Mathematical Programming

, Volume 140, Issue 2, pp 295–322 | Cite as

Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition

  • S. Wogrin
  • B. F. Hobbs
  • D. Ralph
  • E. Centeno
  • J. Barquín
Full Length Paper Series B

Abstract

We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market equilibrium outcomes in the second stage. The latter problem is an equilibrium problem with equilibrium constraints. In both models, the intensity of competition among producers in the energy market is frequently represented using conjectural variations. Considering one load period, we show that for any choice of conjectural variations ranging from perfect competition to Cournot, the closed loop equilibrium coincides with the Cournot open loop equilibrium, thereby obtaining a ‘Kreps and Scheinkman’-like result and extending it to arbitrary strategic behavior. When expanding the model framework to multiple load periods, the closed loop equilibria for different conjectural variations can diverge from each other and from open loop equilibria. We also present and analyze alternative conjectured price response models with switching conjectures. Surprisingly, the rank ordering of the closed loop equilibria in terms of consumer surplus and market efficiency (as measured by total social welfare) is ambiguous. Thus, regulatory approaches that force marginal cost-based bidding in spot markets may diminish market efficiency and consumer welfare by dampening incentives for investment. We also show that the closed loop capacity yielded by a conjectured price response second stage competition can be less or equal to the closed loop Cournot capacity, and that the former capacity cannot exceed the latter when there are symmetric agents and two load periods.

Keywords

Generation expansion planning Capacity pre-commitment   Noncooperative games Equilibrium problem with equilibrium constraints (EPEC) 

Mathematics Subject Classification

90B99 Operations Research and Management Science 91B26 Mathematical economics (Market Models) 91A05 Game Theory (Non-cooperative games) 91A40 Game Theory (Game theoretic models) 

References

  1. 1.
    Allaz, B., Vila, J.-L.: Cournot competition, forward markets and efficiency. J. Econ. Theory 59, 1–16 (1993)CrossRefGoogle Scholar
  2. 2.
    Berry, C.A., Hobbs, B.F., Meroney, W.A., O’Neill, R.P., Stewart, W.R.: Understanding how market power can arise in network competition: a game theoretic approach. Util. Policy 8(3), 139–158 (1999)CrossRefGoogle Scholar
  3. 3.
    Bertrand, J.: Book review of ‘Theorie mathematique de la richesse sociale and of recherchers sur les principles mathematiques de la theorie des richesses’. Journal de Savants 67, 499–508 (1883)Google Scholar
  4. 4.
    Cardell, J.B., Hitt, C.C., Hogan, W.W.: Market power and strategic interaction in electricity networks. Res. Energy Econ. 19, 109–137 (1997)CrossRefGoogle Scholar
  5. 5.
    Centeno, E., Reneses, J., Barquin, J.: Strategic analysis of electricity markets under uncertainty: a conjectured-price-response approach. IEEE Trans. Power Syst. 22(1), 423–432 (2007)Google Scholar
  6. 6.
    Centeno, E., Reneses, J., Garcia, R., Sanchez J.J.: Long-term market equilibrium modeling for generation expansion planning. In: IEEE Power Tech Conference (2003)Google Scholar
  7. 7.
    Centeno, E., Reneses, J., Wogrin, S., Barquín J.: Representation of electricity generation capacity expansion by means of game theory models. In: 8th International Conference on the European Energy Market, Zagreb, Croatia (2011)Google Scholar
  8. 8.
    Cournot, A.A.: Researches into Mathematical Principles of the Theory of Wealth. Kelley, New York, USA (1838)Google Scholar
  9. 9.
    Daxhelet O.: Models of Restructured Electricity Systems. Ph. D. thesis, Université Catholique de Louvain (2008)Google Scholar
  10. 10.
    Day, C.J., Hobbs, B.F., Pang, J.-S.: Oligopolistic competition in power networks: a conjectured supply function approach. IEEE Trans. Power Syst. 17(3), 597–607 (2002)CrossRefGoogle Scholar
  11. 11.
    Figuières, C., Jean-Marie, A., Quérou, N., Tidball, M.: Theory of Conjectural Variations. World Scientific Publishing, Singapore (2004)CrossRefGoogle Scholar
  12. 12.
    Fudenberg, D., Tirole J.: Noncooperative game theory for industrial organization: an introduction and overview. Handbook of Industrial Organization, Volume 1, Chapter 5. Elsevier, pp. 259–327 (1989)Google Scholar
  13. 13.
    Garcia-Bertrand, R., Kirschen, D., Conejo A.J.: Optimal investments in generation capacity under uncertainty. In: 16th Power Systems Computation Conference, Glasgow (2008)Google Scholar
  14. 14.
    Grimm V., Zöttl G.: Investment incentives and electricity spot market design. Under revision, Münchener Wirtschaftswissenschaftliche Beiträge (VWL), 29 (2010)Google Scholar
  15. 15.
    Hobbs, B.F., Helman, U.: Complementarity-based equilibrium modeling for electric power markets. In: Bunn, D.W. (ed.) Modeling Prices in Competitive Electricity Markets. Wiley Series in Financial Economics. Wiley, London (2004)Google Scholar
  16. 16.
    Hobbs, B.F., Metzler, C.B., Pang, J.-S.: Calculating equilibria in imperfectly competitive power markets: an MPEC approach. IEEE Trans. Power Syst. 15, 638–645 (2000)CrossRefGoogle Scholar
  17. 17.
    Hu, X.: Mathematical Programs with Complementarity Constraints and Game Theory Models in Electricity Markets. Ph. D. thesis, The University of Melbourne (2003)Google Scholar
  18. 18.
    Hu, X., Ralph, D.: Using EPECs to model bilevel games in restructured electricity markets with locational prices. Oper. Res. 55(5), 809–827 (2007)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Kazempour, S.J., Conejo, A.J., Ruiz, C.: Strategic generation investment using a complementarity approach. IEEE Trans. Power Syst. 26(2), 940–948 (2011)Google Scholar
  20. 20.
    Kreps, D.M., Scheinkman, J.A.: Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell J. Econ. 14(2), 326–337 (1983)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Leyffer, S., Munson, T.: Solving multi-leader-follower games. Technical Report, ANL/MCS-P1243-0405, Argonne National Laboratory, Argonne, IL (2005)Google Scholar
  22. 22.
    Murphy, F.H., Smeers, Y.: Generation capacity expansion in imperfectly competitive restructured electricity markets. Oper. Res. 53(4), 646–661 (2005)CrossRefGoogle Scholar
  23. 23.
    Murphy, F.H., Smeers, Y.: Withholding investments in energy only markets: can contracts make a difference. J. Regul. Econ. 42(2), 159–179 (2012)CrossRefGoogle Scholar
  24. 24.
    O’Neill, R.P., Helman, U., Hobbs, B.F., Baldick, R.: Independent system operators in the United States: history, lessons learned, and prospects. In: Sioshansi, F., Pfaffenberger, W. (eds.) Market Reform: An International Experience, Global Energy Policy and Economic Series, Chapter 14, pp. 479–528. Elsevier, Amsterdam (2006)Google Scholar
  25. 25.
    Perloff, J.M., Karp, L.S., Golan, A.: Estimating Market Power and Strategies. Cambridge University Press, Cambridge (2007)CrossRefGoogle Scholar
  26. 26.
    All Island Project. The Bidding Code of Practice—A Response and Decision Paper. Commission for Energy Regulation (CER) & the Northern Ireland Authority for Utility Regulation (NIAUR), Dublin, Ireland (2007)Google Scholar
  27. 27.
    Ralph, D., Smeers, Y.: EPECs as models for electricity markets. In: IEEE Power Systems Conference and Exposition (PSCE), Atlanta, GA (2006)Google Scholar
  28. 28.
    Sakellaris, K.: Modeling electricity markets as two-stage capacity constrained price competition games under uncertainty. In: 7th International Conference on the European Energy Market, Madrid (2010)Google Scholar
  29. 29.
    Su C.-L.: Equilibrium Problems with Equilibrium Constraints: Stationarities, Algorithms, and Applications. Ph. D. thesis, Stanford University (2001)Google Scholar
  30. 30.
    Tirole, J.: Theory of Industrial Organization. MIT Press, Cambridge (1988)Google Scholar
  31. 31.
    Ventosa, M., Denis, R., Redondo, C.: Expansion planning in electricity markets. Two different approaches. In: 14th Power Systems Computation Conference, Sevilla (2003)Google Scholar
  32. 32.
    Weber, J.D., Overbye, T.J.: A two-level optimization problem for analysis of market bidding strategies. In: IEEE Power Engineering Society Summer Meeting, Edmonton, Canada, pp. 682–687 (1999)Google Scholar
  33. 33.
    Wogrin, S., Hobbs, B.F., Ralph, D.: Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition—the case of symmetric and asymmetric electricity generation firms, EPRG Working Paper in preparation (2011)Google Scholar
  34. 34.
    Wogrin, S., Hobbs, B.F., Ralph, D., Centeno, E., Barquín, J.: Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition, Optimization Online (2012)Google Scholar
  35. 35.
    Younes, Z., Ilic, M.: Generation strategies for gaming transmission constraints: will the deregulated electric power market be an oligopoly. Decis. Support Syst. 24, 207–222 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013

Authors and Affiliations

  • S. Wogrin
    • 1
  • B. F. Hobbs
    • 2
  • D. Ralph
    • 3
  • E. Centeno
    • 1
  • J. Barquín
    • 1
  1. 1.Instituto de Investigación Tecnológica, Escuela Técnica Superior de Ingeniería (ICAI)Universidad Pontificia ComillasMadridSpain
  2. 2.Department of Geography and Environmental Engineering, and Environment, Energy, Sustainability and Health InstituteThe Johns Hopkins UniversityBaltimoreUSA
  3. 3.Cambridge Judge Business School and Electricity Policy Research GroupUniversity of CambridgeCambridgeUK

Personalised recommendations