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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
Article, Bibliographie

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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.

Item Type: Article
Erschienen: 2022
Creators: Grimm, Veronika ; Nowak, Daniel ; Schewe, Lars ; Schmidt, Martin ; Schwartz, Alexandra ; Zöttl, Gregor
Type of entry: Bibliographie
Title: A tractable multi-leader multi-follower peak-load-pricing model with strategic interaction
Language: English
Date: September 2022
Place of Publication: Berlin ; Heidelberg
Publisher: Springer
Journal or Publication Title: Mathematical Programming: Series A, Series B
Volume of the journal: 195
Issue Number: 1-2
DOI: 10.1007/s10107-021-01708-0
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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.

Uncontrolled Keywords: Game theory, Nash–Cournot equilibria, Multi-leader multi-follower game, Peak-load pricing
Classification DDC: 300 Social sciences > 330 Economics
500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Optimization
04 Department of Mathematics > Optimization > Nonlinear Optimization
Date Deposited: 28 Mar 2024 08:50
Last Modified: 28 Mar 2024 08:50
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