Optimal Strategy Of Two Games On Discrete Space

Game theory on discrete space has an important application. The paper mainly discusses two kinds of games:(1) Take-Away Games, (2) Comparative question Games.The first chapter mainly introduces history and development of game theory. It also explicits the research situation of two kinds of games. Background and main results are given generally in this chapter.The second chapter mainly researches on Mouse model of Take-Away Games under the Misere play convention. A.S. Fraenkel considered a new impartial combinatorial game in 2009, and supplied all the P-positions under the Normal play convention. In this chapter, all the P-positions of Mouse model are determined under the Misere play convention, thereby the optimal strategy of Mouse model is given under the Misere play convention.The third chapter mainly researches on a model andβmodel of Take-Away Games under the Normal play convention. It firstly gives definitions and moving rules of the two models, then determines all the P-positions of the two models separately under the Normal play convention. Thereby the optimal strategies ofαmodel andβmodel are given under the Normal play convention.The forth chapter mainly researches on binary search of comparative questions with delay d and missing answers c of Comparative question Games. For the case of any positive integer d and c=2, we get upper and lower bounds of its search space. If the condition Md(2)(t) establishes, we get the optimal value of its search space; For the case of any positive integer d and c, we get upper bound of its search space.