Merging asymptotic expansions for cooperative gamblers in generalized St. Petersburg games
type: Item
instance of: scholarly article
title: Merging asymptotic expansions for cooperative gamblers in generalized St. Petersburg games
zbMATH Open document ID: 1199.60052
published in: Acta Mathematica Hungarica
publication date: 2009-12-29T00:00:00Z
review text: Merging asymptotic expansions are established for the distribution functions of suitably centered and normed linear combinations of winnings in a full sequence of generalized St. Petersburg games, where a linear combination is viewed as the share of any one of \(n\) cooperative gamblers, who play with a pooling strategy. The expansions are given in terms of Fourier-Stieltjes transforms and are constructed from suitably chosen members of the classes of subsequential semistable infinitely divisible asymptotic distributions for the total winnings of the \(n\) players and from their pooling strategy, where the classes themselves are determined by the two parameters of game. For all values of the tail parameter, the expansions yield best possible rates of uniform merge. Surprisingly, it turns out that for a subclass of strategies, not containing the averaging uniform strategy, the merging approximations reduce to asymptotic expansions of the usual type, derived from a proper limiting distribution. The Fourier-Stieltjes transforms are shown to be numerically invertible in general and it is also demonstrated that the merging expansions provide excellent approximations even for very small \(n\).
reviewed by: Ludwig Paditz
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 91A60
zbMATH DE Number: 5651920
zbMATH Keywords: generalized St. Petersburg games
zbMATH Keywords: cooperative players
zbMATH Keywords: pooling strategies
zbMATH Keywords: linear combinations
zbMATH Keywords: asymptotic distributions
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: best rates of merge
author: Sándor Csörgő
author: Peter Kevei
MaRDI profile type: Publication
full work available at URL: s10474-008-7193-8
OpenAlex ID: W1992656411
Wikidata QID: Q64023170
cites work: Q4815550
cites work: Q5696192
cites work: Q5426260
cites work: Fourier analysis of semistable distributions
cites work: Laws of large numbers for cooperative St. Petersburg gamblers
cites work: Pooling strategies for St. Petersburg gamblers
cites work: Note on the inversion theorem
cites work: Generalized \(n\)-Paul paradox
cites work: A limit theorem which clarifies the ‘Petersburg Paradox'
cites work: Q4515262
cites work: The accuracy of merging approximation in generalized St. Petersburg games
cites work: On the asymptotic distribution of sums of independent identically distributed random variables
DOI: 10.1007/S10474-008-7193-8
description: scientific article; zbMATH DE number 5651920