The Nonlinear Bernstein-Schrödinger Equation in Economics

Alfred Galichon; Scott Kominers; Simon Weber

doi:10.1007/978-3-319-25040-3_6

The Nonlinear Bernstein-Schrödinger Equation in Economics

Alfred Galichon, Scott Kominers, Simon Weber

Economics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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-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.

Original language	English
Title of host publication	GSI 2015: Geometric Science of Information
Subtitle of host publication	International Conference on Geometric Science of Information
Pages	51-59
Number of pages	9
Volume	9389
DOIs	https://doi.org/10.1007/978-3-319-25040-3_6
Publication status	E-pub ahead of print - 3 Apr 2016

Publication series

Name	Lecture Notes in Computer Science
Publisher	Berlin: Springer-Verlag, 1973-
ISSN (Print)	0302-9743

Access to Document

10.1007/978-3-319-25040-3_6

Cite this

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title = "The Nonlinear Bernstein-Schr{\"o}dinger Equation in Economics",

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{\"o}dinger 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.",

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AB - 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.

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