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Exploiting complete linear descriptions for decentralized power market problems with integralities

Author

Listed:
  • Lukas Hümbs

    (Friedrich-Alexander-Universität Erlangen-Nürnberg)

  • Alexander Martin

    (Friedrich-Alexander-Universität Erlangen-Nürnberg)

  • Lars Schewe

    (The University of Edinburgh)

Abstract

It is well known that linear prices supporting a competitive equilibrium exist in the case of convex markets, however, in the presence of integralities this is open and hard to decide in general. We present necessary and sufficient conditions for the existence of such prices for decentralized market problems where market participants have integral decision variables and their feasible sets are given in complete linear description. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications. Furthermore, we compute competitive equilibria for two classes of decentralized market problems arising in energy markets and show that competitive equilibria may exist regardless of integralities.

Suggested Citation

  • Lukas Hümbs & Alexander Martin & Lars Schewe, 2022. "Exploiting complete linear descriptions for decentralized power market problems with integralities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 451-474, June.
    • Handle: RePEc:spr:mathme:v:95:y:2022:i:3:d:10.1007_s00186-022-00775-z
    DOI: 10.1007/s00186-022-00775-z
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    References listed on IDEAS

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    1. 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.
    2. Brian Carlson & Yonghong Chen & Mingguo Hong & Roy Jones & Kevin Larson & Xingwang Ma & Peter Nieuwesteeg & Haili Song & Kimberly Sperry & Matthew Tackett & Doug Taylor & Jie Wan & Eugene Zak, 2012. "MISO Unlocks Billions in Savings Through the Application of Operations Research for Energy and Ancillary Services Markets," Interfaces, INFORMS, vol. 42(1), pages 58-73, February.
    3. WOLSEY, Laurence A., 1981. "Integer programming duality: price functions and sensitivity analysis," LIDAM Reprints CORE 431, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    5. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.
    6. Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    7. Araoz, Veronica & Jörnsten, Kurt, 2011. "Semi-Lagrangean approach for price discovery in markets with non-convexities," European Journal of Operational Research, Elsevier, vol. 214(2), pages 411-417, October.
    8. VAN VYVE, Mathieu, 2011. "Linear prices for non-convex electricity markets: models and algorithms," LIDAM Discussion Papers CORE 2011050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    10. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    11. George Liberopoulos & Panagiotis Andrianesis, 2016. "Critical Review of Pricing Schemes in Markets with Non-Convex Costs," Operations Research, INFORMS, vol. 64(1), pages 17-31, February.
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