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The Game of n-Player Shove and Its Complexity

  • Alessandro CincottiEmail author
Chapter
  • 676 Downloads
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 70)

Abstract

Why are n-player games much more complex than two-player games? Is it much more difficult to cooperate or to compete? The game of n-player Shove is the n-player version of Shove, a two-player combinatorial game. In multi-player games, because of the possibility to form alliances, cooperation between players is a key-factor to determine the winning coalition and, as a consequence, n-player Shove played on a set of finite strips is \(\mathcal{PSPACE}\)-complete.

Keywords

Combinatorial games Complexity n-Player Shove 

References

  1. 1.
    Albert, M.H., Nowakowski, R.J., Wolfe, D.: Lessons in Play: An Introduction to Combinatorial Game Theory. AK Peters, Wellesley (2007) Google Scholar
  2. 2.
    Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Way for Your Mathematical Plays. AK Peters, Wellesley (2001) Google Scholar
  3. 3.
    Cincotti, A.: Three-player partizan games. Theoret. Comput. Sci. 332(1–3), 367–389 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Cincotti, A.: Three-player Hackenbush played on strings is \(\mathcal{NP}\)-complete. In: Ao, S.I., Castillo, O., Douglas, C., Feng, D.D., Lee, J. (eds.) Lecture Notes in Engineering and Computer Science: Proceedings of the International MultiConference of Engineers and Computer Scientists 2008, IMECS 2008, Hong Kong, 19–21 March 2008, pp. 226–230 (2008). Newswood Limited Google Scholar
  5. 5.
    Cincotti, A.: On the complexity of n-player Hackenbush. Integers 9, 621–627 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Cincotti, A.: On the complexity of three-player snort played on complete graphs. In: Li, W., Zhou, J. (eds.) Proceedings of the 2nd IEEE International Conference on Computer Science and Information Technology, Beijing, 8–11 August 2009, pp. 68–70. IEEE Press, New York (2009). Google Scholar
  7. 7.
    Cincotti, A.: Three-player col played on trees is \(\mathcal{NP}\)-complete. In: Ao, S.I., Castillo, O., Douglas, C., Feng, D.D., Lee, J. (eds.) Lecture Notes in Engineering and Computer Science: Proceedings of the International MultiConference of Engineers and Computer Scientists 2009, IMECS 2009, Hong Kong, 18–20 March 2009, pp. 445–447 (2009). Newswood Limited Google Scholar
  8. 8.
    Cincotti, A.: On the complexity of some map-coloring multi-player games. In: Ao, S.I., Castillo, O., Huang, H. (eds.) Intelligent Automation and Computer Engineering. LNEE, vol. 52, Springer, Berlin (2010) Google Scholar
  9. 9.
    Cincotti, A.: On the complexity of n-player toppling dominoes. In: Ao, S.I., Castillo, O., Douglas, C., Feng, D.D., Lee, J. (eds.) Lecture Notes in Engineering and Computer Science: Proceedings of the International MultiConference of Engineers and Computer Scientists 2010, IMECS 2010, Hong Kong, 17–19 March 2010, pp. 461–464 (2010). Newswood Limited Google Scholar
  10. 10.
    Cincotti, A.: Three-player toppling dominoes is \(\mathcal{NP}\)-complete. In: Mahadevan, V., Zhou, J. (eds.) Proceedings of the 2nd International Conference on Computer Engineering and Technology, Chengdu, 16–18 April 2010, pp. 548–550. IEEE Press, New York (2010) Google Scholar
  11. 11.
    Conway, J.H.: On Numbers and Games. AK Peters, Wellesley (2001) zbMATHGoogle Scholar
  12. 12.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, New York (1979) zbMATHGoogle Scholar
  13. 13.
    Li, S.Y.R.: n-Person nim and n-person moore’s games. Int. J. Game Theory 7(1), 31–36 (1978) zbMATHCrossRefGoogle Scholar
  14. 14.
    Loeb, D.E.: Stable winning coalitions. In: Nowakowski, R.J. (ed.) Games of No Chance, pp. 451–471. Cambridge University Press, Cambridge (1996) Google Scholar
  15. 15.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994) zbMATHGoogle Scholar
  16. 16.
    Propp, J.G.: Three-player impartial games. Theoret. Comput. Sci. 233(1–2), 263–278 (2000) MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Straffin Jr., P.D.: Three-person winner-take-all games with Mc-Carthy’s revenge rule. Coll. Math. J. 16(5), 386–394 (1985) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

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

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