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

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  • 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
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    References listed on IDEAS

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    1. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
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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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