Nonconvex equilibrium models for gas market analysis: Failure of standard techniques and alternative modeling approaches

Veronika Grimm, Julia Grübel, Lars Schewe, Martin Schmidt*, Gregor Zöttl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.

Original languageEnglish
Pages (from-to)1097-1108
Number of pages12
JournalEuropean Journal of Operational Research
Issue number3
Early online date17 Sept 2018
Publication statusPublished - 16 Mar 2019

Keywords / Materials (for Non-textual outputs)

  • Fundamental welfare theorems
  • Multiplicity
  • Natural gas markets
  • Nonconvex equilibrium models
  • Perfect competition
  • Uniqueness


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