Study Of Interval Number In Pure Strategy Matrix Game Model And Graph Of Filters And Its Sprague-Grundy Function

This thesis uses the classical theory of the game theory, in the model of the purestrategy matrix, it sets the interval numbers as the elements of the strategy sets ofplayers. And then it discusses the nature and conclusions of interval numbers in themodel of the pure strategy matrix. At last,it studies the application of filters in gametheory, focuses on the nature of the filter graph and on the Sprague-Grundy function,and then discusses the states of points of the filter graph and the conclusion of sumand product.The thesis is divided into the following five chapters:The first chapter mainly introduces the production, development, and researchstatus of the non-standard analysis and game theory.The second chapter gives the basic theory of non-standard analysis, and thendiscuss several diferent types of non-standard model and then got some properties ofthe corresponding non-standard model.The third chapter gives the concept of game theory, and discuss the balance ofgame theory in diferent types.The fourth chapter describes the common types of fuzzy number sets and focuson related properties of the interval numbers in the pure strategy matrix game model.In the fifth Chapter, it uses the concept and nature of filter in non-standardanalysis and deduces the concept of graph of filter,and then discusses its nature,studiesits Sprague-Grundy function, and discusses its Sprague-Grundy function value and therelated points’ state and the conclusion of sum and product.