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STRATEGY, NONTRANSITIVE DOMINANCE AND THE EXPONENTIAL DISTRIBUTION
Author(s) -
Kaminsky K. S.,
Luks E. M.,
Nelson P. I.
Publication year - 1984
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1984.tb01224.x
Subject(s) - mathematics , exponential function , contest , exponential distribution , exponential growth , dominance (genetics) , distribution (mathematics) , mathematical economics , combinatorics , statistics , mathematical analysis , biochemistry , gene , chemistry , political science , law
Summary An easily programmed recursive formula for the evaluation of the distribution function of ratios of linear combinations of independent exponential random variables is developed. This formula is shown to yield the probability that one team beats another in a contest we call the special gladiator game. This game generates tournaments which exhibit nontransitive dominance and have some surprising consequences. Similar results are obtained for a recursive formula based on the geometric distribution.