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Strategic Learning in Teams

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  • Klein, Nicolas

Abstract

This paper analyzes a two-player game of strategic experimentation with three-armed exponential bandits in continuous time. Players face replica bandits, with one arm that is safe in that it generates a known payoff, whereas the likelihood of the risky arms’ yielding a positive payoff is initially unknown. It is common knowledge that the types of the two risky arms are perfectly negatively correlated. I show that the efficient policy is incentive-compatible if, and only if, the stakes are high enough. Moreover, learning will be complete in any Markov perfect equilibrium with continuous value functions if, and only if, the stakes exceed a certain threshold.

Suggested Citation

  • Klein, Nicolas, 2010. "Strategic Learning in Teams," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 333, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    • Handle: RePEc:trf:wpaper:333
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    References listed on IDEAS

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    1. Gustavo Manso, 2011. "Motivating Innovation," Journal of Finance, American Finance Association, vol. 66(5), pages 1823-1860, October.
    2. Nicolas Klein & Sven Rady, 2011. "Negatively Correlated Bandits," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 693-732.
    3. Philippe Aghion & Mathias Dewatripont & Jeremy C. Stein, 2008. "Academic freedom, private‐sector focus, and the process of innovation," RAND Journal of Economics, RAND Corporation, vol. 39(3), pages 617-635, September.
    4. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
    5. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    6. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    7. Sven Rady & Nicolas Klein & Johannes Horner, 2013. "Strongly Symmetric Equilibria in Bandit Games," 2013 Meeting Papers 1107, Society for Economic Dynamics.
    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. Alessandro Bonatti & Johannes Horner, 2011. "Collaborating," American Economic Review, American Economic Association, vol. 101(2), pages 632-663, April.
    10. , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    11. Klein, Nicolas, 2016. "The importance of being honest," Theoretical Economics, Econometric Society, vol. 11(3), September.
    12. Kaylan Chatterjee & Robert Evans, 2004. "Rivals' Search for Buried Treasure: Competition and Duplication in R&D," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 160-183, Spring.
    13. Pauli Murto & Juuso Välimäki, 2011. "Learning and Information Aggregation in an Exit Game," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1426-1461.
    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. Bank, Peter & Föllmer, Hans, 2003. "American Options, Multi-armed Bandits, and Optimal Consumption Plans : A Unifying View," SFB 373 Discussion Papers 2003,46, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Camargo, Braz, 2007. "Good news and bad news in two-armed bandits," Journal of Economic Theory, Elsevier, vol. 135(1), pages 558-566, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Kaustav Das & Nicolas Klein & Katharina Schmid, 2020. "Strategic experimentation with asymmetric players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 1147-1175, June.
    2. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, University of Exeter, Department of Economics.
    3. Nicolas Klein & Tymofiy Mylovanov, 2011. "Should the Flatterers be Avoided?," 2011 Meeting Papers 1273, Society for Economic Dynamics.
    4. Johannes Hoelzemann & Nicolas Klein, 2021. "Bandits in the lab," Quantitative Economics, Econometric Society, vol. 12(3), pages 1021-1051, July.
    5. Külpmann, Philipp, 2015. "Procrastination and projects," Center for Mathematical Economics Working Papers 544, Center for Mathematical Economics, Bielefeld University.
    6. Mayskaya, Tatiana, 2024. "Following beliefs or excluding the worst? The role of unfindable state in learning," European Economic Review, Elsevier, vol. 162(C).
    7. Kaustav Das, 2017. "The Role of Heterogeneity in a model of Strategic Experimentation," Discussion Papers 1703, University of Exeter, Department of Economics.
    8. Das, Kaustav & Klein, Nicolas & Schmid, Katharina, 2024. "Strategic experimentation with asymmetric safe options," Economics Letters, Elsevier, vol. 239(C).
    9. Xie, Yinxi & Xie, Yang, 2017. "Machiavellian experimentation," Journal of Comparative Economics, Elsevier, vol. 45(4), pages 685-711.
    10. Kaustav Das, 2015. "The Role of Heterogeneity in a Model of Strategic Experimentation," Discussion Papers 1507, University of Exeter, Department of Economics.

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    More about this item

    Keywords

    Strategic Experimentation; Three-Armed Bandit; Exponential Distribution; Poisson Process; Bayesian Learning; Markov Perfect 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
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

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