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Strategic Experimentation: The Case of Poisson Bandits

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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.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 737.

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Date of creation: 2002
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Handle: RePEc:ces:ceswps:_737

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Related research

Keywords: strategic experimentation; two-armed bandit; poisson process; Bayesian learning; Markov perfect equilibrium; public goods;

References

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  1. Leslie M. Marx & Steven A. Matthews, 1997. "Dynamic Voluntary Contribution to a Public Project," Discussion Papers 1188, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Bergemann, Dirk & Hege, Ulrich, 1997. "Venture Capital Financing, Moral Hazard and Learning," CEPR Discussion Papers 1738, C.E.P.R. Discussion Papers.
  3. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  4. Admati, Anat R & Perry, Motty, 1991. "Joint Projects without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 259-76, April.
  5. Bergemann, Dirk & Hege, Ulrich, 2001. "The Financing of Innovation: Learning and Stopping," CEPR Discussion Papers 2763, C.E.P.R. Discussion Papers.
  6. 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.
  7. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
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Citations

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Cited by:
  1. Bøg, Martin, 2006. "Whom to Observe?," MPRA Paper 8773, University Library of Munich, Germany, revised 14 May 2008.
  2. Edward Cartwright & Myrna Wooders, 2003. "On Equilibrium in Pure Strategies in Games with Many Players," Working Papers 2003.122, Fondazione Eni Enrico Mattei.
  3. Walde, Klaus, 2003. "Capital accumulation in a model of growth and creative destruction," Royal Economic Society Annual Conference 2003 216, Royal Economic Society.
  4. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Timing Games with Informational Externalities," Levine's Working Paper Archive 122247000000000704, David K. Levine.
  5. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Social Learning in One-Arm Bandit Problems," Discussion Papers 1396, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Krähmer, Daniel, 2003. "Learning and self-confidence in contests," Discussion Papers, Research Unit: Market Processes and Governance SP II 2003-10, Social Science Research Center Berlin (WZB).

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