Mixed Mechanisms for Auctioning Ranked Items
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 on...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2227 |
| _version_ | 1797544623103541248 |
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| author | Estrella Alonso Joaquín Sánchez-Soriano Juan Tejada |
| author_facet | Estrella Alonso Joaquín Sánchez-Soriano Juan Tejada |
| author_sort | Estrella Alonso |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T14:04:06Z |
| format | Article |
| id | doaj.art-9c4b4a636f29444999d53016a27babdf |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:04:06Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9c4b4a636f29444999d53016a27babdf2023-11-21T00:52:57ZengMDPI AGMathematics2227-73902020-12-01812222710.3390/math8122227Mixed Mechanisms for Auctioning Ranked ItemsEstrella Alonso0Joaquín Sánchez-Soriano1Juan Tejada2Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería, Universidad Pontificia Comillas de Madrid, 28015 Madrid, SpainU.I. Center of Operations Research (CIO), Universidad Miguel Hernández de Elche, 03202 Elche, SpainDepartamento de Estadística e I.O. and Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28606 Madrid, SpainThis 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.https://www.mdpi.com/2227-7390/8/12/2227ranked items auctionsBayesian Nash equilibriumexpected revenueauctioneer’s riskvalue at risk |
| spellingShingle | Estrella Alonso Joaquín Sánchez-Soriano Juan Tejada Mixed Mechanisms for Auctioning Ranked Items Mathematics ranked items auctions Bayesian Nash equilibrium expected revenue auctioneer’s risk value at risk |
| title | Mixed Mechanisms for Auctioning Ranked Items |
| title_full | Mixed Mechanisms for Auctioning Ranked Items |
| title_fullStr | Mixed Mechanisms for Auctioning Ranked Items |
| title_full_unstemmed | Mixed Mechanisms for Auctioning Ranked Items |
| title_short | Mixed Mechanisms for Auctioning Ranked Items |
| title_sort | mixed mechanisms for auctioning ranked items |
| topic | ranked items auctions Bayesian Nash equilibrium expected revenue auctioneer’s risk value at risk |
| url | https://www.mdpi.com/2227-7390/8/12/2227 |
| work_keys_str_mv | AT estrellaalonso mixedmechanismsforauctioningrankeditems AT joaquinsanchezsoriano mixedmechanismsforauctioningrankeditems AT juantejada mixedmechanismsforauctioningrankeditems |