论文标题
数学游戏理论：一种新方法
Mathematical Game Theory: A New Approach
论文作者
论文摘要
这些讲义尝试尝试对游戏理论类似于数学物理学的数学处理。游戏实例定义为基础系统的一系列状态。该观点统一了两人，尤其是组合和零和零游戏的经典数学模型，以及用于投资和投注的模型。研究了N-Per-Games的研究，重点是公用事业，潜力和平衡的概念，这使得可以作为特殊情况将合作游戏归纳。 Hilbert空间中游戏理论系统的代表还建立了与量子Mechancis和一般相互作用系统的数学模型的链接。 笔记绘制了该理论的轮廓。详细信息可作为其他地方的教科书获得。
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person and, in particular, combinatorial and zero-sum games as well as models for investing and betting. n-person games are studied with emphasis on notions of utilities, potentials and equilibria, which allows to subsume cooperative games as special cases. The represenation of a game theoretic system in a Hilbert space furthermore establishes a link to the mathematical model of quantum mechancis and general interaction systems. The notes sketch an outline of the theory. Details are available as a textbook elsewhere.
