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Asymmetric Supply Function Equilibria with Forward Contracts

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Abstract

We consider markets in which firms offer supply functions, rather than a quantity or price alone: the most important examples are wholesale electricity markets. The equilibria in such markets can be hard to characterize. In many cases, whole families of supply function equilibria occur so there are difficulties in determining which equilibrium will be chosen. In this paper, we consider supply function equilibria, when firms hold forward contracts, which is common in electricity markets. Under the assumption that contract positions have been fixed in advance, we characterize the families of supply function equilibria in a duopoly. The existence of forward contracts implies a tightening of the conditions for an equilibrium, and a greater likelihood that no equilibrium solution exists. In the case of three firms, there can be at most one supply function equilibrium, provided that the lowest demand be small enough.

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References

  1. Klemperer, P.D., Meyer, M.A.: Supply function equilibria in oligopoly under uncertainty. Econometrica 57, 1243–1277 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Green, R., Newbery, D.: Competition in the British electric spot market. J. Polit. Econ. 100, 929–953 (1992)

    Article  Google Scholar 

  3. Baldick, R., Grant, R., Kahn, E.: Linear supply function equilibrium, generalizations, applications and limitations. J. Regul. Econ. 25(2), 143–167 (2004)

    Article  Google Scholar 

  4. Green, R.: The electricity contract market in England and Wales. J. Ind. Econ. 47, 929–952 (1999)

    Google Scholar 

  5. Holmberg, P.: Numerical calculation of an asymmetric supply function equilibrium with capacity constraints. Department of Economics, Uppsala Universitet, Sweden (2005)

  6. Anderson, E.J., Hu, X.: Finding supply function equilibria with asymmetric firms. Oper. Res. 56, 697–711 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Allaz, B., Vila, J.-L.: Cournot competition, futures markets and efficiency. J. Econ. Theory 59, 1–16 (1993)

    Article  MATH  Google Scholar 

  8. Anderson, E.J., Hu, X.: Strategic retailer behavior in an electricity contract markets. Int. J. Ind. Organ. 26, 679–694 (2008)

    Article  Google Scholar 

  9. Newbery, D.M.: Competition, contracts, and entry in the electricity spot market. Rand J. Econ. 29, 726–749 (1998)

    Article  Google Scholar 

  10. Powell, A.: Trading forward in an imperfect market: the case of electricity in Britain. Econ. J. (Lond.) 103, 444–453 (1993)

    Article  Google Scholar 

  11. Anderson, E.J., Xu, H.: Supply function equilibrium in electricity spot markets with contracts and price caps. J. Optim. Theory Appl. 124, 257–283 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Alvey, T., Goodwin, D., Ma, D., Streiffert, D., Sun, D.: A security-constrained bid-clearing system for the New Zealand wholesale electricity market. IEEE Trans. Power Syst. 13, 340–346 (1998)

    Article  Google Scholar 

  13. Hortacsu, A., Puller, S.L.: Understanding strategic models of bidding in deregulated electricity markets: A case study of ERCOT. Rand J. Econ. 39, 86–114 (2008)

    Article  Google Scholar 

  14. Genc, T., Reynolds, S.: Supply function equilibria with pivotal electricity suppliers. Eller College Working Paper No. 1001-04. University of Arizona (2004)

  15. Holmberg, P.: Supply function equilibrium with asymmetric capacities and constant marginal costs. Energy J. 28(2), 55–82 (2007)

    MathSciNet  Google Scholar 

  16. Anderson, E.J., Philpott, A.B.: Optimal offer construction in electricity markets. Math. Oper. Res. 27, 82–100 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Escobar, J.F., Jofre, A.: Equilibrium analysis of electricity auctions. Department of Economics Stanford University (2008)

  18. Sioshansi, R., Oren, S.: How good are supply function equilibrium models: an empirical analysis of the ERCOT balancing market. J. Regul. Econ. 31, 1–35 (2007)

    Article  Google Scholar 

  19. Aumann, R.: Acceptable points in general cooperative n-person games. In: Contributions to the Theory of Games IV. Princeton University Press, Princeton (1959)

    Google Scholar 

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Authors and Affiliations

  1. University of Sydney Business School, Sydney, NSW, 2006, Australia

    Edward J. Anderson

  2. RepuTex (AU) Pty Ltd, Melbourne, VIC, 3000, Australia

    Xinmin Hu

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  1. Edward J. Anderson
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  2. Xinmin Hu
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Correspondence to Edward J. Anderson.

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Communicated by Liqun Qi.

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Anderson, E.J., Hu, X. Asymmetric Supply Function Equilibria with Forward Contracts. J Optim Theory Appl 152, 198–224 (2012). https://doi.org/10.1007/s10957-011-9879-2

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  • DOI: https://doi.org/10.1007/s10957-011-9879-2

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