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Denumerable-Armed Bandits

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  • Banks, Jeffrey S
  • Sundaram, Rangarajan K

Abstract

This paper studies the class of denumerable-armed (i.e., finite- or countably infinite-armed) Bandit problems with independent arms and geometric discounting over an infinite horizon in which each arm generates rewards according to one of a finite number of distributions. The authors derive certain continuity and curvature properties of the Gittins Index, and provide necessary and sufficient conditions under which this index characterizes the optimal strategies. They then show that at each point in time the arm selected by an optimal strategy will, with positive probability, remain an optimal selection forever. Copyright 1992 by The Econometric Society.

Suggested Citation

  • Banks, Jeffrey S & Sundaram, Rangarajan K, 1992. "Denumerable-Armed Bandits," Econometrica, Econometric Society, vol. 60(5), pages 1071-1096, September.
    • Handle: RePEc:ecm:emetrp:v:60:y:1992:i:5:p:1071-96
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    Cited by:

    1. Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
    2. Araujo, Luis & Camargo, Braz, 2006. "Information, learning, and the stability of fiat money," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1571-1591, October.
    3. Araujo, Luis & Camargo, Braz, 2008. "Endogenous supply of fiat money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 48-72, September.
    4. Kung-Yu Chen & Chien-Tai Lin, 2005. "A note on infinite-armed Bernoulli bandit problems with generalized beta prior distributions," Statistical Papers, Springer, vol. 46(1), pages 129-140, January.
    5. Benkert, Jean-Michel & Letina, Igor & Nöldeke, Georg, 2018. "Optimal search from multiple distributions with infinite horizon," Economics Letters, Elsevier, vol. 164(C), pages 15-18.
    6. Epstein, Gil S., 1996. "The extraction of natural resources from two sites under uncertainty," Economics Letters, Elsevier, vol. 51(3), pages 309-313, June.
    7. Luis Araujo & Braz Camargo, 2005. "Monetary Equilibrium with Decentralized Trade and Learning," University of Western Ontario, Departmental Research Report Series 20051, University of Western Ontario, Department of Economics.
    8. Forand, Jean Guillaume, 2015. "Keeping your options open," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 47-68.
    9. Camargo, Braz, 2014. "Learning in society," Games and Economic Behavior, Elsevier, vol. 87(C), pages 381-396.
    10. Chien-Tai Lin & C. Shiau, 2000. "Some Optimal Strategies for Bandit Problems with Beta Prior Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 397-405, June.
    11. Seok‐ju Cho, 2009. "Retrospective Voting and Political Representation," American Journal of Political Science, John Wiley & Sons, vol. 53(2), pages 276-291, April.
    12. Joseph Deutsch & Gil S. Epstein, 1998. "Changing a Decision Taken under Uncertainty: The Case of the Criminal's Location Choice," Urban Studies, Urban Studies Journal Limited, vol. 35(8), pages 1335-1343, July.
    13. Elena Pastorino, 2004. "Optimal Job Design and Career Dynamics in the Presence of Uncertainty," Econometric Society 2004 North American Summer Meetings 292, Econometric Society.
    14. 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.
    15. Cripps, Martin W., 2013. "Optimal learning of a set: Or how to edit a journal if you must," Economics Letters, Elsevier, vol. 120(3), pages 384-388.
    16. Bergemann, Dirk & Valimaki, Juuso, 1996. "Learning and Strategic Pricing," Econometrica, Econometric Society, vol. 64(5), pages 1125-1149, September.
    17. Klimenko, Mikhail M., 2004. "Industrial targeting, experimentation and long-run specialization," Journal of Development Economics, Elsevier, vol. 73(1), pages 75-105, February.
    18. Bergemann, Dirk & Valimaki, Juuso, 2001. "Stationary multi-choice bandit problems," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1585-1594, October.
    19. Keller, Godfrey & Oldale, Alison, 2003. "Branching bandits: a sequential search process with correlated pay-offs," Journal of Economic Theory, Elsevier, vol. 113(2), pages 302-315, December.

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