A parametric family of two ranked objects auctions: equilibria and associated risk

Abstract

This paper deals with simultaneous auctions of two commonly ranked objects following the model studied in Menezes and Monteiro (J. Real Estate Finance Econ., 17(3):219-232, 1998). For these problems we introduce a parametric family of auction mechanisms which includes the three classic auctions (discriminatory-price auction, uniform-price auction and Vickrey auction) and we call it the family. We provide the unique Bayesian Nash equilibrium for each auction in and prove a revenue equivalence theorem for the parametric family. Likewise, we study the value at risk of the auctioneer as a reasonable decision criterion to determine which auctions in may be better taking into account the interests of the auctioneer. We show that there are auction mechanisms in which are better than the classic auction mechanisms with respect to this criterion.