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Strategic Experimentation with Exponential Bandits

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  • Godfrey Keller
  • Martin Cripps

Abstract

This paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a payoff only after some exponentially distributed random time. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with posterior beliefs as the state variable. After characterizing the unique symmetric Markovian equilibrium of the game, which is in mixed strategies, we construct a variety of pure-strategy equilibria. There is no equilibrium where all players use simple cut-off strategies. 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. 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; moreoever, the expected payoff of an experimenter exhibits the novel feature that it rises as players become more pessimistic. Finally, over the range of beliefs where players use both arms a positive fraction of the time, the symmetric equilibrium is dominated by any asymmetric one in terms of aggregate payoffs.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 143.

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Date of creation: 01 Jan 2003
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Handle: RePEc:oxf:wpaper:143

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Related research

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

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References

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  1. 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.
  2. Keller, Godfrey & Rady, Sven, 2001. "Price Dispersion and Learning in a Dynamic Differentiated-Goods Duopoly," Discussion Papers in Economics 21, University of Munich, Department of Economics.
  3. Bergemann, Dirk & Hege, Ulrich, 2001. "The Financing of Innovation: Learning and Stopping," CEPR Discussion Papers 2763, C.E.P.R. Discussion Papers.
  4. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  5. Marx, Leslie M & Matthews, Steven A, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Wiley Blackwell, vol. 67(2), pages 327-58, April.
  6. Lockwood, B. & Thomas, J.P., 1999. "Gradualism and Irreversibility," The Warwick Economics Research Paper Series (TWERPS) 550, University of Warwick, Department of Economics.
  7. Admati, Anat R & Perry, Motty, 1991. "Joint Projects without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 259-76, April.
  8. Christopher Harris, 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 0044, Boston University - Industry Studies Programme.
  9. Myles,Gareth D., 1995. "Public Economics," Cambridge Books, Cambridge University Press, number 9780521497695.
  10. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
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