Kramer A, Krebs V, Schmidt M (2018)
Publication Language: English
Publication Type: Other publication type
Publication year: 2018
URI: http://www.optimization-online.org/DB_HTML/2018/07/6709.html
This paper mainly studies two topics: linear complementarity problems (LCPs) for modeling electricity market equilibria and optimization under uncertainty. While there have been quite some attempts to deal with uncertain LCPs in a stochastic - i.e., distributional - sense, robust LCPs have only gained attention very recently. In this paper, 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 particularly means that the two classical welfare theorems also hold in both considered robust cases. 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 analogue 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.
APA:
Kramer, A., Krebs, V., & Schmidt, M. (2018). Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash--Cournot Equilibria.
MLA:
Kramer, Anja, Vanessa Krebs, and Martin Schmidt. Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash--Cournot Equilibria. 2018.
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