Sacheth Sathyanarayanan will present an MSE talk "On the Manipulability of Tournament Rules by Throwing Matches" on April 18, 2023 at 12:30pm in CS 301. The talk details follow below. Date: 04/18/2023 Time: 12.30 - 1.00 pm Location: COS 301 ( [ https://csguide.cs.princeton.edu/node/6653 | https://csguide.cs.princeton.edu/node/6653 ] ) Advisor: Matt Weinberg Reader: Mark Braverman Title: On the Manipulability of Tournament Rules by Throwing Matches Abstract: A Tournament Rule takes as input a set of {n choose 2} pairwise match results on n teams and (possibly randomly) selects a ranking of teams, with a prize associated to each place in the ranking. Two teams may manipulate their match outcomes to try and improve their expected prize winnings. [SSW 17] and subsequent works seek to understand the minimum manipulability among all " reasonabl e" ' tournament rules (i.e. tournament rules so that if team i beats team j , and also all teams that j beats, then i appears above j in the ranking with probability 1 ), when these two teams fix the match between them. Our work instead considers the possibility that two teams may both fix the match between them, and additionally throw matches to outside teams (that is, they can intentionally lose a match to a non-colluding team that they could have won). Our main result establishes that no two teams can gain more than 1/3 in expected prize winnings in Nested Randomized King of the Hill (introduced in [DFRSW 22], similar to QuickSort), by together fixing their match and throwing matches to external teams. This is optimal, as any " reasonable'' tournament admits the possibility of two teams gaining 1/3 in expected prize-winnings just by fixing the match between them.