Three-player shove is NP-complete

In two player games players are in conflict to each other and coalitions are not allowed but in three-player games two players can join their efforts against the third player. As a result, cooperation is a key-factor that deeply affects the complexity of three-player games. In the game of Shove, cooperation can be much more difficult than competition and, as a consequence, three-player Shove played on a set of rows of dominoes is NP-complete.

[1]  Alessandro Cincotti,et al.  On the complexity of three-player snort played on complete graphs , 2009, 2009 2nd IEEE International Conference on Computer Science and Information Technology.

[2]  Daniel E. Loeb,et al.  Stable Winning Coalitions , 1996 .

[3]  Philip D. Straffin,et al.  Three Person Winner-Take-All Games with McCarthy's Revenge Rule , 1985 .

[4]  A. Blokhuis.  Winning ways for your mathematical plays , 1984 .

[5]  S. Li,et al.  N-person Nim andn-person Moore's Games , 1978 .

[6]  A. Cincotti.  Three-player Toppling Dominoes is NP-complete , 2010, 2010 2nd International Conference on Computer Engineering and Technology.

[7]  Richard J. Nowakowski,et al.  Lessons in Play: An Introduction to Combinatorial Game Theory , 2007 .

[8]  Alessandro Cincotti,et al.  Notice of RetractionRed-Blue-Yellow Cherries is NP-Complete , 2010, 2010 Second International Conference on Computer Engineering and Applications.

[9]  A. Cincotti.  Three-player partizan games , 2005, Theor. Comput. Sci..

[10]  James Gary Propp.  Three-player impartial games , 2000, Theor. Comput. Sci..

[11]  J. Conway.  On Numbers and Games , 1976 .

[12]  A. Cincotti.  Three-player Hackenbush played on strings is NP-complete , 2008 .

[13]  Alessandro Cincotti.  Three-player Col played on trees isNP-complete , 2009 .