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Article

Mixed Mechanisms for Auctioning Ranked Items

by 1,*,†,‡, 2,‡ and 3,‡
1
Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería, Universidad Pontificia Comillas de Madrid, 28015 Madrid, Spain
2
U.I. Center of Operations Research (CIO), Universidad Miguel Hernández de Elche, 03202 Elche, Spain
3
Departamento de Estadística e I.O. and Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28606 Madrid, Spain
*
Author to whom correspondence should be addressed.
Current address: Calle Alberto Aguilera, 25, despacho 207, 28015 Madrid, Spain.
These authors contributed equally to this work.
Mathematics 2020, 8(12), 2227; https://doi.org/10.3390/math8122227
Received: 26 October 2020 / Revised: 5 December 2020 / Accepted: 8 December 2020 / Published: 15 December 2020
(This article belongs to the Special Issue Statistical and Probabilistic Methods in the Game Theory)
This paper deals with the problem of designing and choosing auctioning mechanisms for multiple commonly ranked objects as, for instance, keyword auctions in search engines on Internet. We shall adopt the point of view of the auctioneer who has to select the auction mechanism to be implemented not only considering its expected revenue, but also its associated risk. In order to do this, we consider a wide parametric family of auction mechanisms which contains the generalizations of discriminatory-price auction, uniform-price auction and Vickrey auction. For completeness, we also analyze the Generalized Second Price (GSP) auction which is not in the family. The main results are: (1) all members of the family satisfy the four basic properties of fairness, no over-payment, optimality and efficiency, (2) the Bayesian Nash equilibrium and the corresponding value at risk for the auctioneer are obtained for the considered auctions, (3) the GSP and all auctions in the family provide the same expected revenue, (4) there are new interesting auction mechanisms in the family which have a lower value at risk than the GSP and the classical auctions. Therefore, a window opens to apply new auction mechanisms that can reduce the risk to be assumed by auctioneers. View Full-Text
Keywords: ranked items auctions; Bayesian Nash equilibrium; expected revenue; auctioneer’s risk; value at risk ranked items auctions; Bayesian Nash equilibrium; expected revenue; auctioneer’s risk; value at risk
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MDPI and ACS Style

Alonso, E.; Sánchez-Soriano, J.; Tejada, J. Mixed Mechanisms for Auctioning Ranked Items. Mathematics 2020, 8, 2227. https://doi.org/10.3390/math8122227

AMA Style

Alonso E, Sánchez-Soriano J, Tejada J. Mixed Mechanisms for Auctioning Ranked Items. Mathematics. 2020; 8(12):2227. https://doi.org/10.3390/math8122227

Chicago/Turabian Style

Alonso, Estrella, Joaquín Sánchez-Soriano, and Juan Tejada. 2020. "Mixed Mechanisms for Auctioning Ranked Items" Mathematics 8, no. 12: 2227. https://doi.org/10.3390/math8122227

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