Efficient Simulation of a Random Knockout Tournament

Journal of Industrial and Systems Engineering, Vol. 2, No. 2, pp 88-96. Summer 2008

Posted: 3 Nov 2013

See all articles by Sheldon Ross

Sheldon Ross

University of Southern California - Viterbi School of Engineering

Samim Ghamami

Securities and Exchange Commission (SEC); New York University (NYU); University of California, Berkeley - Center for Risk Management Research

Date Written: August 20, 2008

Abstract

We consider the problem of using simulation to efficiently estimate the win probabilities for participants in a general random knockout tournament. Both of our proposed estimators, one based on the notion of “observed survivals” and the other based on conditional expectation and post-stratification, are highly effective in terms of variance reduction when compared to the raw simulation estimator. For the special case of a classical 2^n -player random knockout tournament, where each survivor of the previous round plays in the current round, a second conditional expectation based estimator is introduced. At the end, we compare our proposed simulation estimators based on a numerical example and in terms of both variance reduction and the time to complete the simulation experiment. Based on our empirical study, the method of “observed survivals” is the most efficient method.

Keywords: Efficient Monte Carlo simulation, random knockout tournaments

JEL Classification: C15

Suggested Citation

Ross, Sheldon and Ghamami, Samim, Efficient Simulation of a Random Knockout Tournament (August 20, 2008). Journal of Industrial and Systems Engineering, Vol. 2, No. 2, pp 88-96. Summer 2008, Available at SSRN: https://ssrn.com/abstract=2346937

Sheldon Ross

University of Southern California - Viterbi School of Engineering ( email )

3650 McClintock Ave
Los Angeles, CA
United States

Samim Ghamami (Contact Author)

Securities and Exchange Commission (SEC) ( email )

450 Fifth Street, NW
Washington, DC 20549-1105
United States

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
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New York, NY 10003-711
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University of California, Berkeley - Center for Risk Management Research ( email )

581 Evans Hall
Berkely, CA 94720
United States

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