A generalization of the Bradley–Terry model for draws in chess with an application to collusion

Robin K.S. Hankin

Journal of Economic Behavior & Organization, 2020, vol. 180, issue C, 325-333

Abstract: In inference problems where the dataset comprises Bernoulli outcomes of paired comparisons, the Bradley–Terry model offers a simple and easily interpreted framework. However, it does not deal easily with chess because of the existence of draws, and the white player advantage. Here I present a new generalization of Bradley–Terry in which a chess game is regarded as a three-way competition between the two players and an entity that wins if the game is drawn. Bradley–Terry is then further generalized to account for the white player advantage by positing a second entity whose strength is added to that of the white player. These techniques afford insight into players’ strengths, response to playing black or white, and risk-aversion as manifested by probability of drawing. The likelihood functions arising are easily optimised numerically. I analyse a number of datasets of chess results, including the infamous 1963 World Chess Championships, in which Fischer accused three Soviet players of collusion. I conclude, on the basis of a dataset that includes only the scorelines at the event itself, that the Candidates Tournament (Curaçao 1962) exhibits evidence of collusion (p<10−5), in agreement with previous work. I also present scoreline evidence for the effectiveness of such a drawing cartel: noncollusive games are less detrimental to future play than collusive games (p<10−5).

Keywords: Chess draws; Bradley–Terry; Likelihood; Chess collusion; Friendly ghost (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jeborg:v:180:y:2020:i:c:p:325-333

DOI: 10.1016/j.jebo.2020.10.015

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