Making VCG More Robust in Combinatorial Auctions via Submodular Approximation

The Vickrey-Clarke-Groves (VCG) protocol is a theoretically well-founded protocol that can be used for combinatorial auctions. However, the VCG has several limitations such as (a) vulnerability to false-name bids, (b) vulnerability to loser collusion, and (c) the outcome is not in the core. Yokoo, Matsutani, & Iwasaki (2006) presented a new combinatorial auction protocol called the Groves Mechanism with SubModular Approximation (GM-SMA). This protocol satisfies the following characteristics: (1) it is false-name-proof, (2) each winner is included in a Pareto efficient allocation, and (3) as long as a Pareto efficient allocation is achieved, the protocol is robust against the collusion of losers and the outcome is in the core. The GM-SMA is the first protocol that satisfies all three of these characteristics. The basic ideas of the GM-SMA are as follows: (i) it is based on the VCG protocol, i.e., the payment of a winner in this protocol is identical to the payment in one instance of the Groves mechanism, which is a class of protocols that includes the VCG, (ii) when calculating the payment of a bidder, we approximate the valuations of other bidders by using a submodular valuation function (submodular approximation). This paper shows a high-level presentation of the GM-SMA protocol. and discusses open problems and the relationship to other works in AI.