The nonlinear Bernstein-Schr\"odinger equation in Economics

TL;DR

This paper introduces a nonlinear extension of the Bernstein-Schrödinger system to analyze the Equilibrium Assignment Problem in economics, providing new theoretical insights and an efficient computational approach.

Contribution

It establishes a novel nonlinear Bernstein-Schrödinger framework for the EAP and offers an existence proof and computational method for this nonlinear system.

Findings

Proves existence of solutions for the nonlinear system

Develops an efficient algorithm for solving the nonlinear equations

Links the nonlinear system to economic equilibrium models

Abstract

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the "nonlinear Bernstein-Schr\"odinger system", which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.