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Strategic Experimentation with Exponential Bandits

  • Godfrey Keller
  • Sven Rady
  • Martin Cripps

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.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00564.x
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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 1 (01)
Pages: 39-68

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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:1:p:39-68
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  1. Dirk Bergemann & Ulrich Hege, 2001. "The Financing of Innovation: Learning and Stopping," Cowles Foundation Discussion Papers 1292R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2004.
  2. Ben Lockwood & Jonathan P. Thomas, 1999. "Gradualism and Irreversibility," Discussion Paper Series, Department of Economics 199909, Department of Economics, University of St. Andrews.
  3. 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.
  4. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
  5. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  6. Christopher Harris, 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 0044, Boston University - Industry Studies Programme.
  7. 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.
  8. 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.
  9. 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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