Worst-case optimal redistribution of VCG payments in heterogeneous-item auctions with unit demand

Many important problems in multiagent systems involve the allocation of multiple resources among the agents. For resource allocation problems, the well-known VCG mechanism satisfies a list of desired properties, including efficiency, strategy-proofness, individual rationality, and the non-deficit property. However, VCG is generally not budget-balanced. Under VCG, agents pay the VCG payments, which reduces social welfare. To offset the loss of social welfare due to the VCG payments, VCG redistribution mechanisms were introduced. These mechanisms aim to redistribute as much VCG payments back to the agents as possible, while maintaining the aforementioned desired properties of the VCG mechanism. We continue the search for worst-case optimal VCG redistribution mechanisms – mechanisms that maximize the fraction of total VCG payment redistributed in the worst case. Previously, a worst-case optimal VCG redistribution mechanism (denoted by WCO) was characterized for multi-unit auctions with nonincreasing marginal values [7]. Later, WCO was generalized to settings involving heterogeneous items [4], resulting in the HETERO mechanism. [4] conjectured that HETERO is feasible and worst-case optimal for heterogeneous-item auctions with unit demand. In this paper, we propose a more natural way to generalize the WCO mechanism. We prove that our generalized mechanism, though represented differently, actually coincides with HETERO. Based on this new representation of HETERO, we prove that HETERO is indeed feasible and worst-case optimal in heterogeneous-item auctions with unit demand. Finally, we conjecture that HETERO remains feasible and worst-case optimal in the even more general setting of combinatorial auctions with gross substitutes.