Venture capital financing, moral hazard, and learning," Journal of Banking & Finance, Elsevier, vol. 22(6-8), pages 703-735, August.
    3. Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 339-356.
    4. Harris, C., 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 44, Boston University - Industry Studies Programme.
    5. Dirk Bergemann & Ulrigh Hege, 2005. "The Financing of Innovation: Learning and Stopping," RAND Journal of Economics, The RAND Corporation, vol. 36(4), pages 719-752, Winter.
    6. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    7. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    8. Anat R. Admati & Motty Perry, 1991. "Joint Projects without Commitment," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 259-276.
    9. Keller, Godfrey & Rady, Sven, 2003. " Price Dispersion and Learning in a Dynamic Differentiated-Goods Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 138-165, Spring.
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    More about this item

    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
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • 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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