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Supply Function Equilibria Always Exist

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  • Anderson, Edward

Abstract

Supply function equilibria are used in the analysis of divisible good auctions with a large number of identical objects to be sold or bought. An important example occurs in wholesale electricity markets. Despite the substantial literature on supply function equilibria the existence of a pure strategy Nash equilibria for a uniform price auction in asymmetric cases has not been established in a general setting. In this paper we prove the existence of a supply function equilibrium for a duopoly with asymmetric firms having convex costs, with decreasing concave demand subject to an additive demand shock, provided the second derivative of the demand function is small enough. The proof is constructive and also gives insight into the structure of the equilibrium solutions.

Suggested Citation

  • Anderson, Edward, 2011. "Supply Function Equilibria Always Exist," Working Papers 04/2011, University of Sydney Business School, Discipline of Business Analytics.
  • Handle: RePEc:syb:wpbsba:2123/8157
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    File URL: http://hdl.handle.net/2123/8157
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    Cited by:

    1. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.

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