Mixed mechanisms for auctioning ranked items

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Alonso, Estrella and Sánchez-Soriano, Joaquín and Tejada Cazorla, Juan Antonio (2020) Mixed mechanisms for auctioning ranked items. Mathematics, 8 (12). p. 2227. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math8122227




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Ranked items auctions; Bayesian Nash equilibrium; Expected revenue; Auctioneer’s risk; Value at risk
Palabras clave (otros idiomas):Equilibrio bayesiano de Nash
Subjects:Sciences > Mathematics
Sciences > Mathematics > Applied statistics
Sciences > Statistics > Operations research
ID Code:63715
Deposited On:22 Jan 2021 09:25
Last Modified:25 Jan 2021 08:57

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