Random Knockout Tournaments

Ilan Adler, Yang Cao, Richard Karp, Erol A. Peköz, Sheldon M. Ross (2016), Random Knockout Tournaments, INFORMS Operations Research Journal

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 v1, . . . , vn such that a match between i and j will be won by i with probability vi/(vi +vj), 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 v1 > v2 > v3 · · · vn.