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Gambling Problems with a Limit Inferior Payoff

William D. Sudderth
Mathematics of Operations Research
Vol. 8, No. 2 (May, 1983), pp. 287-297
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3689594
Page Count: 11
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Gambling Problems with a Limit Inferior Payoff
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Abstract

In the gambling theory of Dubins and Savage, the payoff from a sequence of states is the limit superior of their utilities. Here the limit inferior is used instead. For example, if the utility function is the indicator of a set G, then the Dubins and Savage payoff is 1 when infinitely many states are in G, while the payoff here is 1 when all but finitely many states are in G. There are some resulting changes in the theory, but it remains true that optimal stationary plans exist for finite problems.

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