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WINNER PLAYS STRUCTURE IN RANDOM KNOCKOUT TOURNAMENTS

Published online by Cambridge University Press:  05 December 2018

Yang Cao
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA E-mail: cao573@usc.edu; smross@usc.edu
Sheldon M. Ross
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA E-mail: cao573@usc.edu; smross@usc.edu

Abstract

Suppose there are n players, with player i having value vi > 0, and suppose that a game between i and j is won by i with probability vi/(vi + vj). In the winner plays random knockout tournament, we suppose that the players are lined up in a random order; the first two play, and in each subsequent game the winner of the last game plays the next in line. Whoever wins the game involving the last player in line, is the tournament winner. We give bounds on players’ tournament win probabilities and make some conjectures. We also discuss how simulation can be efficiently employed to estimate the win probabilities.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2018 

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References

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