Parameterized Analysis of Bribery in Challenge the Champ Tournaments

Juhi Chaudhary, Hendrik Molter, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Challenge the champ tournaments are one of the simplest forms of competition, where a (initially selected) champ is repeatedly challenged by other players.If a player beats the champ, then that player is considered the new (current) champ.Each player in the competition challenges the current champ once in a fixed order.The champ of the last round is considered the winner of the tournament.We investigate a setting where players can be bribed to lower their winning probability against the initial champ.The goal is to maximize the probability of the initial champ winning the tournament by bribing the other players, while not exceeding a given budget for the bribes.In previous work, it was shown that the problem can be solved in pseudo-polynomial time, and that it is in XP when parameterized by the number of players.We show that the problem is weakly NP-hard and W[1]-hard when parameterized by the number of players.On the algorithmic side, we show that the problem is fixed-parameter tractable (FPT) when parameterized either by the number of different bribe values or the number of different probability values.To this end, we establish several results that are of independent interest.In particular, we show that the product knapsack problem is W[1]hard when parameterized by the number of items in the knapsack, and that constructive bribery for cup tournaments is W[1]-hard when parameterized by the number of players.Furthermore, we present a novel way of designing mixed integer linear programs, ensuring optimal solutions where all variables are integers.

Original languageEnglish
Title of host publicationProceedings of the 33rd International Joint Conference on Artificial Intelligence, IJCAI 2024
EditorsKate Larson
PublisherInternational Joint Conferences on Artificial Intelligence
Pages2704-2712
Number of pages9
ISBN (Electronic)9781956792041
StatePublished - 1 Jan 2024
Event33rd International Joint Conference on Artificial Intelligence, IJCAI 2024 - Jeju, Korea, Republic of
Duration: 3 Aug 20249 Aug 2024

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823

Conference

Conference33rd International Joint Conference on Artificial Intelligence, IJCAI 2024
Country/TerritoryKorea, Republic of
CityJeju
Period3/08/249/08/24

ASJC Scopus subject areas

  • Artificial Intelligence

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