Nim游戲的一些限制和推廣
發(fā)布時(shí)間：2019-03-02 12:07
【摘要】：Nim游戲是博弈論中最經(jīng)典的游戲模型之一,可以被描述為：有若干堆石子,每堆各有若干個.游戲參與人為兩人.移動方法是兩名參與者交替從任意一堆中取出任意正整數(shù)個石子.在normal規(guī)則下,誰先取完誰贏.在misere規(guī)則下,誰先取完誰輸.本文深入研究了Nim游戲的限制和擴(kuò)展.分別通過對Nim游戲的移動方法中的從哪堆中取石子和取多少做動態(tài)限制得到了兩種更加復(fù)雜有趣的新游戲模型,我們分別稱其為：有指針限制的Nirn和有指針和Modular雙重限制的Nim.通過增加一堆的Nim游戲的參與人數(shù)而得到了一種新的Nim游戲,我們稱其為一堆有界帶有聯(lián)盟的Nim.本文還研究了在Nim游戲中添加新的移動方法所得到的(s,t)-Wythoff游戲與其P-位置之間的關(guān)系.本文共分四章：第一章,緒論.主要介紹公平組合游戲的歷史與發(fā)展,闡述了國內(nèi)外的研究現(xiàn)狀.第二章,徹底解決了有指針限制的Nim和有指針和Modular雙重限制的Nim這兩種游戲模型在normal規(guī)則下的所有P-位置.第三章,主要研究一堆有界帶有聯(lián)盟的Nim,提出了任意聯(lián)盟的結(jié)構(gòu)形式.本文分別給出了在miscrc規(guī)則下,帶有聯(lián)盟-[1,1]和聯(lián)盟-[2,1]的Nim游戲中各聯(lián)盟的所有非安全位置.指出了Annela R. Kelly在文獻(xiàn)[36,37]中觀點(diǎn)的錯誤原因,并給出了正確答案.第四章,主要研究由Nim游戲推廣所得到的(s,t)-Wythoff游戲與其P-位置之間的關(guān)系.我們將(s,t)-Wythoff的P-位置逐個添加為該游戲附加的合法移動形成新的游戲模型,并分析了這些新游戲模型的P-位置特征.我們的結(jié)果表明,對任意的整數(shù)s≥1,總存在數(shù)對(s,t)使得新游戲模型的P-位置不依賴于附加合法移動的選擇.
[Abstract]:Nim game is one of the most classic game models in game theory, which can be described as: there are several stacks, each of which has several. There are two people involved in the game. The move method is for two participants to alternately remove any positive integer stone from any pile. Under the normal rule, whoever wins first. Under the misere rule, whoever wins first loses. In this paper, the limitations and extensions of Nim games are studied in depth. Two more complex and interesting new game models are obtained by using dynamic restriction on which heap of stones and how much of the moving method of Nim game, respectively. We call them Nirn with pointer restriction and Nim. with pointer and Modular restriction, respectively, which we call the two new game models, namely, Nirn with pointer restriction and Nim. with pointer and Modular restriction, respectively. By increasing the number of players in a bunch of Nim games, we get a new Nim game, which we call a bunch of bounded Nim. with alliances. This paper also studies the relationship between the (s, t)-Wythoff game and its P-position by adding a new mobile method to the Nim game. This paper is divided into four chapters: chapter one, introduction. This paper mainly introduces the history and development of fair combination game, and expounds the research status at home and abroad. In the second chapter, all P-positions of the two game models, Nim with pointer restriction and Nim with pointer and Modular restriction, are completely solved under the normal rule. In the third chapter, we mainly study a bunch of bounded Nim, with alliance, and propose the structure of arbitrary alliance. In this paper, we give all the non-secure positions of the leagues in Nim games with alliance-[1,1] and alliance-[2,1] under the miscrc rule. This paper points out the wrong reason of Annela R. Kelly's viewpoint in reference [36, 37] and gives the correct answer. In chapter 4, we mainly study the relationship between (s, t)-Wythoff game and its P-position, which is derived from the extension of Nim games. We add the P-position of (s, t)-Wythoff to the game one by one to form a new game model, and analyze the P-position features of these new game models. Our results show that for any integer s 鈮，
本文編號：2433037
[Abstract]:Nim game is one of the most classic game models in game theory, which can be described as: there are several stacks, each of which has several. There are two people involved in the game. The move method is for two participants to alternately remove any positive integer stone from any pile. Under the normal rule, whoever wins first. Under the misere rule, whoever wins first loses. In this paper, the limitations and extensions of Nim games are studied in depth. Two more complex and interesting new game models are obtained by using dynamic restriction on which heap of stones and how much of the moving method of Nim game, respectively. We call them Nirn with pointer restriction and Nim. with pointer and Modular restriction, respectively, which we call the two new game models, namely, Nirn with pointer restriction and Nim. with pointer and Modular restriction, respectively. By increasing the number of players in a bunch of Nim games, we get a new Nim game, which we call a bunch of bounded Nim. with alliances. This paper also studies the relationship between the (s, t)-Wythoff game and its P-position by adding a new mobile method to the Nim game. This paper is divided into four chapters: chapter one, introduction. This paper mainly introduces the history and development of fair combination game, and expounds the research status at home and abroad. In the second chapter, all P-positions of the two game models, Nim with pointer restriction and Nim with pointer and Modular restriction, are completely solved under the normal rule. In the third chapter, we mainly study a bunch of bounded Nim, with alliance, and propose the structure of arbitrary alliance. In this paper, we give all the non-secure positions of the leagues in Nim games with alliance-[1,1] and alliance-[2,1] under the miscrc rule. This paper points out the wrong reason of Annela R. Kelly's viewpoint in reference [36, 37] and gives the correct answer. In chapter 4, we mainly study the relationship between (s, t)-Wythoff game and its P-position, which is derived from the extension of Nim games. We add the P-position of (s, t)-Wythoff to the game one by one to form a new game model, and analyze the P-position features of these new game models. Our results show that for any integer s 鈮，
本文編號：2433037
本文鏈接：http://sikaile.net/kejilunwen/yysx/2433037.html
最近更新
教材專著
