279
eng
preprint
0
2019-09-26
2019-09-26
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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.
Former title: "On the existence of solutions to market equilibrium problems with integralities"
2
Creative Commons - CC BY - Namensnennung 4.0 International
Lukas Hümbs
Alexander Martin
Lars Schewe
eng
uncontrolled
Mixed-integer programming
eng
uncontrolled
Competitive equilibrium
eng
uncontrolled
Linear prices
eng
uncontrolled
Total unimodularity
Friedrich-Alexander-Universität Erlangen-Nürnberg
B07
University of Edinburgh
https://opus4.kobv.de/opus4-trr154/files/279/existence_prices.pdf