Composing games into complex institutions

TL;DR

This paper introduces compositional game theory, a modular and abstract framework inspired by programming languages, enabling the design and analysis of complex, real-world institutional games more efficiently and faithfully.

Contribution

It presents a novel computational framework for high-level, compositional design of large, complex games, enhancing expressiveness and analytical capabilities in game theory.

Findings

Enables modular and abstract representation of complex institutional games

Facilitates faster search and design of large game systems

Improves the ability to analyze nested and long-range dependent game structures

Abstract

Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes. Our contribution, compositional game theory, permits another approach of equally general appeal: the high-level design of large games for expressing complex architectures and representing real-world institutions faithfully. Compositional game theory, grounded in the mathematics underlying programming languages, and introduced here as a general computational framework, increases the parsimony of game representations with abstraction and modularity, accelerates search and design, and helps theorists across disciplines express real-world institutional complexity in well-defined ways. Relative to existing approaches in game theory, compositional game theory is especially promising for solving game systems with long-range dependencies, for comparing large numbers of structurally related games, and for nesting games into the larger logical or strategic flows typical of real world policy or institutional systems.