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Uniqueness of market equilibria on networks with transport costs

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  • Krebs, Vanessa
  • Schmidt, Martin

Abstract

We study the existence and uniqueness of equilibria for perfectly competitive markets in capacitated transport networks. The model under consideration is rather general so that it captures basic aspects of related models in, e.g., gas or electricity networks. We formulate the market equilibrium model as a mixed complementarity problem and show the equivalence to a welfare maximization problem. Using the latter we prove uniqueness of the resulting equilibrium for piecewise linear and symmetric transport costs under additional mild assumptions. Moreover, we show the necessity of these assumptions by illustrating examples that possess multiple solutions if our assumptions are violated.

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  • Krebs, Vanessa & Schmidt, Martin, 2018. "Uniqueness of market equilibria on networks with transport costs," Operations Research Perspectives, Elsevier, vol. 5(C), pages 169-173.
    • Handle: RePEc:eee:oprepe:v:5:y:2018:i:c:p:169-173
    DOI: 10.1016/j.orp.2018.05.002
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    3. Blázquez de Paz, Mario, 2015. "Transmission Costs, Transmission Capacities and their Influence on Market Power in Wholesale Electricity Markets," Working Paper Series 1070, Research Institute of Industrial Economics, revised 16 Dec 2015.
    4. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.
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    6. Grimm, Veronika & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2017. "Uniqueness of market equilibrium on a network: A peak-load pricing approach," European Journal of Operational Research, Elsevier, vol. 261(3), pages 971-983.
    7. Chakravorty, Ujjayant & Hochman, Eithan & Umetsu, Chieko & Zilberman, David, 2009. "Water allocation under distribution losses: Comparing alternative institutions," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 463-476, February.
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    Cited by:

    1. Kramer, Anja & Krebs, Vanessa & Schmidt, Martin, 2021. "Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria," Operations Research Perspectives, Elsevier, vol. 8(C).
    2. Lars Schewe & Martin Schmidt, 2020. "The impact of potential-based physics models on pricing in energy networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1003-1029, September.
    3. Ambrosius, Mirjam & Grimm, Veronika & Kleinert, Thomas & Liers, Frauke & Schmidt, Martin & Zöttl, Gregor, 2020. "Endogenous price zones and investment incentives in electricity markets: An application of multilevel optimization with graph partitioning," Energy Economics, Elsevier, vol. 92(C).
    4. Egerer, Jonas & Grimm, Veronika & Grübel, Julia & Zöttl, Gregor, 2022. "Long-run market equilibria in coupled energy sectors: A study of uniqueness," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1335-1354.
    5. Grimm, Veronika & Grübel, Julia & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2019. "Nonconvex equilibrium models for gas market analysis: Failure of standard techniques and alternative modeling approaches," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1097-1108.
    6. Veronika Grimm & Lars Schewe & Martin Schmidt & Gregor Zöttl, 2019. "A multilevel model of the European entry-exit gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 223-255, April.

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