Annals of Operations Research

, Volume 225, Issue 1, pp 141–160

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

  • Estrella Alonso
  • Joaquin Sanchez-Soriano
  • Juan Tejada

DOI: 10.1007/s10479-012-1297-9

Cite this article as:
Alonso, E., Sanchez-Soriano, J. & Tejada, J. Ann Oper Res (2015) 225: 141. doi:10.1007/s10479-012-1297-9


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.


Multi-object auctionsBayesian Nash equilibriumExpected revenueValue at risk

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Estrella Alonso
    • 1
  • Joaquin Sanchez-Soriano
    • 2
  • Juan Tejada
    • 3
  1. 1.Escuela Tecnica Superior de IngenieriaUniversidad Pontificia Comillas de MadridMadridSpain
  2. 2.U.I. Center Operations Research (CIO)Miguel Hernandez University of ElcheElcheSpain
  3. 3.Departamento de Estadistica e I.O. and Instituto de Matematica InterdisciplinarUniversidad Complutense de MadridMadridSpain