Geodesic
The Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi
Mathematica Applicanda, Tome 44 (2016) no. 1, pp. 45-61.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The optimal stopping problem of maximizing the probability of stopping on the last success of a finite sequence of independent Bernoulli trials has been studied by Hill and Krengel (1992), Hsiau and Yang (2000) and Bruss (2000). The optimal stopping rule of Bruss stops when the sum of the odds of future successes is less than one. This Sum-the-Odds Theorem is extended in several ways. First, an infinite number of Bernoulli trials is allowed. Second, the payoff for not stopping is allowed to be different from the payoff of stopping on a success that is not the last success. Third, the Bernoulli variables are allowed to be dependent. Fourth, the model is generalized to allow at each stage other dependent random variables to be observed that may influence the assessment of the probability of success at future stages. Finally, application is made to a game of Sakaguchi (1984) in which two players vie for predicting the last success, but in which one of the players is given priority of acting first. 
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Thomas S. Ferguson. The Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi. Mathematica Applicanda, Tome 44 (2016) no. 1, pp.  45-61. doi : 10.14708/ma.v44i1.1192. http://geodesic.mathdoc.fr/articles/10.14708/ma.v44i1.1192/

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