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.

翻译：这些演讲笔记试图用数学方法处理类似于数学物理学的游戏理论。 游戏实例被定义为一个基础系统的一系列状态。 这个观点统一了2人的传统数学模型, 特别是组合游戏和零和游戏以及投资和赌注模式。 以公用事业、 潜力和平衡概念为主的对人游戏的研究可以将合作游戏作为特例进行。 希尔伯特空间游戏理论系统的反射进一步建立了与量子机械化和一般互动系统的数学模型的联系。