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

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 $\mathcal{DUV}$ family. We provide the unique Bayesian Nash equilibrium for each auction in $\mathcal{DUV}$ 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 $\mathcal{DUV}$ may be better taking into account the interests of the auctioneer. We show that there are auction mechanisms in $\mathcal{DUV}$ which are better than the classic auction mechanisms with respect to this criterion. Copyright Springer Science+Business Media New York 2015