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Jingdong book

纳什博弈论论文集

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纳什博弈论论文集

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这是纳什先生生前亲授版权的著作,它收录了纳什一生最精彩的7篇论文,这些论文提出并论证了后被学界尊称为纳什均衡的理论,正是这一理论使博弈论真正成为一种分析问题的工具,也因此奠定了他在学术界的地位。书后所附的访谈录,将帮助读者了解纳什的魅力不仅在于他是一个充满传奇色彩的数学家,同时也是一个令人折服的生活强者。

Content Description

《纳什博弈论论文集》收录了诺贝尔经济学奖得住纳什的七篇经典论文,这几篇论文中体现出纳什对博弈论的革命性创造——创立了纳什均衡理论。
Author Description

约翰·纳什(1928—2015),是美国普林斯顿大学数学系教授,博弈论的奠基人之一。他青年时代提出的“纳什均衡”及其后续理论影响了数学界,也改变了经济学乃至整个社会科学的面貌。30岁后,纳什先生开始遭受妄想型精神分裂症的折磨,事业停顿,家庭解体。30年后,他病情好转,重新回到工作岗位。1994年因其对“非合作博弈均衡分析,以及对博弈论的其他贡献”荣获“诺贝尔经济学奖”。
Catalogue

致谢
序言
1 讨价还价问题
2 n人博弈的均衡点
3 一个简单的三人扑克牌博弈
4 非合作博弈
5 两人合作博弈
6 双头垄断情况几种处理方法的比较
7 n人博弈的一些实验
名词中英文索引
约翰·纳什主要作品年表
附录 纳什访谈录1
纳什访谈录2
Book Abstract

《纳什博弈论论文集》:
我们可以定义n人博弈的概念,其中,每一个参与人有有限个纯策略,且对每一个n维纯策略(每一个参与人选择一个纯策略),每个参与人都有确定的支付与之对应。混合策略即为纯策略上的概率分布,支付函数即为各参与人的期望,它是关于各参与人选择不同的纯策略的概率的多重线性形式。
任何n维策略,每一个分量对应于一个参与人,都可以看作由n个参与人的n个策略空间的乘积而得到的积空间的一个点。一个这样的n维策略对抗另一个n维策略,指的是在这个n维对抗策略中,相对于其他n-1个参与人在被对抗的n维策略中的策略选择,每一个参与人都选择了能使他获得最高期望支付的策略。一个自我对抗的n维策略就称为均衡点。
每一个n维策略与它对抗的n维策略的集合的对应,给出了一个从积空间到其自身的一对多的映射。从对抗的定义我们可以看出,一个点的对抗点的集合是凸的。再由支付函数的连续性可知,这个映射的图像是闭的。闭性等于说:如果P1,P2,……Pn,和Q1,Q2,…,Qn,…均是积空间中的点列,其中Qn-Q,Pn-P,Qn与Pn对抗,那么Q与P对抗。
由于映射的图像是闭的,并且每个点在该映射下的像是凸的,我们由角谷静夫(Kakutani)定理①可推断出该映射有一个不动点(即,该点包含于它的象集里)。由此可知存在一个均衡点。
在二人零和博弈情形中,其“主要定理”②与均衡点的存在性是等价的。在这种情况下,两参与人在任何两个均衡点都得到相同的支付,但在一般的情况下,这一点不一定成立。
……

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