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


  • Roland G. Fryer, Jr.
  • Philipp Harms


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
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    References listed on IDEAS

    1. Nicolas Klein & Sven Rady, 2011. "Negatively Correlated Bandits," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 693-732.
    2. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    3. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    4. Rady, Sven & Keller, Godfrey, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    5. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    6. 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.
    7. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-654, May.
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    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

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