Supply function equilibria of pay-as-bid auctions |
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Authors: | Pär Holmberg |
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Institution: | (1) Research Institute of Industrial Economics, Box 55665, SE-102 15 Stockholm, Sweden |
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Abstract: | This paper characterizes the Nash equilibrium in a pay-as-bid (discriminatory), divisible-good, procurement auction. Demand
by the auctioneer is uncertain as in the supply function equilibrium model. A closed form expression is derived for a one
shot game. Existence of an equilibrium is ensured if the hazard rate of the demand distribution is monotonically decreasing
with respect to the shock outcome and sellers have non-decreasing marginal costs. Multiple equilibria can be ruled out for
markets, for which the auctioneer’s demand exceeds suppliers’ capacity with a positive probability. The derived equilibrium
can be used to model strategic bidding behavior in pay-as-bid electricity auctions, such as the balancing mechanism of United
Kingdom. Offer curves and mark-ups of the derived equilibrium are compared to results for the SFE of a uniform-price auction.
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Keywords: | Supply function equilibrium Pay-as-bid auction Discriminatory auction Divisible good auction Oligopoly Electricity market |
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