Convergence to equilibrium for a class of exchange economies

2025/06/13 by Robert S. MacKay, MacKay, R. S. · 2 citations
Economics, Econometrics and Finance · #60J28 #Economic theories and models #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2506.11770

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

For a class of stochastic dynamical models of exchange economies that we call ``fully connected Cobb-Douglas'', the paper proves convergence of the probability distribution to an equilibrium, in total variation metric as time goes to infinity. The convergence is exponential and the equilibrium is determined uniquely by the number of agents, their ``exponents'', and the initial amounts of money and goods in the economy.

Citations

• Thermal Macroeconomics: An axiomatic theory of aggregate economic phenomena
• Twenty-five years of random asset exchange modeling

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• Stochastic Redistribution of Indistinguishable Items in Shared Habitation: A Multi-Agent Simulation Framework
• Entropy for a class of micro-economic models

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