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 non-decreasing marginal costs, with decreasing concave demand subject to an additive demand shock, provided that the second derivative of the demand function is small enough and not increasing. The proof is constructive and also gives insight into the structure of the equilibrium solutions.
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