The Nonlinear Bernstein-Schrödinger Equation in Economics

Alfred Galichon (1) , Scott Kominers (2) , Simon Weber (1)

1 ECON - Département d'économie (Sciences Po)
2 Harvard University [Cambridge]

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-Schrödinger 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.

Keywords: Equilibrium Assignment Problem; Economics model; Nonlinear Bernstein-Schrödinger system

Domains: Humanities and Social Sciences; Economics and Finance

Alfred Galichon, Scott Kominers, Simon Weber. The Nonlinear Bernstein-Schrödinger Equation in Economics. Frank Nielson; Frédéric Barbaresco. Geometric Science of Information, Springer, pp.51 - 59, 2015, 9783319250397. ⟨hal-03393000⟩