  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.
