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

Robin Fritsch, Younjoo Lee, Adrian Meier, Ye Wang, Roger Wattenhofer

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.