Abstract
Peter offers to play exactly one St Petersburg game with each of players, Paul, , Paul, whose conceivable pooling strategies are described by all possible probability distributions . Comparing infinite expectations, we characterize among all those admissible strategies for which the pooled winnings, each distributed as , yield a finite added value for each and every one of Paul, , Paul in comparison with their individual winnings , even though their total winnings is the same. We show that the added value of an admissible is just its entropy , and we determine the best admissible strategy . Moreover, for every and we construct semistable approximations to . We show in particular that has a proper semistable asymptotic distribution as along the entire sequence of natural numbers whenever for a sequence of admissible strategies, which is in sharp contrast to Peter offers to play exactly one St Petersburg game with each of players, Paul, ..., Paul, whose conceivable pooling strategies are described by all possible probability distributions . Comparing infinite expectations, we characterize among all those admissible strategies for which the pooled winnings, each distributed as , yield a finite added value for each and every one of Paul, ..., Paul in comparison with their individual winnings , even though their total winnings is the same. We show that the added value of an admissible is just its entropy , and we determine the best admissible strategy . Moreover, for every and we construct semistable approximations to . We show in particular that has a proper semistable asymptotic distribution as along the entire sequence of natural numbers whenever for a sequence of admissible strategies, which is in sharp contrast to , and the rate of convergence is very fast for . , and the rate of convergence is very fast for .
Citation
Sandor Csörgö. Gordon Simons. "Pooling strategies for St Petersburg gamblers." Bernoulli 12 (6) 971 - 1002, dec 2006. https://doi.org/10.3150/bj/1165269147
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