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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 19043.

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Date of creation: May 2013
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Handle: RePEc:nbr:nberwo:19043

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  1. Kohlmann, M., 1982. "Existence of optimal controls for a partially observed semimartingale," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 13(2), pages 215-226, August.
  2. Keller, Godfrey & Rady, Sven, 2009. "Strategic Experimentation with Poisson Bandits," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 260, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  3. Nicolas Klein & Sven Rady, 2008. "Negatively Correlated Bandits," Working Papers, Bavarian Graduate Program in Economics (BGPE) 040, Bavarian Graduate Program in Economics (BGPE).
  4. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(2), pages 185-202, October.
  5. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, Econometric Society, vol. 73(1), pages 39-68, 01.
  6. M. L. Weitzman, 1978. "Optimal Search for the Best Alternative," Working papers 214, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
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