Patrick W. Schmitz
Journal of Mathematical Economics, Vol. 39 (8), 2003, 901-909.
Abstract. Consider two sellers each of whom has one unit of an indivisible good and two buyers each of whom is interested in buying one unit. The sellers simultaneously set reserve prices and use second price auctions as rationing device. An equilibrium in pure strategies where each seller has a regular customer is characterized. The result is applied in order to demonstrate that not allowing sellers to use second price auctions may enhance total surplus.
The working paper version is available for download (CEPR Discussion Paper 3774).
Another working paper version is available for download at SSRN.
The paper is available for download.