Dependent Types for Extensive Games

TL;DR

This paper formalizes infinite extensive games in economics using the COQ proof assistant with dependent types, enabling precise modeling of complex game structures and their properties.

Contribution

It introduces a formal framework for infinite extensive games using dependent types in COQ, enhancing the precision and expressiveness of game modeling.

Findings

Formalization of infinite extensive games in COQ

Use of dependent types to model game components

Discussion on infiniteness in game theory

Abstract

Extensive games are tools largely used in economics to describe decision processes ofa community of agents. In this paper we propose a formal presentation based on theproof assistant COQ which focuses mostly on infinite extensive games and theircharacteristics. COQ proposes a feature called "dependent types", which meansthat the type of an object may depend on the type of its components. For instance,the set of choices or the set of utilities of an agent may depend on the agentherself. Using dependent types, we describe formally a very general class of gamesand strategy profiles, which corresponds somewhat to what game theorists are used to.We also discuss the notions of infiniteness in game theory and how this can beprecisely described.