IDEAS home Printed from https://ideas.repec.org/p/nwu/cmsems/1396.html
   My bibliography  Save this paper

Social Learning in One-Arm Bandit Problems

Author

Listed:
  • Dinah Rosenberg
  • Eilon Solan
  • Nicolas Vieille

Abstract

We study a two-player one-arm bandit problem in discrete time, in which the risky arm can have two possible types, high and low, the decision to stop experimenting is irreversible, and players observe each other's actions but not each other's payoffs. We prove that all equilibria are in cutoff strategies and provide several qualitative results on the sequence of cutoffs.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Social Learning in One-Arm Bandit Problems," Discussion Papers 1396, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1396
    as

    Download full text from publisher

    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1396.pdf
    File Function: main text
    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. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 475-507.
    3. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    4. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
    5. Chamley, Christophe, 2004. "Delays and equilibria with large and small information in social learning," European Economic Review, Elsevier, vol. 48(3), pages 477-501, June.
    6. Dirk Bergemann & Juuso Valimaki, 1997. "Market Diffusion with Two-Sided Learning," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 773-795, Winter.
    7. Dirk Bergemann & Juuso Välimäki, 2000. "Experimentation in Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 213-234.
    8. Martin Cripps & Godfrey Keller & Sven Rady, 2000. "Strategic Experimentation: The Case of the Poisson Bandits," Econometric Society World Congress 2000 Contributed Papers 0878, Econometric Society.
    9. Bulow, Jeremy & Klemperer, Paul, 1994. "Rational Frenzies and Crashes," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 1-23, February.
    10. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    11. Caplin, Andrew & Leahy, John, 1994. "Business as Usual, Market Crashes, and Wisdom after the Fact," American Economic Review, American Economic Association, vol. 84(3), pages 548-565, June.
    12. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    13. Guiseppe Moscarini & Francesco Squintani, 2004. "Competitive Experimentation with Private Information," Cowles Foundation Discussion Papers 1489, Cowles Foundation for Research in Economics, Yale University.
    14. Chamley, Christophe & Gale, Douglas, 1994. "Information Revelation and Strategic Delay in a Model of Investment," Econometrica, Econometric Society, vol. 62(5), pages 1065-1085, September.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    Full references (including those not matched with items on IDEAS)

    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. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004. "Timing Games with Informational Externalities," Levine's Working Paper Archive 122247000000000704, David K. Levine.
    2. Dirk Bergemann & Juuso Välimäki, 2000. "Experimentation in Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 213-234.
    3. Moscarini, Giuseppe & Squintani, Francesco, 2010. "Competitive experimentation with private information: The survivor's curse," Journal of Economic Theory, Elsevier, vol. 145(2), pages 639-660, March.
    4. Doruk Cetemen & Can Urgun & Leeat Yariv, 2023. "Collective Progress: Dynamics of Exit Waves," Journal of Political Economy, University of Chicago Press, vol. 131(9), pages 2402-2450.
    5. 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.
    6. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
    7. Amador, Manuel & Weill, Pierre-Olivier, 2012. "Learning from private and public observations of othersʼ actions," Journal of Economic Theory, Elsevier, vol. 147(3), pages 910-940.
    8. Camargo, Braz, 2014. "Learning in society," Games and Economic Behavior, Elsevier, vol. 87(C), pages 381-396.
    9. Wagner, Peter A., 2018. "Who goes first? Strategic delay under information asymmetry," Theoretical Economics, Econometric Society, vol. 13(1), January.
    10. Wagner, Peter A. & Klein, Nicolas, 2022. "Strategic investment and learning with private information," Journal of Economic Theory, Elsevier, vol. 204(C).
    11. Murto, Pauli & Välimäki, Juuso, 2013. "Delay and information aggregation in stopping games with private information," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2404-2435.
    12. Davide Crapis & Bar Ifrach & Costis Maglaras & Marco Scarsini, 2017. "Monopoly Pricing in the Presence of Social Learning," Management Science, INFORMS, vol. 63(11), pages 3586-3608, November.
    13. Levin, Dan & Peck, James, 2008. "Investment dynamics with common and private values," Journal of Economic Theory, Elsevier, vol. 143(1), pages 114-139, November.
    14. , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    15. Andrei Barbos, 2015. "Information Acquisition and Innovation under Competitive Pressure," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(2), pages 325-347, June.
    16. Wang, Xinru & Kim, Maria H. & Suardi, Sandy, 2022. "Herding and China's market-wide circuit breaker," Journal of Banking & Finance, Elsevier, vol. 141(C).
    17. Keller, Godfrey & Rady, Sven, 2020. "Undiscounted bandit games," Games and Economic Behavior, Elsevier, vol. 124(C), pages 43-61.
    18. Rauch, James E. & Watson, Joel, 2003. "Starting small in an unfamiliar environment," International Journal of Industrial Organization, Elsevier, vol. 21(7), pages 1021-1042, September.
    19. Osnat Zohar, 2019. "Boom-Bust Cycles of Learning, Investment and Disagreement," Bank of Israel Working Papers 2019.06, Bank of Israel.
    20. Pablo D. Fajgelbaum & Edouard Schaal & Mathieu Taschereau-Dumouchel, 2017. "Uncertainty Traps," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1641-1692.

    More about this item

    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:nwu:cmsems:1396. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Fran Walker (email available below). General contact details of provider: https://edirc.repec.org/data/cmnwuus.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.