Variance Distributions from Round Robin Series of Zero-Sum Competitions

17 Pages Posted: 8 Dec 2013 Last revised: 10 Dec 2013

See all articles by M. Kevin McGee

M. Kevin McGee

University of Wisconsin - Oshkosh

Eric Kuennen

University of Wisconsin - Oshkosh

Date Written: May 6, 2013

Abstract

When observations involve the outcomes of many series of simple zero-sum games, with competitor i facing competitor j in some of those games, competitor i’s observed value will not be independent of competitor j’s value. Therefore, the sampling distribution of the sum of squared deviations from the mean cannot be assumed to have a chi-squared distribution. In this paper we derive moments and the sampling distributions for the sum of squared deviations in these situations and show that they are asymptotically gamma distributions. For n competitors and sufficiently large number of games g in each series, the sampling distribution of sum of squared deviations will have a gamma distribution, with parameters α = (n−1)/2 and β = 2n/(n−1). This distribution approaches the chi-squared distribution as the number of competitors approaches infinity.

Keywords: Non-cooperative Games, Gamma distribution, Asymptotic Distribution Theory

JEL Classification: C12

Suggested Citation

McGee, M. Kevin and Kuennen, Eric, Variance Distributions from Round Robin Series of Zero-Sum Competitions (May 6, 2013). Available at SSRN: https://ssrn.com/abstract=2364654 or http://dx.doi.org/10.2139/ssrn.2364654

M. Kevin McGee (Contact Author)

University of Wisconsin - Oshkosh ( email )

800 Algoma Blvd
Oshkosh, WI WI 54901
United States

Eric Kuennen

University of Wisconsin - Oshkosh ( email )

800 Algoma Blvd
Oshkosh, WI WI 54901
United States

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