Journal
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Volume 271, Issue 1, Pages 165-178Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.ejor.2018.05.016
Keywords
Networks; Market equilibria; Uniqueness; Multiplicity; DC power flow
Funding
- Bavarian State Government
- DFG [CRC TRR 154]
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We consider uniqueness and multiplicity of market equilibria in a short-run setup where traded quantities of electricity are transported through a capacitated network in which power flows have to satisfy the classical lossless DC approximation. The firms face fluctuating demand and decide on their production, which is constrained by given capacities. Today, uniqueness of such market outcomes are especially important in more complicated multilevel models for measuring market (in)efficiency. Thus, our findings are important prerequisites for such studies. We show that market equilibria are unique on tree networks under mild assumptions and we also present a priori conditions under which equilibria are unique on cycle networks. On general networks, uniqueness fails to hold and we present simple examples for which multiple equilibria exist. However, we prove different a posteriori criteria for the uniqueness of a given solution and thereby specify properties of unique solutions. (C) 2018 Elsevier B.V. All rights reserved.
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