The Annals of Mathematical Statistics

On a Theorem of De Finetti, Oddsmaking, and Game Theory

David C. Heath and William D. Sudderth

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A theorem of de Finetti states that if odds are posted on each set in a finite partition of a probability space, then either the odds are consistent with a finitely additive probability measure or a sure win is possible. A generalization of this result is proved which in turn implies a generalization of Von Neumann's theorem on the existence of the value of a game. Also, two horse race examples are considered.

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Ann. Math. Statist., Volume 43, Number 6 (1972), 2072-2077.

First available in Project Euclid: 27 April 2007

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Heath, David C.; Sudderth, William D. On a Theorem of De Finetti, Oddsmaking, and Game Theory. Ann. Math. Statist. 43 (1972), no. 6, 2072--2077. doi:10.1214/aoms/1177690887.

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