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Pay-as-bid: selling divisible goods


Pycia, Marek; Woodward, Kyle (2016). Pay-as-bid: selling divisible goods. SSRN 2417512, SSRN eLibrary.

Abstract

Pay-as-bid is the most popular auction format for selling treasury securities. We prove the uniqueness of pure-strategy Bayesian-Nash equilibria in pay-as-bid auctions where symmetrically-informed bidders face uncertain supply, and we establish a tight sufficient condition for the existence of this equilibrium. Equilibrium bids have a convenient separable representation: the bid for any unit is a weighted average of marginal values for larger quantities. With optimal supply and reserve price, the pay-as-bid auction is revenue-equivalent to the uniform-price auction.

Abstract

Pay-as-bid is the most popular auction format for selling treasury securities. We prove the uniqueness of pure-strategy Bayesian-Nash equilibria in pay-as-bid auctions where symmetrically-informed bidders face uncertain supply, and we establish a tight sufficient condition for the existence of this equilibrium. Equilibrium bids have a convenient separable representation: the bid for any unit is a weighted average of marginal values for larger quantities. With optimal supply and reserve price, the pay-as-bid auction is revenue-equivalent to the uniform-price auction.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Language:English
Date:December 2016
Deposited On:03 Jul 2018 14:31
Last Modified:24 Mar 2020 11:47
Series Name:SSRN
Number of Pages:55
ISSN:1556-5068
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.2139/ssrn.2417512
Official URL:https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2417512

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