Abstract
Combinatorial auctions (CAs) allow bidders to express complex preferences for bundles of goods being auctioned, which are widely applied in the web-based business. 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. We further show that the VCG-nearest payment rule is non-decreasing with no more than five bidders.
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Fritsch, R., Lee, Y., Meier, A., Wang, Y., Wattenhofer, R. (2023). Understanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial Auctions. In: Li, M., Sun, X., Wu, X. (eds) Frontiers of Algorithmics. IJTCS-FAW 2023. Lecture Notes in Computer Science, vol 13933. Springer, Cham. https://doi.org/10.1007/978-3-031-39344-0_1
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