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

Abstract

The Debreu–Koopmans theorem [14] 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, multi-factor 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.