Auctions of divisible goods with endogenous supply
K. Back and J.F. Zender
Economics Letters 73 (2001) 29–34
I’m working on a research problem that has some relationship to auction theory, so I’m trying to read up on some of the literature. I finally found this paper, which is more related to what I’m doing — an auction in which the amount of the divisible good is determined after the bidding. This is used in Treasury auctions in some countries, but is also a reasonable model for a kind of “middleman scenario” I think, where the seller is a middleman and uses the bids to purchase the good to be sold from a supplier.
In a uniform-price auction (where the bidders bid demand curves and the seller sets a price), equilibria exists where the bidders bid really low and then get the good for free. This can be arbitrarily bad for the seller. In a discriminatory-price auction (where the price bidders pay is kind of like an integral of their demand curve), this problem doesn’t happen, since bidders are interested in their entire demand curve. This is good for the seller.
But you can fix up a uniform price auction by letting the seller restrict the supply after the bids come in, This paper shows that in that case, the equilibria are better for the seller, and in fact the seller will not have to restrict the supply. So by retaining the right to restrict the supply, the situation is improved, but that right need not be exercised.