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A theory of probabilistic economic equilibria

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  • Jacobo, Juan

Abstract

This paper develops an information-theoretic framework that integrates the principle of minimum relative entropy with Bellman’s principle of optimality to formally characterize how purposeful individual behavior gives rise to spontaneous order in market economies. Under standard assumptions from dynamic programming theory, I prove that a probabilistic formulation of Bellman’s equation, subject to an upper bound on relative entropy, admits a unique solution in the form of a dynamic logit function. This function generates a Markov transition with a unique invariant probability distribution, which characterizes economic equilibria as emergent outcomes arising from the purposeful behavior of private agents. I apply these results to neoclassical models of consumption and investment, illustrating that the theory can effectively account for key cross-sectional and time-series properties of economic systems.

Suggested Citation

  • Jacobo, Juan, 2026. "A theory of probabilistic economic equilibria," Journal of Mathematical Economics, Elsevier, vol. 124(C).
    • Handle: RePEc:eee:mateco:v:124:y:2026:i:c:s0304406826000285
    DOI: 10.1016/j.jmateco.2026.103240
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    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

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