Krawec (2012) introduced a method of analyzing multi-player impartial games, and derived a recursive function capable of determining which of the   n     n        players has a winning strategy. The present paper is devoted to the game “Misere   N     N       -pile Nim with   n     n        players”, abbreviated by MiNim(  N,n     N  ,  n       ), assuming that the standard alliance matrix is adopted. The game values of MiNim(  N,n     N  ,  n       ) are completely determined for three cases:   n>N+1     n  >  N  +  1       ,   n=N+1     n  =  N  +  1        and   n=N     n  =  N       . The case   n     n    N        is more complicated, we present the game values of MiNim(  N,n     N  ,  n       ) only for   n=3     n  =  3        and   N=4     N  =  4       .
['Wen An Liu', 'Jia Wei Duan']
Misère Nim with multi-player