Document Open Access Logo

On Controlling Knockout Tournaments Without Perfect Information

Authors Václav Blažej , Sushmita Gupta , M. S. Ramanujan , Peter Strulo

PDF
Thumbnail PDF

File

LIPIcs.IPEC.2024.7.pdf
  • Filesize: 0.97 MB
  • 15 pages

Document Identifiers

Author Details

Václav Blažej
  • University of Warwick, Coventry, UK
Sushmita Gupta
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
M. S. Ramanujan
  • University of Warwick, Coventry, UK
Peter Strulo
  • University of Warwick, Coventry, UK

Funding

Supported by the Engineering and Physical Sciences Research Council (grant number EP/V044621/1).
  • Gupta, Sushmita: Supported by SERB’s MATRICS Grant (MTR/2021/000869) and SUPRA Grant (SPR/2021/000860).

Cite As Get BibTex

Václav Blažej, Sushmita Gupta, M. S. Ramanujan, and Peter Strulo. On Controlling Knockout Tournaments Without Perfect Information. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.IPEC.2024.7

Abstract

Over the last decade, extensive research has been conducted on the algorithmic aspects of designing single-elimination (SE) tournaments. Addressing natural questions of algorithmic tractability, we identify key properties of input instances that enable the tournament designer to efficiently schedule the tournament in a way that maximizes the chances of a preferred player winning. Much of the prior algorithmic work on this topic focuses on the perfect (complete and deterministic) information scenario, especially in the context of fixed-parameter algorithm design. Our contributions constitute the first fixed-parameter tractability results applicable to more general settings of SE tournament design with potential imperfect information.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized algorithms
  • Tournament design
  • Imperfect information

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Haris Aziz, Serge Gaspers, Simon Mackenzie, Nicholas Mattei, Paul Stursberg, and Toby Walsh. Fixing balanced knockout and double elimination tournaments. Artif. Intell., 262:1-14, 2018. URL: https://doi.org/10.1016/J.ARTINT.2018.05.002.
  2. John J. Bartholdi, Craig A. Tovey, and Michael A. Trick. The computational difficulty of manipulating an election. Social Choice and Welfare, 6(3):227-241, 1989. URL: http://www.jstor.org/stable/41105918.
  3. John J. Bartholdi, Craig A. Tovey, and Michael A. Trick. How hard is it to control an election? Mathematical and Computer Modelling, 16(8):27-40, 1992. URL: https://doi.org/10.1016/0895-7177(92)90085-Y.
  4. Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang, and Ariel D. Procaccia. Handbook of Computational Social Choice. Cambridge University Press, USA, 1st edition, 2016. Google Scholar
  5. Juhi Chaudhary, Hendrik Molter, and Meirav Zehavi. How to make knockout tournaments more popular? CoRR, abs/2309.09967, 2023. URL: https://doi.org/10.48550/arXiv.2309.09967.
  6. Juhi Chaudhary, Hendrik Molter, and Meirav Zehavi. Parameterized analysis of bribery in challenge the champ tournaments. CoRR, abs/2403.17587, 2024. URL: https://doi.org/10.48550/arXiv.2403.17587.
  7. Connolly and Rendleman. Tournament qualification, seeding and selection efficiency. Technical Report 2011-96, Tuck School of Business, 2011. Google Scholar
  8. András Frank and Éva Tardos. An application of simultaneous diophantine approximation in combinatorial optimization. Comb., 7(1):49-65, 1987. URL: https://doi.org/10.1007/BF02579200.
  9. Sushmita Gupta, Sanjukta Roy, Saket Saurabh, and Meirav Zehavi. When rigging a tournament, let greediness blind you. In IJCAI, pages 275-281. ijcai.org, 2018. URL: https://doi.org/10.24963/IJCAI.2018/38.
  10. Sushmita Gupta, Sanjukta Roy, Saket Saurabh, and Meirav Zehavi. Winning a tournament by any means necessary. In IJCAI, pages 282-288. ijcai.org, 2018. URL: https://doi.org/10.24963/IJCAI.2018/39.
  11. Sushmita Gupta, Saket Saurabh, Ramanujan Sridharan, and Meirav Zehavi. On succinct encodings for the tournament fixing problem. In IJCAI, pages 322-328. ijcai.org, 2019. URL: https://doi.org/10.24963/IJCAI.2019/46.
  12. Sushmita Gupta, Ramanujan Sridharan, and Peter Strulo. An exercise in tournament design: When some matches must be scheduled. In AAAI, pages 9749-9756. AAAI Press, 2024. URL: https://doi.org/10.1609/AAAI.V38I9.28833.
  13. Noam Hazon, Paul E. Dunne, Sarit Kraus, and Michael J. Wooldridge. How to rig elections and competitions. In Second International Workshop on Computational Social Choice (COMSOC), pages 301-312, 2008. Google Scholar
  14. Jeff Horen and Raymond Riezman. Comparing draws for single elimination tournaments. Oper. Res., 33(2):249-262, 1985. URL: https://doi.org/10.1287/OPRE.33.2.249.
  15. Hendrik W. Lenstra Jr. Integer programming with a fixed number of variables. Math. Oper. Res., 8(4):538-548, 1983. URL: https://doi.org/10.1287/MOOR.8.4.538.
  16. Ravi Kannan. Minkowski’s convex body theorem and integer programming. Math. Oper. Res., 12(3):415-440, 1987. URL: https://doi.org/10.1287/MOOR.12.3.415.
  17. Michael P. Kim and Virginia Vassilevska Williams. Fixing tournaments for kings, chokers, and more. In IJCAI, pages 561-567. AAAI Press, 2015. URL: http://ijcai.org/Abstract/15/085.
  18. Kathrin Konczak and Jérôme Lang. Voting procedures with incomplete preferences. In IJCAI-05 Multidisciplinary Workshop on Advances in Preference Handling, 2005. Google Scholar
  19. Jérôme Lang, Maria Silvia Pini, Francesca Rossi, Kristen Brent Venable, and Toby Walsh. Winner determination in sequential majority voting. In IJCAI, pages 1372-1377, 2007. URL: http://ijcai.org/Proceedings/07/Papers/221.pdf.
  20. J.-Francois Laslier. Tournament solutions and majority voting. Springer-Verlag, 1997. Google Scholar
  21. Nicholas Mattei, Judy Goldsmith, Andrew Klapper, and Martin Mundhenk. On the complexity of bribery and manipulation in tournaments with uncertain information. J. Appl. Log., 13(4):557-581, 2015. URL: https://doi.org/10.1016/J.JAL.2015.03.004.
  22. Maria Silvia Pini, Francesca Rossi, Kristen Brent Venable, and Toby Walsh. Possible and necessary winners in voting trees: majority graphs vs. profiles. In AAMAS, pages 311-318. IFAAMAS, 2011. URL: http://portal.acm.org/citation.cfm?id=2030516&CFID=69153967&CFTOKEN=38069692.
  23. M. S. Ramanujan and Stefan Szeider. Rigging nearly acyclic tournaments is fixed-parameter tractable. In AAAI, pages 3929-3935. AAAI Press, 2017. URL: https://doi.org/10.1609/AAAI.V31I1.11132.
  24. Sherwin Rosen. Prizes and incentives in elimination tournaments. The American Economic Review, 76(4):701-715, 1986. Google Scholar
  25. Tyrel Russell and Peter van Beek. An empirical study of seeding manipulations and their prevention. In IJCAI, pages 350-356. IJCAI/AAAI, 2011. URL: https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-068.
  26. Isabelle Stanton and Virginia Vassilevska Williams. Manipulating stochastically generated single-elimination tournaments for nearly all players. In WINE, volume 7090 of Lecture Notes in Computer Science, pages 326-337. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-25510-6_28.
  27. Isabelle Stanton and Virginia Vassilevska Williams. Rigging tournament brackets for weaker players. In IJCAI, pages 357-364. IJCAI/AAAI, 2011. URL: https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-069.
  28. Tullock. Toward a theory of the rent-seeking society. Texas A&M University Press, 1980. Google Scholar
  29. Thuc Vu, Alon Altman, and Yoav Shoham. On the complexity of schedule control problems for knockout tournaments. In AAMAS (1), pages 225-232. IFAAMAS, 2009. URL: https://dl.acm.org/citation.cfm?id=1558044.
  30. Virginia Vassilevska Williams. Fixing a tournament. In AAAI, pages 895-900. AAAI Press, 2010. URL: https://doi.org/10.1609/AAAI.V24I1.7617.
  31. Meirav Zehavi. Tournament fixing parameterized by feedback vertex set number is FPT. In AAAI, pages 5876-5883. AAAI Press, 2023. URL: https://doi.org/10.1609/AAAI.V37I5.25728.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact