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Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash-Cournot Equilibria

Anja Kramer (anjakkramer***at***web.de)
Vanessa Krebs (vanessa.krebs***at***fau.de)
Martin Schmidt (martin.schmidt***at***uni-trier.de)

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 classical 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 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.

Keywords: Robust optimization, Linear complementarity problems, Electricity market equilibrium models, Perfect competition, Nash-Cournot competition

Category 1: Robust Optimization

Category 2: Other Topics (Game Theory )

Category 3: Applications -- OR and Management Sciences (Finance and Economics )


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Entry Submitted: 07/12/2018
Entry Accepted: 07/12/2018
Entry Last Modified: 07/26/2021

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