Winning is not the only metric: the complexity of control manipulation in knockout tournaments for a redefined goal

Abstract

We study control manipulation by generalizing the notion of success in knockout tournaments. The definition of success can be broadened to include other concepts of accomplishment rather than focusing solely on the identity of the tournament winner. Manipulation can be done in favor of diverse stakeholders. Each stakeholder may have a different goal to maximize concerning its party of interest—a player or a set of players. To formalize this, we use a weighted tournament graph model and define a score function that measures the success of the party of interest. Given the match outcome for any pair of players, we analyze the complexity of performing the manipulation for various manipulation types. We consider manipulation in favor of a single player achieving the highest score in the tournament and in favor of a set of players achieving a higher score than the complementary set. Furthermore, using the suggested model, we analyze the complexities of the manipulations done in favor of a particular player or set that wishes to prevail over another player or set. We define problems that address these types of manipulation and analyze their complexity. Although the general problems are NP-complete, we show broad scenarios in which the problems are polynomial-time solvable.