Formal Game Grammar and Equivalence

TL;DR

This paper introduces a formal grammar-based framework for describing and comparing finite discrete games, enabling analysis of game structure, design, and player agency through equivalence and distance measures.

Contribution

It develops a formalism for representing and comparing games, including methods to determine game equivalence and measure distances insensitive to superficial differences.

Findings

Defined a grammar-like formalism for finite discrete games.

Established equivalence relations based on player agency.

Proposed a method to measure game similarity ignoring cosmetic differences.

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.