IDEAS home Printed from https://ideas.repec.org/p/trf/wpaper/387.html
   My bibliography  Save this paper

Strategic Experimentation with Private Payoffs

Author

Listed:
  • Heidhues, Paul
  • Rady, Sven
  • Strack, Philipp

Abstract

We consider two players facing identical discrete-time bandit problems with a safe and a risky arm. In any period, the risky arm yields either a success or a failure, and the first success reveals the risky arm to dominate the safe one. When payoffs are public information, the ensuing free-rider problem is so severe that the equilibrium number of experiments is at most one plus the number of experiments that a single agent would perform. When payoffs are private information and players can communicate via cheap talk, the socially optimal symmetric experimentation profile can be supported as a perfect Bayesian equilibrium for sufficiently optimistic prior beliefs. These results generalize to more than two players whenever the success probability per period is not too high. In particular, this is the case when successes occur at the jump times of a Poisson process and the period length is sufficiently small.

Suggested Citation

  • Heidhues, Paul & Rady, Sven & Strack, Philipp, 2012. "Strategic Experimentation with Private Payoffs," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 387, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  • Handle: RePEc:trf:wpaper:387
    as

    Download full text from publisher

    File URL: https://epub.ub.uni-muenchen.de/14041/1/387.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Decamps, Jean-Paul & Mariotti, Thomas, 2004. "Investment timing and learning externalities," Journal of Economic Theory, Elsevier, vol. 118(1), pages 80-102, September.
    2. Nicolas Klein & Sven Rady, 2011. "Negatively Correlated Bandits," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 693-732.
    3. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    4. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
    5. Johannes Hörner & Larry Samuelson, 2013. "Incentives for experimenting agents," RAND Journal of Economics, RAND Corporation, vol. 44(4), pages 632-663, December.
    6. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2007. "Social Learning in One-Arm Bandit Problems," Econometrica, Econometric Society, vol. 75(6), pages 1591-1611, November.
    7. David A. Malueg & Shunichi O. Tsutsui, 1997. "Dynamic R&D Competition with Learning," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 751-772, Winter.
    8. repec:dau:papers:123456789/12074 is not listed on IDEAS
    9. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    10. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    11. Sven Rady & Nicolas Klein & Johannes Horner, 2013. "Strongly Symmetric Equilibria in Bandit Games," 2013 Meeting Papers 1107, Society for Economic Dynamics.
    12. Dirk Bergemann & Ulrigh Hege, 2005. "The Financing of Innovation: Learning and Stopping," RAND Journal of Economics, The RAND Corporation, vol. 36(4), pages 719-752, Winter.
    13. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    14. Alessandro Bonatti & Johannes Horner, 2011. "Collaborating," American Economic Review, American Economic Association, vol. 101(2), pages 632-663, April.
    15. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    16. 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.
    17. Keller, Godfrey & Rady, Sven, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    18. Blume, Andreas & Heidhues, Paul, 2006. "Private monitoring in auctions," Journal of Economic Theory, Elsevier, vol. 131(1), pages 179-211, November.
    19. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    20. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    21. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    22. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    23. Daron Acemoglu & Kostas Bimpikis & Asuman Ozdaglar, 2011. "Experimentation, Patents, and Innovation," American Economic Journal: Microeconomics, American Economic Association, vol. 3(1), pages 37-77, February.
    24. Caroline D Thomas, 2010. "Strategic Experimentation with Congestion," Department of Economics Working Papers 130907, The University of Texas at Austin, Department of Economics, revised 04 Nov 2014.
    25. Hugo A. Hopenhayn & Francesco Squintani, 2011. "Preemption Games with Private Information," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 667-692.
    26. David Besanko & Jianjun Wu, 2013. "The Impact of Market Structure and Learning on the Tradeoff between R&D Competition and Cooperation," Journal of Industrial Economics, Wiley Blackwell, vol. 61(1), pages 166-201, March.
    27. Jay P. Choi, 1991. "Dynamic R&D Competition under "Hazard Rate" Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 22(4), pages 596-610, Winter.
    28. repec:cwl:cwldpp:1726rrr is not listed on IDEAS
    29. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
    30. repec:cwl:cwldpp:1726rr is not listed on IDEAS
    31. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    32. Pauli Murto & Juuso Välimäki, 2011. "Learning and Information Aggregation in an Exit Game," Review of Economic Studies, Oxford University Press, vol. 78(4), pages 1426-1461.
    33. Kamien, Morton I. & Tauman, Yair & Zamir, Shmuel, 1990. "On the value of information in a strategic conflict," Games and Economic Behavior, Elsevier, vol. 2(2), pages 129-153, June.
    34. Marina Halac & Navin Kartik & Qingmin Liu, 2016. "Optimal Contracts for Experimentation," Review of Economic Studies, Oxford University Press, vol. 83(3), pages 1040-1091.
    35. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Svetlana Boyarchenko, 2020. "Super- and submodularity of stopping games with random observations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 983-1022, November.
    2. 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.
    3. Sven Rady & Nicolas Klein & Johannes Horner, 2013. "Strongly Symmetric Equilibria in Bandit Games," 2013 Meeting Papers 1107, Society for Economic Dynamics.
    4. Ganglmair, Bernhard & Simcoe, Timothy & Tarantino, Emanuele, 2018. "Learning When to Quit: An Empirical Model of Experimentation," CEPR Discussion Papers 12733, C.E.P.R. Discussion Papers.
    5. Dosis, Anastasios & Muthoo, Abhinay, 2019. "Experimentation in Dynamic R&D Competition," CRETA Online Discussion Paper Series 52, Centre for Research in Economic Theory and its Applications CRETA.
    6. Song, Yangbo & Zhao, Mofei, 2021. "Dynamic R&D competition under uncertainty and strategic disclosure," Journal of Economic Behavior & Organization, Elsevier, vol. 181(C), pages 169-210.
    7. Keller, Godfrey & Novák, Vladimír & Willems, Tim, 2019. "A note on optimal experimentation under risk aversion," Journal of Economic Theory, Elsevier, vol. 179(C), pages 476-487.
    8. Georgiadis, George, 2017. "Deadlines and infrequent monitoring in the dynamic provision of public goods," Journal of Public Economics, Elsevier, vol. 152(C), pages 1-12.
    9. Simina Br^anzei & Yuval Peres, 2019. "Multiplayer Bandit Learning, from Competition to Cooperation," Papers 1908.01135, arXiv.org, revised Oct 2019.
    10. Caroline D. Thomas, 2010. "Strategic Experimentation with Congestion," Department of Economics Working Papers 130813, The University of Texas at Austin, Department of Economics, revised Aug 2013.
    11. Johannes Horner & Nicolas Klein & Sven Rady, 2019. "Overcoming Free-Riding in Bandit Games," Papers 1910.08953, arXiv.org, revised Mar 2021.
    12. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, University of Exeter, Department of Economics.
    13. Wuggenig, Mirjam, 2015. "Learning faster or more precisely? Strategic experimentation in networks," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113196, Verein für Socialpolitik / German Economic Association.
    14. Keller, Godfrey & Rady, Sven, 2015. "Breakdowns," Theoretical Economics, Econometric Society, vol. 10(1), January.
    15. KLEIN, Nicolas & WAGNER, Peter, 2018. "Strategic investment and learning with private information," Cahiers de recherche 2018-10, Universite de Montreal, Departement de sciences economiques.
    16. Gomes, Renato & Gottlieb, Daniel & Maestri, Lucas, 2016. "Experimentation and project selection: Screening and learning," Games and Economic Behavior, Elsevier, vol. 96(C), pages 145-169.
    17. Svetlana Boyarchenko, 0. "Super- and submodularity of stopping games with random observations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 0, pages 1-40.
    18. Xie, Yinxi & Xie, Yang, 2017. "Machiavellian experimentation," Journal of Comparative Economics, Elsevier, vol. 45(4), pages 685-711.
    19. Thijssen, Jacco J.J. & Bregantini, Daniele, 2017. "Costly sequential experimentation and project valuation with an application to health technology assessment," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 202-229.
    20. Wuggenig, Mirjam, 2014. "Learning faster or more precisely? Strategic experimentation in networks," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 485, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Chia-Hui & Ishida, Junichiro, 2018. "Hierarchical experimentation," Journal of Economic Theory, Elsevier, vol. 177(C), pages 365-404.
    2. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    3. Besanko, David & Tong, Jian & Wu, Jianjun, 2016. "Subsidizing research programs with "if" and "when" uncertainty in the face of severe informational constraints," Discussion Paper Series In Economics And Econometrics 1605, Economics Division, School of Social Sciences, University of Southampton.
    4. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
    5. 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.
    6. Keller, Godfrey & Rady, Sven, 2015. "Breakdowns," Theoretical Economics, Econometric Society, vol. 10(1), January.
    7. Khalil, Fahad & Lawarree, Jacques & Rodivilov, Alexander, 2020. "Learning from failures: Optimal contracts for experimentation and production," Journal of Economic Theory, Elsevier, vol. 190(C).
    8. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    9. Svetlana Boyarchenko, 0. "Super- and submodularity of stopping games with random observations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 0, pages 1-40.
    10. Simina Br^anzei & Yuval Peres, 2019. "Multiplayer Bandit Learning, from Competition to Cooperation," Papers 1908.01135, arXiv.org, revised Oct 2019.
    11. Svetlana Boyarchenko, 2020. "Super- and submodularity of stopping games with random observations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 983-1022, November.
    12. Bonatti, Alessandro & Hörner, Johannes, 2017. "Learning to disagree in a game of experimentation," Journal of Economic Theory, Elsevier, vol. 169(C), pages 234-269.
    13. Francis Bloch & Simona Fabrizi & Steffen Lippert, 2015. "Learning and collusion in new markets with uncertain entry costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 273-303, February.
    14. Wagner, Peter A., 2018. "Who goes first? Strategic delay under information asymmetry," Theoretical Economics, Econometric Society, vol. 13(1), January.
    15. Nicolas KLEIN & Peter WAGNER, 2018. "Strategic Investment and Learning with Private Information," Cahiers de recherche 13-2018, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    16. Thomas, Caroline, 2020. "Stopping with congestion and private payoffs," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 18-42.
    17. Thomas, Caroline, 2019. "Experimentation with reputation concerns – Dynamic signalling with changing types," Journal of Economic Theory, Elsevier, vol. 179(C), pages 366-415.
    18. Gomes, Renato & Gottlieb, Daniel & Maestri, Lucas, 2016. "Experimentation and project selection: Screening and learning," Games and Economic Behavior, Elsevier, vol. 96(C), pages 145-169.
    19. Johannes Hörner & Larry Samuelson, 2013. "Incentives for experimenting agents," RAND Journal of Economics, RAND Corporation, vol. 44(4), pages 632-663, December.
    20. Keller, Godfrey & Rady, Sven, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.

    More about this item

    Keywords

    Strategic Experimentation; Bayesian Learning; Cheap Talk; Two-Armed Bandit; Information Externality.;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:trf:wpaper:387. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tamilla Benkelberg). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.