Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria
Kramer A, Krebs V, Schmidt M (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 8
Article Number: 100197
DOI: 10.1016/j.orp.2021.100197
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.
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APA:
Kramer, A., Krebs, V., & Schmidt, M. (2021). Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria. Operations Research Perspectives, 8. https://dx.doi.org/10.1016/j.orp.2021.100197
MLA:
Kramer, Anja, Vanessa Krebs, and Martin Schmidt. "Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria." Operations Research Perspectives 8 (2021).
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