A unifying framework for economic equilibrium and optimal transport in infinite-dimensional Hilbert spaces
Ian Helfrich
Introduces a framework that unifies economic equilibrium and optimal transport on infinite-dimensional Hilbert spaces, building on tensor-valued measures and nonlinear operator theory. Establishes existence and uniqueness of equilibrium under mild assumptions on preferences and endowments, characterizes equilibrium allocations as optimal transport plans, and represents equilibrium prices as gradients of convex potential functions. The paper is the analytical foundation for the closed-loop observation work in Papers 0 and 1.
The paper is the seed of what has become the Penumbra program (closed-loop observation under measurement gaps). Equilibrium-as-transport is the right algebraic spine; making it work in infinite-dimensional settings is what lets the framework absorb the satellite-economics observation operators that follow in Paper 0 and Paper 1.
Working draft on SSRN. The framework is being extended in two follow-on papers: Paper 1 (AROE) generalizes to measure-dependent costs with stochastic observation operators, and Paper 0 (Penumbra) uses the framework to formalize the measurement-gap problem in sanctioned-trade settings.