A Tractable Multi-Leader Multi-Follower Peak-Load-Pricing Model with Strategic Interaction

37 Pages Posted: 27 Aug 2020 Last revised: 15 Sep 2021

See all articles by Veronika Grimm

Veronika Grimm

University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg

Daniel Nowak

Technische Universita ̈t Darmstadt

Lars Schewe

University of Edinburgh

Martin Schmidt

Trier University

Alexandra Schwartz

Technische Universita ̈t Darmstadt; Dresden University of Technology - Faculty of Mathematics

Gregor Zöttl

Friedrich Alexander Universität Erlangen Nürnberg

Date Written: July 20, 2020

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.

Keywords: Game Theory, Nash-Cournot Equilibria, Multi-Leader Multi-Follower Game, Peak-Load Pricing

JEL Classification: C02, C61, C68, C72, L95, D5, D43

Suggested Citation

Grimm, Veronika and Nowak, Daniel and Schewe, Lars and Schmidt, Martin and Schwartz, Alexandra and Zöttl, Gregor, A Tractable Multi-Leader Multi-Follower Peak-Load-Pricing Model with Strategic Interaction (July 20, 2020). Available at SSRN: https://ssrn.com/abstract=3656965 or http://dx.doi.org/10.2139/ssrn.3656965

Veronika Grimm

University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg ( email )

Schloßplatz 4
Erlangen, DE Bavaria 91054
Germany

Daniel Nowak

Technische Universita ̈t Darmstadt ( email )

Germany

Lars Schewe

University of Edinburgh ( email )

James Clerk Maxwell Building
Peter Guthrie Tait Rd
Edinburgh, EH9 3FD
United Kingdom

Martin Schmidt

Trier University ( email )

Trier, 54286
Germany

Alexandra Schwartz (Contact Author)

Technische Universita ̈t Darmstadt ( email )

Germany

Dresden University of Technology - Faculty of Mathematics ( email )

Einsteinstrasse 3
Dresden
Germany

Gregor Zöttl

Friedrich Alexander Universität Erlangen Nürnberg ( email )

Nuremburg
Germany

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