Advertisement

Controlling sub-tournaments: easy or hard problem?

Theoretical vs. practical analysis
  • Noa EidelsteinEmail author
  • Lior Aronshtam
  • Eitan Eidelstein
  • Tammar Shrot
Article
  • 11 Downloads

Abstract

Is it possible for the organizers of a sports tournament to influence the identity of the final winner by manipulating the initial seeding of the tournament? Is it possible to ensure a specific good (i.e. king) player will win at least a certain number of rounds in the tournament? This paper investigates these questions both by means of a theoretical method and a practical approach. The theoretical method focuses on the attempt to identify sufficient conditions to ensure a king player will win at least a pre–defined number of rounds in the tournament. It seems that the tournament must adhere to very strict conditions to ensure the outcome, suggesting that this is a hard problem. The practical approach, on the other hand, uses the Monte Carlo method to demonstrate that these problems are solvable in realistic computational time. A comparison of the results lead to the realization that players with equivalent representation might relax the actual complexity of the problem, and enable manipulation of tournaments that can be controlled in reality.

Keywords

Manipulation in sports Knockout tournaments Monte Carlo algorithm Control Manipulation Voting King player 

Mathematics Subject Classification (2010)

68Q25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Aronshtam, L., Cohen, H., Shrot, T.: Tennis manipulation: Can we help serena williams win another tournament? Ann. Math. Artif. Intell. 80(2), 153–169 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Arrow, KJ., Sen, A., Suzumura, K.: Handbook of Social Choice and Welfare, vol. 2. Elsevier (2010)Google Scholar
  3. 3.
    Aziz, H., Gaspers, S., Mackenzie, S., Mattei, N., Stursberg, P., Walsh, T.: Fixing a balanced knockout tournament. In: AAAI, pp. 552–558 (2014)Google Scholar
  4. 4.
    Bartholdi, J.J., Tovey, C.A., Trick, M.A.: The computational difficulty of manipulating an election. Soc. Choice Welf. 6(3), 227–241 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bartholdi, J.J, Tovey, C.A, Trick, M.A: The computational difficulty of manipulating an election. Soc. Choice Welf. 6(3), 227–241 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bartholdi, Jo.J., Tovey, C.A., Trick, M.A.: How hard is it to control an election? Math. Comput. Model. 16(8–9), 27–40 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Betzler, N., Uhlmann, J.: Parameterized complexity of candidate control in elections and related digraph problems. Theor. Comput. Sci. 410(52), 5425–5442 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Binder, K., Heermann, D. W.: Monte Carlo Simulation in Statistical Physics. Springer (2002)Google Scholar
  9. 9.
    Chang, M.: Monte Carlo Simulation for the Pharmaceutical Industry CRC Biostatistics Series (2010)Google Scholar
  10. 10.
    Chaslot, G, Saito, J.t., Uiterwijk, J.W.H.M., Bouzy, B., Herik, H.J.: Monte-Carlo strategies for computer goGoogle Scholar
  11. 11.
    Chaslot, G.M.J-B., Winands, M.H.M., van den Herik, J.H., Uiterwijk, J.W.H.M., Bouzy, B.: Progressive strategies for monte-carlo tree search. Math. Nat. Comput. 4, 343–357 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Conitzer, V., Sandholm, T., Lang, J.: When are elections with few candidates hard to manipulate? J. ACM (JACM) 54(3), 14 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Erdélyi, G., Fellows, M.R., Rothe, J., Schend, L.: Control complexity in bucklin and fallback voting: An experimental analysis. J. Comput. Syst. Sci. 81(4), 661–670 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. SSC-4(2), 100–107 (1968)CrossRefGoogle Scholar
  15. 15.
    Hazon, N., Dunne, P.E., Kraus, S, Wooldridge, M.: How to rig elections and competitions. Proc. COMSOC (2008)Google Scholar
  16. 16.
    Holte, R., Schaeffer, J., Felner, A.: Mechanical generation of admissible heuristics. Part I: Heuristics, 43 (2010)Google Scholar
  17. 17.
    Kim, M.P, Suksompong, W., Williams, V.V.: Who can win a single-elimination tournament? In: AAAI, pp 516–522 (2016)Google Scholar
  18. 18.
    Kim, M.P., Williams, V.V.: Fixing tournaments for kings, chokers, and more. In: IJCAI, pp. 561–567 (2015)Google Scholar
  19. 19.
    Korf, R.E.: Depth-first iterative-deepening: An optimal admissible tree search. Artif. Intell. 27, 97–109 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Lang, J., Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Winner determination in sequential majority voting. In: IJCAI, vol. 7, pp. 1372–1377 (2007)Google Scholar
  21. 21.
    Lang, J., Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Winner determination in sequential majority voting. In: IJCAI, vol. 7, pp. 1372–1377 (2007)Google Scholar
  22. 22.
    Mattei, N., Goldsmith, J., Klapper, A., Mundhenk, M.: On the complexity of bribery and manipulation in tournaments with uncertain information. J. Appl. Log. 13(4), 557–581 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Moulin, H., Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D.: Handbook of Computational Social Choice. Cambridge University Press (2016)Google Scholar
  24. 24.
    Pearl, J.: Heuristics: Intelligent Search Strategies for Computer Problem-Solving. Addison-Wesley, Reading (1985)Google Scholar
  25. 25.
    Russell, T., Van Beek, P: Detecting manipulation in cup and round robin sports competitions. In: 2012 IEEE 24th International Conference on Tools with Artificial Intelligence (ICTAI), vol. 1, pp. 285–290. IEEE (2012)Google Scholar
  26. 26.
    Russell, T., Walsh, T.: Manipulating tournaments in cup and round robin competitions. In: International Conference on Algorithmic DecisionTheory, pp. 26–37. Springer (2009)Google Scholar
  27. 27.
    Schadd, M.P.D., Winands, M.H.M., Van Den Herik, J.H., Aldewereld, H.: Addressing np-complete puzzles with monte-carlo methods. In: Proceedings of the AISB 2008 Symposium on Logic and the Simulation of Interaction and Reasoning, vol. 9 (2008)Google Scholar
  28. 28.
    Shrot, T., Aumann, Y., Kraus, S.: On agent types in coalition formation problems. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 757–764. International Foundation for Autonomous Agents and Multiagent Systems (2010)Google Scholar
  29. 29.
    Stanton, I., Williams, V.V.: Manipulating stochastically generated single-elimination tournaments for nearly all players. In: WINE, pp. 326–337. Springer (2011)Google Scholar
  30. 30.
    Stanton, I., Williams, V.V.: Rigging tournament brackets for weaker players. In: IJCAI Proceedings-International Joint Conference on Artificial Intelligence, vol. 22, pp. 357 (2011)Google Scholar
  31. 31.
    Thuc, V u, Altman, Alon, Shoham, Yoav: On the Agenda Control Problem in Knockout Tournaments. Proc COMSOC (2008)Google Scholar
  32. 32.
    Vu, T., Altman, A., Shoham, Y.: On the complexity of schedule control problems for knockout tournaments. In: Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 225–232. International Foundation for Autonomous Agents and Multiagent Systems (2009)Google Scholar
  33. 33.
    Williams, V.V.: Fixing a tournament. In: AAAI (2010)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ben Gurion UniversityBeer ShevaIsrael
  2. 2.Sami Shamoon College of EngineeringAshdodIsrael
  3. 3.Department of PhysicsNRCNBeer ShevaIsrael
  4. 4.Tel Aviv UniversityTel Aviv-YafoIsrael

Personalised recommendations