Central European Journal of Operations Research

, Volume 27, Issue 4, pp 953–984 | Cite as

On the efficiency of local electricity markets under decentralized and centralized designs: a multi-leader Stackelberg game analysis

  • Hélène Le CadreEmail author
Original Paper


In this paper, we analytically compare centralized and decentralized market designs involving a national and local market operators, strategic generators having market power and bidding sequentially in local markets, to determine which design is more efficient for the procurement of energy. In the centralized design, used as benchmark, the national market operator optimizes the exchanges between local markets and the generators’ block bids. In the decentralized design, generators act as Stackelberg leaders, anticipating the local market prices and the flows on the transmission lines. Clearing of the local markets can be either simultaneous or sequential. The resulting two-stage game with competitive leaders that are not price takers is formulated as a bilevel mathematical programming problem which is reformulated as a Nash–Cournot game, and conditions for existence and uniqueness of market equilibrium are studied. Imperfect information is also considered, resulting from the lack of incentives from the generators to share their RES-based generations. Through a case study, we determine that the decentralized design is as efficient as the centralized one with high share of renewables, using as performance measure the price of anarchy, and that imperfect information has a limited impact on the efficiency of the decentralized market design. Furthermore, we check numerically that there exists an upper-limit on the block bid length maximizing the social welfare under both centralized and decentralized designs.


Bilevel mathematical programming Complementarity theory Electricity market Bidding Price of anarchy 


  1. Barquin J, Vazquez M (2003) Cournot equilibrium computation on electricity networks. In: 2nd international workshop on liberalization and modernization of power systems, congestion management problemsGoogle Scholar
  2. Bose S, Cai D, Low S, Wierman A (2014) The role of a market maker in networked cournot competition. In: Proceedings of 53rd IEEE conference on decision and control, pp 4479–4484Google Scholar
  3. Borenstein S, Bushnell J, Stoft S (2000) The competitive effects of transmission capacity in a deregulated electricity industry. RAND J Econ 31(2):294–325CrossRefGoogle Scholar
  4. California ISO, Shift Factors: Methodology and Example, CAISO Market Operations. Online Dec 2016
  5. Cardell J, Hitt CC, Hogan WW (1996) Market power and strategic interactions in electricity networks. Resour Energy Econ 19(1–2):25–60Google Scholar
  6. Chao H-P, Peck SC (1996) A market mechanism for electric power transmission. J Regul Econ 10(1):25–60CrossRefGoogle Scholar
  7. Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann Oper Res 153:235–256CrossRefGoogle Scholar
  8. Dempe S (2010) Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optim J Math Program Oper Res 52(3):333–359Google Scholar
  9. Dempe S, Dutta J (2012) Is bilevel programming a special case of a mathematical program with complementarity constraints? Math Program 131(1):37–48CrossRefGoogle Scholar
  10. Dempe S, Kalashnikov V, Perez-Valdes GA, Kalashnikova N (2015) Bilevel programming problems: theory, algorithms and applications to energy networks. Springer, Energy Systems, BerlinCrossRefGoogle Scholar
  11. Economides N, Tag J (2012) Net neutrality on the Internet: a two-sided market analysis. Inf Econ Policy 24:91–104CrossRefGoogle Scholar
  12. Ehrenmann A, Neuhoff K (2009) A comparison of electricity market designs in networks. Oper Res 57(2):274–286CrossRefGoogle Scholar
  13. Gabriel SA, Conejo AJ, Fuller JD, Hobbs BF, Ruiz C (2013) Complementarity modeling in energy markets. International Series in Operations Research & Management ScienceGoogle Scholar
  14. Gonzalez Vaya M, Andersson G (2013) Optimal bidding strategy of a plug-in electric vehicle aggregator in day-ahead electricity markets. In: Proceedings European Energy Market (EEM) conferenceGoogle Scholar
  15. Karamardian S (1972) The complementarity problem. Math Program 2:107–129CrossRefGoogle Scholar
  16. Kolstad CD, Mathiesen L (1991) Computing Cournot–Nash equilibria. Oper Res 39:739–748CrossRefGoogle Scholar
  17. Koutsoupias E, Papadimitriou CH (1999) Worst-case equilibria. In: Proceedings of 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS), vol 1563Google Scholar
  18. Kulkarni AA, Shanbhag UV (2014) A shared-constraint approach to multi-leader multi-follower games. Set Valued Var Anal 22(4):691–720CrossRefGoogle Scholar
  19. Le Cadre H (2017) On the efficiency of local electricity markets. In: Proceedings of 14th International Conference on the European Energy Market (EEM).
  20. Le Cadre H, Papavasiliou A, Smeers Y (2015) Wind farm portfolio optimization. Eur J Oper Res (EJOR) 247(2):560–574CrossRefGoogle Scholar
  21. Lieberman MB, Montgomery DB (1988) First-mover advantages. Strateg Manag J 9:41–58CrossRefGoogle Scholar
  22. Matamoros J, Gregoratti D, Dohler M (2012) Trading microgrids energy, in islanding mode. In: Proceedings of IEEE SmartGridComm 2012 Symposium, Demand Side Management, Demand Response, Dynamic PricingGoogle Scholar
  23. Moré JJ, Rheinbold WC (1973) On P- and S- functions and related classes of \(n\)-dimensional nonlinear mappings. Linear Algebra Appl 6:45–68CrossRefGoogle Scholar
  24. Neuhoff K, Barquin J, Maroeska GB, Ehrenmann A, Hobbs B, Rijkers FAM, Vázquez M (2005) Network-constrained Cournot models of liberalized electricity markets: the devil is in the details. Energy Econ 27:495–525CrossRefGoogle Scholar
  25. Nisan N, Roughgarden T, Tardos E, Vazirani VV (2007) Algorithmic game theory. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  26. Optimate Platform, A numerical simulation platform to recommend new electricity market designs integrating massive flexible generation in Europe. Online Jan 2017
  27. Osborne MJ, Rubinstein A (1994) Course in game theory. MIT Press, CambridgeGoogle Scholar
  28. Papavasiliou A (2017) Analysis of distribution locational marginal prices, IEEE Transactions on SmartGrid, vol 99.
  29. Perez-Arriaga I (ed) (2013) Regulation of the power sector. Springer, BerlinGoogle Scholar
  30. Poli D, Marracci M (2011) Clearing procedures for day-ahead Italian electricity market: are complex bids really required? Int J Energy 3(5):70–77Google Scholar
  31. Purchala K, Meeus L, Van Dommelen D, Belmans R (2005) Usefulness of DC power flow for active power flow analysis. In: Proceedings of IEEE PES General Meeting, pp 2457–2462Google Scholar
  32. Ruiz C, Conejo AJ (2009) Pool strategy of a producer with endogenous formation of locational marginal prices. IEEE Trans Power Syst 24:1855–1866CrossRefGoogle Scholar
  33. Schwalbe U, Walker P (2001) Zermelo and the early history of game theory. Games Econ Behav 34(1):123–137CrossRefGoogle Scholar
  34. Smeers Y, Oggioni G, Allevi E, Schaible S (2012) Generalized Nash equilibrium and market coupling in the European power system. Netw Spat Econ 12(4):503–560CrossRefGoogle Scholar
  35. Stoft S (2002) Power system economics: designing market for power. IEEE Press, PiscatawayCrossRefGoogle Scholar
  36. Szidarovsky F, Yakowitz S (1977) A new proof of the existence and uniqueness of the Cournot equilibrium. Int Econ Rev 18:787–789CrossRefGoogle Scholar
  37. Xu Y, Cai D, Bose S, Wierman A (2015) On the efficiency of networked Stackelberg competition. In: Proceedings of IEEE conference on decision and controlGoogle Scholar
  38. Yao J, Adler I, Oren SS (2008) Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network. Oper Res 56(1):34–47CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.VITO/EnergyVille Research CenterGenkBelgium

Personalised recommendations