多人Large Nim博弈的最优策略

Optimal strategies of multi-player Large Nim games

研究包含任意多个竞争者的Large Nim博弈模型,它是传统的Large Nim由两个竞争者到多个竞争者的一般化.在标准联盟矩阵下,运用递归函数,针对竞争者人数与堆数的三大类关系,得到了相应的博弈值和获胜的最优策略.

This paper is devoted to the game"Multi-player Large Nim Games"which is the generalization of the classic Large Nim games from two players to arbitrarily many players.Assuming that the standard alliance matrix be adopted,by using a recursive function,the game values are completely determined for three kinds of relation between the numbers of players and piles.These game values are capable of determining which of the players has a winning optimal strategy.