Auctions: A New Method for Selling Objects with Bimodal Density Functions

In this paper we define a new auction, called the Draw auction. It is based on the implementation of a draw when a minimum price of sale is not reached. We find that a Bayesian Nash equilibrium is reached in the Draw auction when each player bids his true personal valuation of the object. Furthermor...

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Detalles Bibliográficos
Autores: Castro Cantalejo, Javier, Espínola Vílchez, María Rosario, Gutiérrez García-Pardo, Inmaculada, Gómez González, Daniel
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71561
Acceso en línea:https://hdl.handle.net/20.500.14352/71561
Access Level:acceso abierto
Palabra clave:Auctions and Bidding
Bimodal Distribution
Myerson Auction
Second-Price Auction
Draw auction
Estadística
Probabilidades (Estadística)
1209 Estadística
1208 Probabilidad
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repository_id_str
spelling Auctions: A New Method for Selling Objects with Bimodal Density FunctionsCastro Cantalejo, JavierEspínola Vílchez, María RosarioGutiérrez García-Pardo, InmaculadaGómez González, DanielAuctions and BiddingBimodal DistributionMyerson AuctionSecond-Price AuctionDraw auctionEstadísticaProbabilidades (Estadística)1209 Estadística1208 ProbabilidadIn this paper we define a new auction, called the Draw auction. It is based on the implementation of a draw when a minimum price of sale is not reached. We find that a Bayesian Nash equilibrium is reached in the Draw auction when each player bids his true personal valuation of the object. Furthermore, we show that the expected profit for the seller in the Draw auction is greater than in second-price auctions, with or without minimum price of sale. We make this affirmation for objects whose valuation can be modeled as a bimodal density function in which the first mode is much greater than the second one. Regarding the Myerson auction, we show that the expected profit for the seller in the Draw auction is nearly as good as the expected profit in the optimal auction, with the difference that our method is much more simple to implement than Myerson’s one. All these results are shown by computational tests, for whose development we have defined an algorithm to calculate Myerson auction.Springer NatureUniversidad Complutense de Madrid20222022-04-0320222022-04-03journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/71561reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/715612026-06-02T12:44:21Z
dc.title.none.fl_str_mv Auctions: A New Method for Selling Objects with Bimodal Density Functions
title Auctions: A New Method for Selling Objects with Bimodal Density Functions
spellingShingle Auctions: A New Method for Selling Objects with Bimodal Density Functions
Castro Cantalejo, Javier
Auctions and Bidding
Bimodal Distribution
Myerson Auction
Second-Price Auction
Draw auction
Estadística
Probabilidades (Estadística)
1209 Estadística
1208 Probabilidad
title_short Auctions: A New Method for Selling Objects with Bimodal Density Functions
title_full Auctions: A New Method for Selling Objects with Bimodal Density Functions
title_fullStr Auctions: A New Method for Selling Objects with Bimodal Density Functions
title_full_unstemmed Auctions: A New Method for Selling Objects with Bimodal Density Functions
title_sort Auctions: A New Method for Selling Objects with Bimodal Density Functions
dc.creator.none.fl_str_mv Castro Cantalejo, Javier
Espínola Vílchez, María Rosario
Gutiérrez García-Pardo, Inmaculada
Gómez González, Daniel
author Castro Cantalejo, Javier
author_facet Castro Cantalejo, Javier
Espínola Vílchez, María Rosario
Gutiérrez García-Pardo, Inmaculada
Gómez González, Daniel
author_role author
author2 Espínola Vílchez, María Rosario
Gutiérrez García-Pardo, Inmaculada
Gómez González, Daniel
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Auctions and Bidding
Bimodal Distribution
Myerson Auction
Second-Price Auction
Draw auction
Estadística
Probabilidades (Estadística)
1209 Estadística
1208 Probabilidad
topic Auctions and Bidding
Bimodal Distribution
Myerson Auction
Second-Price Auction
Draw auction
Estadística
Probabilidades (Estadística)
1209 Estadística
1208 Probabilidad
description In this paper we define a new auction, called the Draw auction. It is based on the implementation of a draw when a minimum price of sale is not reached. We find that a Bayesian Nash equilibrium is reached in the Draw auction when each player bids his true personal valuation of the object. Furthermore, we show that the expected profit for the seller in the Draw auction is greater than in second-price auctions, with or without minimum price of sale. We make this affirmation for objects whose valuation can be modeled as a bimodal density function in which the first mode is much greater than the second one. Regarding the Myerson auction, we show that the expected profit for the seller in the Draw auction is nearly as good as the expected profit in the optimal auction, with the difference that our method is much more simple to implement than Myerson’s one. All these results are shown by computational tests, for whose development we have defined an algorithm to calculate Myerson auction.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-04-03
2022
2022-04-03
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/71561
url https://hdl.handle.net/20.500.14352/71561
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución 3.0 España
https://creativecommons.org/licenses/by/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución 3.0 España
https://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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