Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches

31 Pages Posted: 27 Nov 2017 Last revised: 4 Aug 2018

See all articles by Veronika Grimm

Veronika Grimm

University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg - School of Business & Economics

Julia Grübel

Friedrich-Alexander-Universität Erlangen-Nürnberg

Lars Schewe

University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg

Martin Schmidt

Trier University

Gregor Zöttl

Friedrich Alexander Universität Erlangen Nürnberg

Date Written: November 21, 2017

Abstract

This paper provides a first approach to assess gas market interaction on a network with nonconvex flow models. In the simplest possible setup that adequately reflects gas transport and market interaction, we elaborate on the relation of the solution of a simultaneous competitive gas market game, its corresponding mixed nonlinear complementarity problem (MNCP), and a first-best benchmark. We provide conditions under which the solution of the simultaneous game is also the solution of the corresponding MNCP. However, equilibria cannot be determined by the MNCP as the transmission system operator's (TSO’s) first-order conditions are insufficient, which goes back to nonconvexities of the gas flow model. This also implies that the welfare maximization problem may have multiple solutions that sometimes do not even coincide with any of the market equilibria. Our analysis shows that, even in the absence of strategic firms, market interaction fails to implement desirable outcomes from a welfare perspective due to the TSO’s incentive structure. We conclude that the technical environment calls for a market design that commits the TSO to a welfare objective through regulation and propose a design where the market solution corresponds to a welfare maximum and vice versa.

Keywords: Natural Gas Markets, Nonconvex Equilibrium Models, Uniqueness, Multiplicity, Fundamental Welfare Theorems, Perfect Competition

JEL Classification: C62, D41, D47, D5, D60, R41

Suggested Citation

Grimm, Veronika and Grübel, Julia and Schewe, Lars and Schmidt, Martin and Zöttl, Gregor, Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches (November 21, 2017). Available at SSRN: https://ssrn.com/abstract=3075209 or http://dx.doi.org/10.2139/ssrn.3075209

Veronika Grimm

University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg - School of Business & Economics ( email )

Nuremburg
Germany

Julia Grübel

Friedrich-Alexander-Universität Erlangen-Nürnberg ( email )

Lange Gasse 20
Lange Gasse 20,
Nürnberg, 90403
Germany

Lars Schewe

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

Cauerstraße 11
Erlangen, 91058
Germany

Martin Schmidt (Contact Author)

Trier University ( email )

Trier, 54286
Germany

Gregor Zöttl

Friedrich Alexander Universität Erlangen Nürnberg ( email )

Nuremburg
Germany

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