Approximately strategyproof tournament rules in the probabilistic setting

Kimberly Ding, S. Matthew Weinberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the manipulability of tournament rules which map the results of (n 2) pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match to improve their probability of winning by more than 1/3, and this is the best possible among any Condorcet-consistent tournament rule (which selects an undefeated team whenever one exists) [14, 15]. These lower bounds require the manipulators to know precisely the outcome of all future matches. We take a beyond worst-case view and instead consider tournaments which are “close to uniform”: the outcome of all matches are independent, and no team is believed to win any match with probability exceeding 1/2+ε. We show that Randomized Single Elimination Bracket [14] and a new tournament rule we term Randomized Death Match have the property that no pair of teams can manipulate the outcome of their match to improve their probability of winning by more than ε/3 + 2ε2/3, for all ε, and this is the best possible among any Condorcet-consistent tournament rule. Our main technical contribution is a recursive framework to analyze the manipulability of certain forms of tournament rules. In addition to our main results, this view helps streamline previous analysis of Randomized Single Elimination Bracket, and may be of independent interest.

Original languageEnglish (US)
Title of host publication12th Innovations in Theoretical Computer Science Conference, ITCS 2021
EditorsJames R. Lee
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771771
DOIs
StatePublished - Feb 1 2021
Event12th Innovations in Theoretical Computer Science Conference, ITCS 2021 - Virtual, Online
Duration: Jan 6 2021Jan 8 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume185
ISSN (Print)1868-8969

Conference

Conference12th Innovations in Theoretical Computer Science Conference, ITCS 2021
CityVirtual, Online
Period1/6/211/8/21

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Incentive compatibility
  • Recursive analysis
  • Social choice theory
  • Tournaments

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