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Zbl 1138.60026
Kevei, Péter
Generalized $n$-Paul paradox. (English)
[J] Stat. Probab. Lett. 77, No. 11, 1043-1049 (2007). ISSN 0167-7152

The present paper has as starting point the results of S. Csörgö and G. Simons (2002--2006) on the classical St. Petersburg(1/2) game, played by two gamblers with an unbiased coin. The author considers the generalized St. Petersburg($p$) game with $p\in (0, 1)$ as the probability of the ``heads" at each throw of a possibly biased coin. An interesting result is that, while the stochastic dominance is preserved for the case of two players and an arbitrary parameter $p\in(0, 1)$, for three or more players, the admissibly pooled winning strategies generally fail to stochastically dominate the individual strategies. The main result of the article consists in determining the best admissible pooling strategies for a rational value of $p$, illustrating also the algebraic depth of the problem for an irrational value of the parameter $p$.
[Neculai Curteanu (Iaşi)]

MSC 2000:: *60E99 Distribution theory in probability theory
60G50 Sums of independent random variables

Keywords: generalized St. Petersburg games; comparison of infinite expectations; admissible pooling strategies

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Zentralblatt MATH Berlin [Germany]