Formal Game Grammar and Equivalence

Abstract

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.