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Strategic Experimentation with Exponential Bandits

  • Cripps, Martin William
  • Keller, R Godfrey
  • Rady, Sven

This Paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a pay-off 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; moreover, the expected pay-off 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 pay-offs.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 3814.

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Date of creation: Mar 2003
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Handle: RePEc:cpr:ceprdp:3814
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  1. Leslie M. Marx & Steven A. Matthews, . ""Dynamic Voluntary Contribution to a Public Project''," CARESS Working Papres 99-01, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  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. Lockwood, Ben & Thomas, Jonathan P, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Wiley Blackwell, vol. 69(2), pages 339-56, April.
  4. Dirk Bergemann & Ulrich Hege, 2001. "The Financing of Innovation: Learning and Stopping," Cowles Foundation Discussion Papers 1292, Cowles Foundation for Research in Economics, Yale University.
  5. repec:cup:cbooks:9780521497695 is not listed on IDEAS
  6. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  7. repec:dgr:kubcen:200116 is not listed on IDEAS
  8. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  9. 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.
  10. Harris, C., 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 44, Boston University - Industry Studies Programme.
  11. Admati, Anat R & Perry, Motty, 1991. "Joint Projects without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 259-76, April.
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