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.

翻译：这些讲义尝试以数学物理的方式对博弈论进行数学处理。博弈实例被定义为底层系统状态的序列。这一观点统一了两人博弈的经典数学模型，特别是组合博弈和零和博弈，以及投资和投注模型。研究n人博弈时，重点放在效用、势和均衡的概念上，从而将合作博弈作为特例纳入其中。在希尔伯特空间中对博弈论系统的表示进一步建立了与量子力学和一般交互系统数学模型之间的联系。本讲义勾勒了该理论的框架。详细内容另见教科书。