Asymmetric first-price auctions with uniform distributions: Analytic solutions to the general case

Todd R. Kaplan; Shmuel Zamir

doi:10.1007/s00199-010-0563-9

Asymmetric first-price auctions with uniform distributions: Analytic solutions to the general case

Todd R. Kaplan, Shmuel Zamir

Department of Economics

Research output: Contribution to journal › Article › peer-review

Abstract

In 1961, Vickrey posed the problem of finding an analytic solution to a first-price auction with two buyers having valuations uniformly distributed on [v{script} ₂, v{script} ₂] and [v{script} ₂, v{script} ₂]. To date, only special cases of the problem have been solved. In this paper, we solve this general problem and in addition allow for the possibility of a binding minimum bid. Several interesting examples are presented, including a class where the two bid functions are linear.

Original language	English
Pages (from-to)	269-302
Number of pages	34
Journal	Economic Theory
Volume	50
Issue number	2
DOIs	https://doi.org/10.1007/s00199-010-0563-9
State	Published - Jun 2012

Keywords

Asymmetric auctions
First-price auctions
Incomplete information

ASJC Scopus subject areas

Economics and Econometrics

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10.1007/s00199-010-0563-9

Cite this

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abstract = "In 1961, Vickrey posed the problem of finding an analytic solution to a first-price auction with two buyers having valuations uniformly distributed on [v\{script\} 2, v\{script\} 2] and [v\{script\} 2, v\{script\} 2]. To date, only special cases of the problem have been solved. In this paper, we solve this general problem and in addition allow for the possibility of a binding minimum bid. Several interesting examples are presented, including a class where the two bid functions are linear.",

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N2 - In 1961, Vickrey posed the problem of finding an analytic solution to a first-price auction with two buyers having valuations uniformly distributed on [v{script} 2, v{script} 2] and [v{script} 2, v{script} 2]. To date, only special cases of the problem have been solved. In this paper, we solve this general problem and in addition allow for the possibility of a binding minimum bid. Several interesting examples are presented, including a class where the two bid functions are linear.

AB - In 1961, Vickrey posed the problem of finding an analytic solution to a first-price auction with two buyers having valuations uniformly distributed on [v{script} 2, v{script} 2] and [v{script} 2, v{script} 2]. To date, only special cases of the problem have been solved. In this paper, we solve this general problem and in addition allow for the possibility of a binding minimum bid. Several interesting examples are presented, including a class where the two bid functions are linear.

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KW - First-price auctions

KW - Incomplete information

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Asymmetric first-price auctions with uniform distributions: Analytic solutions to the general case

Abstract

Keywords

ASJC Scopus subject areas

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