We propose the study of mathematical ludology, which aims to formally interrogate questions of interest to game studies and game design in particular. The goal is to extend our mathematical understanding of complex games beyond decision-making---the typical focus of game theory and artificial intelligence efforts---to explore other aspects such as game mechanics, structure, relationships between games, and connections between game rules and user-interfaces, as well as exploring related gameplay phenomena and typical player behavior. In this paper, we build a basic foundation for this line of study by developing a hierarchy of game descriptions, mathematical formalism to compactly describe complex discrete games, and equivalence relations on the space of game systems.

中文翻译：

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数学运筹学工具

我们提议研究数学游戏学，旨在正式询问对游戏研究和特别是游戏设计感兴趣的问题。目标是将我们对复杂游戏的数学理解扩展到决策之外——博弈论和人工智能工作的典型焦点——探索其他方面，如游戏机制、结构、游戏之间的关系以及游戏之间的联系规则和用户界面，以及探索相关的游戏现象和典型的玩家行为。在本文中，我们通过开发博弈描述的层次结构、数学形式来紧凑地描述复杂的离散博弈以及博弈系统空间上的等价关系，为这一研究线奠定了基础。