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Strategic Experimentation: The Case of Poisson Bandits

Author

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  • Martin W. Cripps
  • Godfrey Keller
  • Sven Rady

Abstract

This paper studies a game of strategic experimentation in which the players have access to two-armed bandits where the risky arm distributes lumpsum payoffs according to a Poisson process with unknown intensity. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies. We characterize the unique symmetric Markovian equilibrium of the game, which is in mixed strategies. A variety of asymmetric pure-strategy equilibria is then constructed for the special case where there are two players and the arrival of the first lump-sum fully reveals the quality of the risky arm. Equilibria where players switch finitely often between the roles of experimenter and free-rider all lead to the same pattern of information acquisition; the efficiency of these equilibria depends on the way players share the burden of experimentation among them. We show that at least for relatively pessimistic beliefs, even the worst asymmetric equilibrium is more efficient than the symmetric one. In equilibria where players switch roles infinitely often, they can acquire an approximately efficient amount of information, but the rate at which it is acquired still remains inefficient.

Suggested Citation

  • Martin W. Cripps & Godfrey Keller & Sven Rady, 2002. "Strategic Experimentation: The Case of Poisson Bandits," CESifo Working Paper Series 737, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_737
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    File URL: http://www.cesifo-group.de/DocDL/737.pdf
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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. David A. Malueg & Shunichi O. Tsutsui, 1997. "Dynamic R&D Competition with Learning," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 751-772, Winter.
    4. Dirk Bergemann & Ulrigh Hege, 2005. "The Financing of Innovation: Learning and Stopping," RAND Journal of Economics, The RAND Corporation, pages 719-752.
    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. Anat R. Admati & Motty Perry, 1991. "Joint Projects without Commitment," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 259-276.
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    Citations

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    Cited by:

    1. Krähmer, Daniel, 2003. "Learning and self-confidence in contests
      [Lernen und Selbstvertrauen in Wettkämpfen]
      ," Discussion Papers, Research Unit: Market Processes and Governance SP II 2003-10, Social Science Research Center Berlin (WZB).
    2. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Timing Games with Informational Externalities," Levine's Working Paper Archive 122247000000000704, David K. Levine.
    3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, pages 1591-1611.
    4. Klaus Walde, 2001. "Capital accumulation in a model of growth and creative destruction," Discussion Paper / Institute for Empirical Macroeconomics 139, Federal Reserve Bank of Minneapolis.
    5. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 137-153, March.
    6. Bøg, Martin, 2006. "Whom to Observe?," MPRA Paper 8773, University Library of Munich, Germany, revised 14 May 2008.

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