Deconstruction of Infinite Extensive Games using coinduction

TL;DR

This paper introduces coinduction as a formal method to analyze infinite extensive games, redefining key concepts like Nash equilibrium and subgame perfect equilibrium, and demonstrating its application to classic infinite games.

Contribution

It develops a coinductive framework for infinite games, providing new definitions and insights into rationality and equilibrium concepts in infinite game theory.

Findings

Coinduction effectively models infinite games.

Human rationality can be understood through coinductive reasoning.

Analysis of infinite games like dollar auction and centipede game.

Abstract

Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite (discrete) extensive games the basic notions of game theory. Among others, we introduce a definition of Nash equilibrium and a notion of subgame perfect equilibrium for infinite games. We use those concepts to analyze well known infinite games, like the dollar auction game and the centipede game and we show that human behaviors that are often considered as illogic are perfectly rational, if one admits that human agents reason coinductively.