The Annals of Applied Probability

The number of potential winners in Bradley–Terry model in random environment

Raphael Chetrite, Roland Diel, and Matthieu Lerasle

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Abstract

We consider a Bradley–Terry model in random environment where each player faces each other once. More precisely, the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number of potential winners. First, we prove that under moment and convexity conditions, the asymptotic probability that the best player wins is 1. The convexity condition is natural when the distribution of strengths is unbounded and, in the bounded case, when this convexity condition fails the number of potential winners grows at a rate depending on the tail of the distribution. We also study the minimal strength required for an additional player to win in this last case.

Article information

Source
Ann. Appl. Probab., Volume 27, Number 3 (2017), 1372-1394.

Dates
Received: October 2015
Revised: July 2016
First available in Project Euclid: 19 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1500451225

Digital Object Identifier
doi:10.1214/16-AAP1231

Mathematical Reviews number (MathSciNet)
MR3678473

Zentralblatt MATH identifier
1372.60138

Subjects
Primary: 60K37: Processes in random environments 60G70: Extreme value theory; extremal processes 60K40: Other physical applications of random processes

Keywords
Bradley–Terry model random environment paired comparisons extreme values

Citation

Chetrite, Raphael; Diel, Roland; Lerasle, Matthieu. The number of potential winners in Bradley–Terry model in random environment. Ann. Appl. Probab. 27 (2017), no. 3, 1372--1394. doi:10.1214/16-AAP1231. https://projecteuclid.org/euclid.aoap/1500451225


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