Random Knockout Tournaments
Ilan Adler, Yang Cao, Richard Karp, Erol A. Peköz, Sheldon M. Ross
Operations Research · 2017 · Volume 65 · Issue 6
Abstract
We consider a random knockout tournament among players 1,…, n , in which each match involves two players. The match format is specified by the number of matches played in each round, where the constitution of the matches in a round is random. Supposing that there are numbers v 1 ,…, v n such that a match between i and j will be won by i with probability v i /( v i + v j ), we obtain a lower bound on the tournament win probability for the best player, as well as upper and lower bounds for all of the players. We also obtain additional bounds by considering the best and worst formats for player 1 in the special case v 1 > v 2 = v 3 = … = v n .
Keywords
games/group decisions, stochastic model applications, probability, sequential decision analysis
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