Tools for Mathematical Ludology
This foundational work addresses the need for rigorous tools in game studies and design, though it is incremental as it builds a basic framework without specific applications.
The paper tackles the problem of formally analyzing complex games beyond decision-making by proposing mathematical ludology, developing a hierarchy of game descriptions, mathematical formalism for compact representation, and equivalence relations on game systems.
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.