ArticleEntropy (Basel, Switzerland)2026
The Gittins Index for a Transparent One-Armed Bandit with a Continuous Payoff Spectrum in Equilibrium States.
Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
We present an analogue of the classical Gittins index for a one-armed decision problem with a continuous spectrum of payoffs. The model assumes that the decision-maker observes independent realizations of a random variable and, at each step, decides whether to accept the current opportunity or continue observing. We show that the optimal strategy takes the form of a threshold rule, while the corresponding reservation index is determined by a one-dimensional fixed-point equation with a direct decision-theoretic interpretation. The model is illustrated with an example of bookmaker betting related to horse racing and the Kelly criterion. This perspective allows the proposed index to be viewed as a threshold of informational advantage. This, in turn, points to potential applications in optimal stopping problems and decision-making under uncertainty.
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