Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

TL;DR

This paper demonstrates that Product Distribution theory unifies the treatment of bounded rationality in game theory with approximation methods in statistical physics, revealing their fundamental connection.

Contribution

It introduces PD theory as a unified framework that addresses both bounded rationality in game theory and decoupling approximations in statistical physics.

Findings

PD theory provides a principled formulation of bounded rationality.

PD theory offers new mean field approaches in statistical physics.

The paper reveals the fundamental equivalence of these topics.

Abstract

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principled formulation of bounded rationality and a set of new types of mean field theory in statistical physics. It also shows that those topics are fundamentally one and the same.