Summary
General linear combinations of independent winnings in generalized \St~Petersburg games are interpreted as individual gains that result from pooling strategies of different cooperative players. A weak law of large numbers is proved for all such combinations, along with some almost sure results for the smallest and largest accumulation points, and a considerable body of earlier literature is fitted into this cooperative framework. Corresponding weak laws are also established, both conditionally and unconditionally, for random pooling strategies.
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Csörgő, S., Simons, G. Laws of large numbers for cooperative St. Petersburg gamblers. Period Math Hung 50, 99–115 (2005). https://doi.org/10.1007/s10998-005-0005-9
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DOI: https://doi.org/10.1007/s10998-005-0005-9