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Published May 1994 | Published
Journal Article Open

Switching Costs and the Gittins Index


The Theorem of Gittins and Jones (1974) is, perhaps, the single most powerful result in the literature on Bandit problems. This result establishes that in independent-armed Bandit problems with geometric discounting over an infinite horizon, all optimal strategies may be obtained by solving a family of simple optimal stopping problems that associate with each arm an index known as the dynamic allocation index or, more popularly, as the Gittins index. Importantly, the Gittins index of an arm depends solely on the characteristics of that arm and the rate of discounting, and is otherwise completely independent of the problem under consideration. These features simplify significantly the task of characterizing optimal strategies in this class of problems.

Additional Information

© 1994 The Econometric Society. Manuscript received March, 1992; final revision received August, 1993. We are very grateful to Andy McLennan for several helpful conversations. We would also like to thank Martin Hellwig and two referees for their comments. The first author gratefully acknowledges financial support provided by the Sloan Foundation and the NSF. An earlier version of this paper was written during the second author's sabbatical at the California Institute of Technology, and he would like to thank them for their hospitality.

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August 20, 2023
August 20, 2023