On Core-Selecting and Core-Competitive Mechanisms for Binary Single-Parameter Auctions

Markakis, Evangelos; Tsikiridis, Artem

doi:10.1007/978-3-030-35389-6_20

Cited by 4 publications

(1 citation statement)

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“…The non-decreasing property has been observed for the VN payment rule in LLG auctions [2], but does not hold in other single-minded CAs [5]. Markakis and Tsikirdis examined two other payment rules, 0-nearest and b-nearest, which select the closest point in the minimum-revenue core to the origin and to the actual bids, respectively [14]. They prove that these two payment rules satisfy the non-decreasing property in single-minded CAs.…”

Section: Related Workmentioning

confidence: 99%

Understanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial Auctions

Fritsch¹,

Lee²,

Meier³

et al. 2022

Preprint

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Combinatorial auctions (CAs) allow bidders to express complex preferences for bundles of goods being auctioned. However, the behavior of bidders under different payment rules is often unclear. In this paper, we aim to understand how core constraints interact with different core-selecting payment rules. In particular, we examine the natural and desirable non-decreasing property of payment rules, which states that bidders cannot decrease their payments by increasing their bids. Previous work showed that, in general, the widely used VCG-nearest payment rule violates the non-decreasing property in single-minded CAs. We prove that under a single effective core constraint, the VCG-nearest payment rule is non-decreasing. In order to determine in which auctions single effective core constraints occur, we introduce a conflict graph representation of single-minded CAs and find sufficient conditions for the single effective core constraint in CAs. Finally, we study the consequences on the behavior of the bidders and show that no over-bidding exists in any Nash equilibrium for non-decreasing core-selecting payment rules.

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Section: Related Workmentioning

confidence: 99%