Strategy/False-Name Proof Protocols for Combinatorial Multi-attribute Procurement Auction: Handling Arbitrary Utility of the Buyer
In this paper, we develop new protocols for a combinatorial, multi-attribute procurement auction in which each sales item (task) is defined by several attributes called quality, the buyer is the auctioneer (e.g., a government), and the sellers are the bidders. Furthermore, there exist multiple tasks, and both buyer and sellers can have arbitrary (e.g., complementary/substitutable) preferences on a bundle of tasks.
In this setting, there is a chance that a VCG protocol cannot satisfy Individual Rationality (IR) for the buyer, i.e., the buyer’s utility can be negative. We show that if a surplus function is concave, then the VCG protocol satisfies IR and the protocol is also false-name-proof, i.e., using multiple identifiers provides no advantage. Furthermore, we present a modification of the VCG protocol that satisfies IR even if the concavity condition is not satisfied. The key idea of this protocol is to introduce a special type of bidder called the reference bidder. We assume that the auctioneer knows the upper-bound of the reference bidder’s cost. Introducing such a reference bidder is similar to setting reservation prices in standard combinatorial auctions. Furthermore, we develop a new false-name-proof protocol that is based on the idea of the Leveled Division Set (LDS) protocol.
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