IDEAS home Printed from https://ideas.repec.org/a/eee/eneeco/v138y2024ics0140988324005577.html

A note on the uniqueness of Nash–Cournot equilibria in an oligopolistic energy market with renewable generation and demand uncertainty

Author

Listed:
  • Chaiken, Benjamin
  • Duggan, Joseph E.

Abstract

This work explores the uniqueness of Nash–Cournot equilibria in wholesale electricity markets with both thermal and renewable generation in the presence of demand uncertainty. Criteria guaranteeing a unique equilibrium are derived for an energy market where each firm owns a share of renewable generation. This work expands upon the uniqueness results proven by Lagerlöf (2006) to incorporate the presence of renewable generation into the market in the manner of Acemoglu et al. (2017). A numerical case study is used to illustrate the potential impacts of increasing renewable generation on equilibrium uniqueness and directions for future research are discussed.

Suggested Citation

  • Chaiken, Benjamin & Duggan, Joseph E., 2024. "A note on the uniqueness of Nash–Cournot equilibria in an oligopolistic energy market with renewable generation and demand uncertainty," Energy Economics, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:eneeco:v:138:y:2024:i:c:s0140988324005577
    DOI: 10.1016/j.eneco.2024.107849
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0140988324005577
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.eneco.2024.107849?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Crampes, Claude & Renault, Jérôme, 2019. "How many markets for wholesale electricity when supply ispartially flexible?," Energy Economics, Elsevier, vol. 81(C), pages 465-478.
    2. repec:aen:journl:ej40-6-sioshansi is not listed on IDEAS
    3. repec:aen:journl:ej38-si1-acemoglu is not listed on IDEAS
    4. Joseph E. Duggan Jr. & Ramteen Sioshansi, 2019. "Another Step Towards Equilibrium Offers in Unit Commitment Auctions with Nonconvex Costs: Multi-Firm Oligopolies," The Energy Journal, , vol. 40(6), pages 249-282, November.
    5. Daron Acemoglu & Ali Kakhbod & Asuman Ozdaglar, 2017. "Competition in Electricity Markets with Renewable Energy Sources," The Energy Journal, , vol. 38(1_suppl), pages 137-156, June.
    6. Paul L Joskow, 2019. "Challenges for wholesale electricity markets with intermittent renewable generation at scale: the US experience," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 35(2), pages 291-331.
    7. Chaiken, Benjamin & Duggan, Joseph E. & Sioshansi, Ramteen, 2021. "Paid to produce absolutely nothing? A Nash-Cournot analysis of a proposed power purchase agreement," Energy Policy, Elsevier, vol. 156(C).
    8. Heidrun Hoppe & Benny Moldovanu & Emre Ozdenoren, 2011. "Coarse matching with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 75-104, May.
    9. James Bushnell, 2007. "Oligopoly equilibria in electricity contract markets," Journal of Regulatory Economics, Springer, vol. 32(3), pages 225-245, December.
    10. William Novshek, 1985. "On the Existence of Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 85-98.
    11. Antweiler, Werner & Muesgens, Felix, 2021. "On the long-term merit order effect of renewable energies," Energy Economics, Elsevier, vol. 99(C).
    12. Tselika, Kyriaki & Tselika, Maria & Demetriades, Elias, 2024. "Quantifying the short-term asymmetric effects of renewable energy on the electricity merit-order curve," Energy Economics, Elsevier, vol. 132(C).
    13. Rabah Amir & Val E. Lambson, 2000. "On the Effects of Entry in Cournot Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 235-254.
    14. Blaise Allaz & Jean-Luc Vila, 1993. "Cournot Competition, Forward Markets and Efficiency," Post-Print hal-00511806, HAL.
    15. Antweiler, Werner, 2021. "Microeconomic models of electricity storage: Price Forecasting, arbitrage limits, curtailment insurance, and transmission line utilization," Energy Economics, Elsevier, vol. 101(C).
    16. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    17. Albert Banal-Estañol & Augusto Rupérez Micola, 2009. "Composition of Electricity Generation Portfolios, Pivotal Dynamics, and Market Prices," Management Science, INFORMS, vol. 55(11), pages 1813-1831, November.
    18. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    19. Christian Ewerhart, 2013. "Regular type distributions in mechanism design and $$\rho $$ -concavity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 591-603, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Duggan, Joseph E. & Ogland-Hand, Jonathan D. & Middleton, Richard S., 2025. "Modeling CCS policy support: Implications for market performance, net emissions, and welfare," Applied Energy, Elsevier, vol. 389(C).
    2. Su, Chi-Wei & Wu, Ying & Qin, Meng, 2025. "Preserving energy security: Can renewable energy withstand the energy-related uncertainty risk?," Energy, Elsevier, vol. 320(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:aen:journl:ej38-si1-acemoglu is not listed on IDEAS
    2. Duggan, Joseph E. & Ogland-Hand, Jonathan D. & Middleton, Richard S., 2025. "Modeling CCS policy support: Implications for market performance, net emissions, and welfare," Applied Energy, Elsevier, vol. 389(C).
    3. Christian Ewerhart, 2013. "Regular type distributions in mechanism design and $$\rho $$ -concavity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 591-603, August.
    4. de Bragança, Gabriel Godofredo Fiuza & Daglish, Toby, 2017. "Investing in vertical integration: electricity retail market participation," Energy Economics, Elsevier, vol. 67(C), pages 355-365.
    5. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    6. Xiaodong Du & David A. Hennessy & Cindy L. Yu, 2012. "Testing Day's Conjecture that More Nitrogen Decreases Crop Yield Skewness," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 94(1), pages 225-237.
    7. Dihan Zou, 2025. "Log-concave functions and transformations thereof," Papers 2512.07768, arXiv.org, revised Dec 2025.
    8. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    9. David P. Brown & Andrew Eckert, 2018. "Analyzing the Impact of Electricity Market Structure Changes and Mergers: The Importance of Forward Commitments," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 52(1), pages 101-137, February.
    10. Gama, Adriana & Rietzke, David, 2019. "Monotone comparative statics in games with non-monotonic best-replies: Contests and Cournot oligopoly," Journal of Economic Theory, Elsevier, vol. 183(C), pages 823-841.
    11. Mier, Mathias, 2021. "Efficient pricing of electricity revisited," Energy Economics, Elsevier, vol. 104(C).
    12. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    13. Dressler, Luisa, 2016. "Support schemes for renewable electricity in the European Union: Producer strategies and competition," Energy Economics, Elsevier, vol. 60(C), pages 186-196.
    14. Jonathan B. Berk, 1999. "Statistical Discrimination in a Competitive Labor Market," NBER Working Papers 6871, National Bureau of Economic Research, Inc.
    15. Domenico Colucci & Nicola Doni & Vincenzo Valori, 2015. "Information policies in procurement auctions with heterogeneous suppliers," Journal of Economics, Springer, vol. 114(3), pages 211-238, April.
    16. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, vol. 4(3), pages 1-21, June.
    17. Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    18. Adrien de Hauteclocque & Jean-Michel Glachant, 2011. "Long-term Contracts and Competition Policy in European Energy Markets," Chapters, in: Jean-Michel Glachant & Dominique Finon & Adrien de Hauteclocque (ed.), Competition, Contracts and Electricity Markets, chapter 9, Edward Elgar Publishing.
    19. Abate, Arega Getaneh & Riccardi, Rossana & Ruiz, Carlos, 2022. "Contract design in electricity markets with high penetration of renewables: A two-stage approach," Omega, Elsevier, vol. 111(C).
    20. Jesús M. López-Lezama & David Tob�n-Orozco & Esteban Velilla & Jorge Barrientos & Fernando Villada, 2018. "Long-term seasonal forwards in electricity generation markets: an application to Colombia," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, vol. 37(74), pages 287-314.
    21. Jeon, Doh-Shin & Hurkens, Sjaak & Menicucci, Domenico, 2016. "Leveraging Dominance with Credible Bundling," CEPR Discussion Papers 11304, Centre for Economic Policy Research.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:eneeco:v:138:y:2024:i:c:s0140988324005577. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eneco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.