The Game of n-Player White-Black Cutthroat and Its Complexity

Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 110)

Abstract

The game of N-player White-Black Cutthroat is an n-player version of White-Black Cutthroat, a two-player combinatorial game played on graphs. Because of queer games, i.e., games where no player has a winning strategy, cooperation is a key-factor in n-player games and, as a consequence, n-player White-Black Cutthroat played on stars is PSPACE-complete.

Keywords

Combinatorial game Complexity Cutthroat n-player game 

References

  1. 1.
    Albert MH, Nowakowski RJ, Wolfe D (2007) Lessons in play: an introduction to combinatorial game theory. AK Peters, USAMATHGoogle Scholar
  2. 2.
    Berlekamp ER, Conway JH, Guy RK (2001) Winning way for your mathematical plays. AK Peters, USAGoogle Scholar
  3. 3.
    Cincotti A (2005) Three-player partizan games. Theor Comput Sci 332(1–3):367–389CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Cincotti A (2009) On the complexity of n-player Hackenbush. Integers 9:621–627CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Cincotti A (2010) N-player partizan games. Theor Comput Sci 411(34–36):3224–3234CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Cincotti A (2010) On the complexity of n-player Toppling Dominoes. In: Ao SI, Castillo O, Douglas C, Feng DD, Lee J (eds) Lecture notes in engineering and computer science: Proceedings of the international MultiConference of engineers and computer scientists 2010, IMECS 2010, 17–19 March, 2010, Hong Kong. Newswood Limited, pp 461–464Google Scholar
  7. 7.
    Cincotti A (2010) On the complexity of n-player cherries. In: Hang Y, Desheng W, Sandhu PS (eds) Proceedings of the 2010 3rd IEEE international conference on computer science and information technology, 9-11 July, 2010, Chengdu. IEEE Press, pp 481–483CrossRefGoogle Scholar
  8. 8.
    Cincotti A (2010) On the complexity of some map-coloring multi-player games. In: Ao SI, Castillo O, Huang H (eds) Intelligent automation and computer engineering, vol 52 of LNEE. Springer, pp 271–278Google Scholar
  9. 9.
    Cincotti A (2010) The game of n-player Shove and its complexity. In: Ao SI, Castillo O, Huang H (eds) Intelligent control and computer engineering, vol 70 of LNEE. Springer, pp 285–292Google Scholar
  10. 10.
    Cincotti A (2011) N-player Cutthroat played on stars is PSPACE-complete. In: Ao SI, Castillo O, Douglas C, Feng DD, Lee J (eds) Lecture notes in engineering and computer science: Proceedings of the international MultiConference of engineers and computer scientists 2011, IMECS 2011, 16–18 March, 2011, Hong Kong. Newswood Limited, pp 269–271Google Scholar
  11. 11.
    Conway JH (2001) On numbers and games. A K Peters, USAMATHGoogle Scholar
  12. 12.
    Li SYR (1978) n-person nim and n-person moore’s games. Intl J Game Theor 7(1):31–36CrossRefMATHGoogle Scholar
  13. 13.
    Loeb DE (1996) Stable winning coalitions. In: Nowakowski RJ (ed) Games of no chance. Cambridge University Press, Cambridge, pp 451–471Google Scholar
  14. 14.
    McCurdy SK (2003) Cherries and cutthroat: two games on graphs. Master’s thesis, Dalhousie UniversityGoogle Scholar
  15. 15.
    McCurdy SK (2005) Cutthroat, an all-small game on graphs. INTEGERS: Electron J Combin Number Theor 5(2):#A13Google Scholar
  16. 16.
    Papadimitriou CH (1994) Computational complexity. Addison-Wesley, MAMATHGoogle Scholar
  17. 17.
    Propp JG (2000) Three-player impartial games. Theor Comput Sci 233(1–2):263–278CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Straffin Jr PD (1985) Three-person winner-take-all games with mc-carthy’s revenge rule. Coll Math J 16(5):386–394CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan

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