On Debreu-Koopmans Theorem: Bridging Neoclassical and Behavioral Economics via Star Quasiconvexity

TL;DR

This paper introduces star quasiconvexity as a unifying concept that extends the Debreu-Koopmans theorem, bridging classical and behavioral economics by allowing multiple nonconvex components in economic models.

Contribution

It proves that separable functions are star quasiconvex if and only if each component is star quasiconvex, expanding the scope of economic modeling beyond classical constraints.

Findings

Star quasiconvexity applies to separable sums of quasiconvex functions.

Develops calculus tools for star quasiconvex functions, including composition and minima.

Applies the framework to models in finance and risk management.

Abstract

The Debreu Koopmans theorem restricts separable aggregation to at most one nonconvex component. We solve this by proving that a separable, additive or multiplicative, function is star quasiconvex, those with star shaped sublevel sets about minimizers, if and only if each component is star quasiconvex. This immediately yields star quasiconvexity of separable sums of quasiconvex functions, formally bridging diversification theory with the S shaped value functions of Prospect Theory. Furthermore, we develop a complete calculus, monotonic composition, pointwise minima, quasi-arithmetic means, and we apply it to Cobb-Douglas functions, multifactor risk models, and constant function market makers in decentralized finance. Star quasiconvexity thus provides a unified framework for economic modeling beyond the classical Debreu Koopmans constraint.