Tools for Mathematical Ludology

TL;DR

This paper introduces mathematical ludology, a formal framework to analyze complex games beyond decision-making, focusing on game mechanics, structure, and player behavior, to deepen understanding of game design and phenomena.

Contribution

It develops a foundational hierarchy of game descriptions, formalism for complex discrete games, and equivalence relations on game systems, advancing the mathematical study of games.

Findings

Established a hierarchy of game descriptions

Developed formalism for complex discrete games

Defined equivalence relations on game systems

Abstract

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.