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.
A.Galichon—gratefully acknowledges funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreements no 313699 and 295298, and FiME.
S.D.Kominers—gratefully acknowledges the support of NSF grants CCF-1216095 and, as well as the Harvard Milton Fund.
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Galichon, A., Kominers, S.D., Weber, S. (2015). The Nonlinear Bernstein-Schrödinger Equation in Economics. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_6
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DOI: https://doi.org/10.1007/978-3-319-25040-3_6
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