A Compositional Treatment of Iterated Open Games

TL;DR

This paper advances compositional game theory by providing a coalgebraic semantics for infinite games and introducing a new operator to model subgame perfection, enabling recursive analysis of complex economic games.

Contribution

It extends compositional game theory with a coalgebraic framework for infinite games and a novel operator for subgame perfection, enhancing the modeling of complex economic interactions.

Findings

Developed a final coalgebra semantics for infinite games.

Introduced a new operator to model subgame perfection.

Enabled recursive equilibrium analysis of complex games.

Abstract

Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria of these complex games can be defined recursively from the equilibria of their simpler subgames. This paper extends the model by providing a final coalgebra semantics for infinite games. In the course of this, we introduce a new operator on games to model the economic concept of subgame perfection.