Multi-player Subtraction Games And Its Stochastic Models

This paper makes an in-depth study of multi-player subtraction games and its stochas-tic models under the standard alliance matrix. This paper is divided into four chapters:The first chapter is the introduction which mainly introduces the development of impartial combinatorial games under two players and more than two players, the basic conceptions and the research status.In the second chapter, we mainly study the case that the subtraction set is weakly increasing. We extend the Krawec’s result from n = 3 players to an arbitrary int,eger n ≥ 3 and extend the order of the subtraction set from b=2 t,o any b≥>2.In the third chapter, we mainly study the case that the weakly increasing condition of the subtraction set disappears. We completely solve the subtraction game, while the subtraction set of order 2 and 3 players. Our results show that the sequence of the game value of the model is periodic, and the analytic expressions of the period and the preperiod length are determined, and the exact structure of the sequence of game values in each period, as well as the exact structure of the sequence of the preperiod.The fourth chapter mainly studies two special subtraction games. In these two games,we get the game value under the probability model proposed by Krawec.