Revenue Deficiency Under Second-price Auctions in a Supply-chain Setting

Dolores Romero Morales, Richard Steinberg

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Consider a firm, called the buyer, that satisfies its demand over two periods by assigning both demands to a supplier via a second-price procurement auction; call this the Standard auction. In the hope of lowering its purchase cost, the firm is considering an alternative procedure in which it will also allow bids on each period individually, where there can be either one or two winners covering the two demands; call this the Multiple Winner auction. Choosing the Multiple Winner auction over the Standard auction can in fact result in a higher cost to the buyer. We provide a bound on how much greater the buyer’s cost can be in the Multiple Winner auction and show that this bound is tight. We then sharpen this bound for two scenarios that can arise when the buyer announces his demands close to the beginning of the demand horizon. Under a monotonicity condition, we achieve a further sharpening of the bound in one of the scenarios. Finally, this monotonicity condition allows us to generalize this bound to the T-period case in which bids are allowed on any subset of period demands.
Original languageEnglish
JournalEuropean Journal of Operational Research
Volume233
Issue number1
Pages (from-to)131–144
ISSN0377-2217
DOIs
Publication statusPublished - 2014
Externally publishedYes

Cite this

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title = "Revenue Deficiency Under Second-price Auctions in a Supply-chain Setting",
abstract = "Consider a firm, called the buyer, that satisfies its demand over two periods by assigning both demands to a supplier via a second-price procurement auction; call this the Standard auction. In the hope of lowering its purchase cost, the firm is considering an alternative procedure in which it will also allow bids on each period individually, where there can be either one or two winners covering the two demands; call this the Multiple Winner auction. Choosing the Multiple Winner auction over the Standard auction can in fact result in a higher cost to the buyer. We provide a bound on how much greater the buyer’s cost can be in the Multiple Winner auction and show that this bound is tight. We then sharpen this bound for two scenarios that can arise when the buyer announces his demands close to the beginning of the demand horizon. Under a monotonicity condition, we achieve a further sharpening of the bound in one of the scenarios. Finally, this monotonicity condition allows us to generalize this bound to the T-period case in which bids are allowed on any subset of period demands.",
keywords = "Procurement, Supply chain, Second-price auction, VCG mechanism, Revenue deficiency",
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Revenue Deficiency Under Second-price Auctions in a Supply-chain Setting. / Romero Morales, Dolores ; Steinberg, Richard.

In: European Journal of Operational Research, Vol. 233, No. 1, 2014, p. 131–144.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Revenue Deficiency Under Second-price Auctions in a Supply-chain Setting

AU - Romero Morales, Dolores

AU - Steinberg, Richard

PY - 2014

Y1 - 2014

N2 - Consider a firm, called the buyer, that satisfies its demand over two periods by assigning both demands to a supplier via a second-price procurement auction; call this the Standard auction. In the hope of lowering its purchase cost, the firm is considering an alternative procedure in which it will also allow bids on each period individually, where there can be either one or two winners covering the two demands; call this the Multiple Winner auction. Choosing the Multiple Winner auction over the Standard auction can in fact result in a higher cost to the buyer. We provide a bound on how much greater the buyer’s cost can be in the Multiple Winner auction and show that this bound is tight. We then sharpen this bound for two scenarios that can arise when the buyer announces his demands close to the beginning of the demand horizon. Under a monotonicity condition, we achieve a further sharpening of the bound in one of the scenarios. Finally, this monotonicity condition allows us to generalize this bound to the T-period case in which bids are allowed on any subset of period demands.

AB - Consider a firm, called the buyer, that satisfies its demand over two periods by assigning both demands to a supplier via a second-price procurement auction; call this the Standard auction. In the hope of lowering its purchase cost, the firm is considering an alternative procedure in which it will also allow bids on each period individually, where there can be either one or two winners covering the two demands; call this the Multiple Winner auction. Choosing the Multiple Winner auction over the Standard auction can in fact result in a higher cost to the buyer. We provide a bound on how much greater the buyer’s cost can be in the Multiple Winner auction and show that this bound is tight. We then sharpen this bound for two scenarios that can arise when the buyer announces his demands close to the beginning of the demand horizon. Under a monotonicity condition, we achieve a further sharpening of the bound in one of the scenarios. Finally, this monotonicity condition allows us to generalize this bound to the T-period case in which bids are allowed on any subset of period demands.

KW - Procurement

KW - Supply chain

KW - Second-price auction

KW - VCG mechanism

KW - Revenue deficiency

U2 - 10.1016/j.ejor.2013.07.041

DO - 10.1016/j.ejor.2013.07.041

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JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

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ER -