Local contractivity of the process of a player rating variation in the Elo model with one adversary

V. A. Avdeev

Lomonosov Moscow State University

Abstract: We study the process of variation of a player rating in an infinite series of games with the same adversary in the Elo rating model. This process is shown to have a stationary distribution, an upper estimate of the rate of convergence to which is established. In a previous paper by the author, the existence of a limit distribution was proved under more stringent assumptions on the parameters of a rating model.

Keywords: Markov chains, iterated function system, limit distributions, local contractivity, models of rating systems.

UDC: 519.217.2

Received: 11.11.2014

DOI: 10.4213/dm1311

 English version: Discrete Mathematics and Applications, 2015, 25:5, 261–276

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