On the existence of solutions to market equilibrium problems with integralities

  • It is well known that linear prices supporting a competitive equilibrium exist in the case of convex markets, however, in the presence of integralities this is open and hard to decide in general. We present necessary and sufficient conditions for the existence of such prices for market equilibrium problems where market participants have integral decision variables. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications of this result.

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Author:Lukas Hümbs, Alexander Martin, Lars Schewe
Document Type:Preprint
Date of Publication (online):2019/09/26
Date of first Publication:2019/09/26
Release Date:2019/09/26
Tag:Competitive equilibrium; Linear prices; Mixed-integer programming; Total unimodularity
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
University of Edinburgh
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International