Game Theory, Statistical Mechanics and Income Inequality

TL;DR

This paper introduces a game theoretic approach linking statistical mechanics to income inequality, proposing that in ideal free markets, the fairest pay distribution is lognormal, with implications for understanding wealth disparities.

Contribution

It develops a novel game theoretic framework connecting entropy and fairness, showing that lognormal distributions emerge as equilibrium states in ideal free markets.

Findings

Lognormal distribution is the fairest equilibrium pay distribution for homogeneous agents.

In mixed populations, the combined distribution appears as a mixture of two lognormals.

The theory links potential game theory with statistical mechanics through entropy.

Abstract

The widening inequality in income distribution in recent years, and the associated excessive pay packages of CEOs in the U.S. and elsewhere, is of growing concern among policy makers as well as the common person. However, there seems to be no satisfactory answer, in conventional economic theories and models, to the fundamental question of what kind of pay distribution we ought to see, at least under ideal conditions, in a free market environment and whether this distribution is fair. We propose a game theoretic framework that addresses these questions and show that the lognormal distribution is the fairest inequality of pay in an organization comprising of homogenous agents, achieved at equilibrium, under ideal free market conditions. We also show that for a population of two different classes of agents, the final distribution is a combination of two different lognormal distributions where one of them, corresponding to the top 3-5% of the population, can be misidentified as a Pareto distribution. Our theory also shows the deep and direct connection between potential game theory and statistical mechanics through entropy, which is a measure of fairness in a distribution. This leads us to propose the fair market hypothesis, that the self-organizing dynamics of the ideal free market, i.e., Adam Smith's "invisible hand", not only promotes efficiency but also maximizes fairness under the given constraints.