Exploiting complete linear descriptions for decentralized power market 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 decentralized market problems where market participants have integral decision variables and their feasible sets are given in complete linear description. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications. Furthermore, we compute competitive equilibria for two classes of decentralized market problems arising in energy markets and show that competitive equilibria may exist regardless of integralities.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
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
Former title: "On the existence of solutions to market equilibrium problems with integralities"
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
University of Edinburgh
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International