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WINNER PLAYS COMPETITION MODELS

Published online by Cambridge University Press:  18 October 2019

Yang Cao Open the ORCID record for Yang Cao [Opens in a new window]  and
Sheldon M. Ross
Yang Cao
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California Los Angeles CA 90089, USA E-mail: [email protected]; [email protected]
Sheldon M. Ross
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California Los Angeles CA 90089, USA E-mail: [email protected]; [email protected]
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Abstract

Suppose there are n players in an ongoing competition, with player i having value vi, and suppose that a game between i and j is won by i with probability vi/(vi + vj). Consider the winner plays competition where in each stage two players play a game, and the winner keeps playing in the next game. We consider two models for choosing its opponent, analyze both models as Markov chains, and determine their stationary probabilities as well as other quantities of interest.

Keywords

winner playsMarkov chainstationary probabilitiestime reversible
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 2 , April 2021 , pp. 236 - 241
Copyright
Copyright © Cambridge University Press 2019

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