Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria

Anja Kramer, Vanessa Krebs and Martin Schmidt

Operations Research Perspectives, 2021, vol. 8, issue C

Abstract: This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of Γ-robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.

Keywords: Robust optimization; Linear complementarity problems; Electricity market equilibrium models; Perfect competition; Nash–Cournot competition (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:oprepe:v:8:y:2021:i:c:s221471602100018x

DOI: 10.1016/j.orp.2021.100197

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