IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/19043.html
   My bibliography  Save this paper

Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability

Author

Listed:
  • Roland G. Fryer, Jr.
  • Philipp Harms

Abstract

We present a two-armed bandit model of decision making under uncertainty where the expected return to investing in the "risky arm'' increases when choosing that arm and decreases when choosing the "safe'' arm. These dynamics are natural in applications such as human capital development, job search, and occupational choice. Using new insights from stochastic control, along with a monotonicity condition on the payoff dynamics, we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with Gittins' index. Our result implies the indexability of a new class of "restless'' bandit models.

Suggested Citation

  • Roland G. Fryer, Jr. & Philipp Harms, 2013. "Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability," NBER Working Papers 19043, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:19043
    Note: IO LS
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w19043.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    2. Will Dobbie & Roland G. Fryer Jr., 2013. "Getting beneath the Veil of Effective Schools: Evidence from New York City," American Economic Journal: Applied Economics, American Economic Association, vol. 5(4), pages 28-60, October.
    3. , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    4. Kohlmann, M., 1982. "Existence of optimal controls for a partially observed semimartingale," Stochastic Processes and their Applications, Elsevier, vol. 13(2), pages 215-226, August.
    5. Flavio Cunha & James J. HECKMAN, 2009. "Investing in our Young People," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 117(3), pages 387-418.
    6. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    7. Nicolas Klein & Sven Rady, 2011. "Negatively Correlated Bandits," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 693-732.
    8. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-654, May.
    9. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    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. Suvi Vasama, 2016. "Unraveling of Cooperation in Dynamic Collaboration," SFB 649 Discussion Papers SFB649DP2016-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    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. Roland Fryer & Philipp Harms, 2018. "Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 399-427, May.
    2. Asaf Cohen & Eilon Solan, 2013. "Bandit Problems with Lévy Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 92-107, February.
    3. 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.
    4. Nicolas Klein & Tymofiy Mylovanov, 2011. "Should the Flatterers be Avoided?," 2011 Meeting Papers 1273, Society for Economic Dynamics.
    5. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    6. Deimen, Inga & Wirtz, Julia, 2016. "A Bandit Model of Two-Dimensional Uncertainty -- Rationalizing Mindsets," VfS Annual Conference 2016 (Augsburg): Demographic Change 145931, Verein für Socialpolitik / German Economic Association.
    7. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    8. Johannes Hoelzemann & Nicolas Klein, 2021. "Bandits in the lab," Quantitative Economics, Econometric Society, vol. 12(3), pages 1021-1051, July.
    9. Kaustav Das, 2014. "Strategic Experimentation with Competition and Private Arrival of Information," Discussion Papers 1404, University of Exeter, Department of Economics.
    10. , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    11. 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.
    12. Deimen, Inga & Wirtz, Julia, 2022. "Control, cost, and confidence: Perseverance and procrastination in the face of failure," Games and Economic Behavior, Elsevier, vol. 134(C), pages 52-74.
    13. Sorensen, Morten, 2007. "Learning by Investing: Evidence from Venture Capital," SIFR Research Report Series 53, Institute for Financial Research.
    14. Kaustav Das, 2017. "The Role of Heterogeneity in a model of Strategic Experimentation," Discussion Papers 1703, University of Exeter, Department of Economics.
    15. Rosenberg, Dinah & Salomon, Antoine & Vieille, Nicolas, 2013. "On games of strategic experimentation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 31-51.
    16. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    17. Xie, Yinxi & Xie, Yang, 2017. "Machiavellian experimentation," Journal of Comparative Economics, Elsevier, vol. 45(4), pages 685-711.
    18. 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.
    19. Mira Frick & Yuhta Ishii, 2015. "Innovation Adoption by Forward-Looking Social Learners," Cowles Foundation Discussion Papers 1877, Cowles Foundation for Research in Economics, Yale University.
    20. Kostas Bimpikis & Shayan Ehsani & Mohamed Mostagir, 2019. "Designing Dynamic Contests," Operations Research, INFORMS, vol. 67(2), pages 339-356, March.

    More about this item

    JEL classification:

    • J0 - Labor and Demographic Economics - - General
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • L0 - Industrial Organization - - General

    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:nbr:nberwo:19043. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.