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Overcoming Free-Riding in Bandit Games

Author

Listed:
  • Hörner, Johannes
  • Klein, Nicolas
  • Rady, Sven

Abstract

This paper considers a class of experimentation games with L´evy bandits encompassing those of Bolton and Harris (1999) and Keller, Rady and Cripps (2005). Its main result is that efficient (perfect Bayesian) equilibria exist whenever players’ payoffs have a diffusion component. Hence, the trade-offs emphasized in the literature do not rely on the intrinsic nature of bandit models but on the commonly adopted solution concept (MPE). This is not an artifact of continuous time: we prove that such equilibria arise as limits of equilibria in the discretetime game. Furthermore, it suffices to relax the solution concept to strongly symmetric equilibrium.

Suggested Citation

  • Hörner, Johannes & Klein, Nicolas & Rady, Sven, 2020. "Overcoming Free-Riding in Bandit Games," TSE Working Papers 20-1132, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:124603
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    References listed on IDEAS

    as
    1. Johannes Hörner & Larry Samuelson, 2013. "Incentives for experimenting agents," RAND Journal of Economics, RAND Corporation, vol. 44(4), pages 632-663, December.
    2. Drew Fudenberg & David K. Levine & Satoru Takahashi, 2008. "Perfect public equilibrium when players are patient," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 16, pages 345-367, World Scientific Publishing Co. Pte. Ltd..
    3. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 345-390.
    4. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    5. Tomasz Sadzik & Ennio Stacchetti, 2015. "Agency Models With Frequent Actions," Econometrica, Econometric Society, vol. 83, pages 193-237, January.
    6. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    7. , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    8. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    9. Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
    10. Abrea Dilip & Pearce David & Stacchetti Ennio, 1993. "Renegotiation and Symmetry in Repeated Games," Journal of Economic Theory, Elsevier, vol. 60(2), pages 217-240, August.
    11. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
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    14. Bergin, James & MacLeod, W Bentley, 1993. "Continuous Time Repeated Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
    15. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
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    More about this item

    Keywords

    Two-Armed Bandit; Bayesian Learning; Strategic Experimentation; Strongly Symmetric Equilibrium.;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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