We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe finite discrete games without hidden information, allowing for randomness, and mixed sequential and simultaneous play. We make minimal assumptions about the form or content of game rules or user interface. The associated game trees resemble hybrid extensive- and strategic-form games, in the game theory sense. By transforming and comparing game trees, we develop equivalence relations on the space of game systems, which equate games that give players the same meaningful agency. We bring these together to suggest a method to measure distance between games, insensitive to cosmetic variations in the game logic descriptions.

中文翻译：

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形式博弈语法和对等

我们开发了正式描述和比较游戏的方法，以探究游戏结构和设计的问题，并作为从设计模式预测玩家行为的垫脚石。我们定义了类似语法的形式主义来描述没有隐藏信息的有限离散游戏，允许随机性以及混合的顺序和同时玩法。我们对游戏规则或用户界面的形式或内容的假设最少。从博弈论的角度来看，相关的博弈树类似于混合形式的博弈和战略形式的博弈。通过转换和比较游戏树，我们在游戏系统的空间上发展了等价关系，这等同于赋予玩家相同意义的游戏的游戏。我们将它们结合在一起，提出了一种衡量游戏之间距离的方法，