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A tractable multi-leader multi-follower peak-load-pricing model with strategic interaction

Grimm, Veronika ; Nowak, Daniel ; Schewe, Lars ; Schmidt, Martin ; Schwartz, Alexandra ; Zöttl, Gregor (2022)
A tractable multi-leader multi-follower peak-load-pricing model with strategic interaction.
In: Mathematical Programming: Series A, Series B, 195 (1-2)
doi: 10.1007/s10107-021-01708-0
Artikel, Bibliographie

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Kurzbeschreibung (Abstract)

While single-level Nash equilibrium problems are quite well understood nowadays, less is known about multi-leader multi-follower games. However, these have important applications, e.g., in the analysis of electricity and gas markets, where often a limited number of firms interacts on various subsequent markets. In this paper, we consider a special class of two-level multi-leader multi-follower games that can be applied, e.g., to model strategic booking decisions in the European entry-exit gas market. For this nontrivial class of games, we develop a solution algorithm that is able to compute the complete set of Nash equilibria instead of just individual solutions or a bigger set of stationary points. Additionally, we prove that for this class of games, the solution set is finite and provide examples for instances without any Nash equilibria in pure strategies. We apply the algorithm to a case study in which we compute strategic booking and nomination decisions in a model of the European entry-exit gas market system. Finally, we use our algorithm to provide a publicly available test library for the considered class of multi-leader multi-follower games. This library contains problem instances with different economic and mathematical properties so that other researchers in the field can test and benchmark newly developed methods for this challenging class of problems.

Typ des Eintrags: Artikel
Erschienen: 2022
Autor(en): Grimm, Veronika ; Nowak, Daniel ; Schewe, Lars ; Schmidt, Martin ; Schwartz, Alexandra ; Zöttl, Gregor
Art des Eintrags: Bibliographie
Titel: A tractable multi-leader multi-follower peak-load-pricing model with strategic interaction
Sprache: Englisch
Publikationsjahr: September 2022
Ort: Berlin ; Heidelberg
Verlag: Springer
Titel der Zeitschrift, Zeitung oder Schriftenreihe: Mathematical Programming: Series A, Series B
Jahrgang/Volume einer Zeitschrift: 195
(Heft-)Nummer: 1-2
DOI: 10.1007/s10107-021-01708-0
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Kurzbeschreibung (Abstract):

While single-level Nash equilibrium problems are quite well understood nowadays, less is known about multi-leader multi-follower games. However, these have important applications, e.g., in the analysis of electricity and gas markets, where often a limited number of firms interacts on various subsequent markets. In this paper, we consider a special class of two-level multi-leader multi-follower games that can be applied, e.g., to model strategic booking decisions in the European entry-exit gas market. For this nontrivial class of games, we develop a solution algorithm that is able to compute the complete set of Nash equilibria instead of just individual solutions or a bigger set of stationary points. Additionally, we prove that for this class of games, the solution set is finite and provide examples for instances without any Nash equilibria in pure strategies. We apply the algorithm to a case study in which we compute strategic booking and nomination decisions in a model of the European entry-exit gas market system. Finally, we use our algorithm to provide a publicly available test library for the considered class of multi-leader multi-follower games. This library contains problem instances with different economic and mathematical properties so that other researchers in the field can test and benchmark newly developed methods for this challenging class of problems.

Freie Schlagworte: Game theory, Nash–Cournot equilibria, Multi-leader multi-follower game, Peak-load pricing
Sachgruppe der Dewey Dezimalklassifikatin (DDC): 300 Sozialwissenschaften > 330 Wirtschaft
500 Naturwissenschaften und Mathematik > 510 Mathematik
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Optimierung
04 Fachbereich Mathematik > Optimierung > Nonlinear Optimization
Hinterlegungsdatum: 28 Mär 2024 08:50
Letzte Änderung: 28 Mär 2024 08:50
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