【摘要】：本文研究標準聯(lián)盟矩陣下,多個參與者的subtraction博弈及其隨機模型.全文分為四章:第一章緒論.主要介紹2人和多人參與的公平組合博弈的歷史及發(fā)展,闡述了基本概念與研究現(xiàn)狀.第二章主要研究subtraction集是弱增的情況.我們將Krawec的結果從3個參與者擴展到任意多個參與者,并將subtraction集的階由b = 2擴展到任意b ≥ 2.第三章主要研究subtraction集是非弱增的情況.我們徹底解決了subtraction集的階為2且3個參與者的subtraction博弈.我們的結果表明,該模型的博弈值序列具有周期性,并且確定出周期和預周期長度的解析表達式,以及每個周期內博弈值序列的精確結構,以及預周期內博弈值序列的精確結構.第四章主要研究了兩類特殊的subtraction博弈模型.在這兩類博弈中,我們得到了基于Krawec提出的概率模型下的博弈值.
[Abstract]:In this paper, we study the subtraction game and its stochastic model of multiple participants under the standard alliance matrix. The full text is divided into four chapters: the first chapter is an introduction. This paper mainly introduces the history and development of fair combination game in which two or more people participate, and expounds the basic concept and research status. In the second chapter, we study the situation that the subtraction set is weakly increasing. We extend the result of Krawec from 3 participants to any number of participants, and extend the order of subtraction set from b = 2 to any b 鈮，

本文編號：2189614