An Approach to VCG-like Approximate Allocation and Pricing for Large-scale Multi-unit Combinatorial Auctions

A multi-unit combinatorial auction is a combinatorial auction that has some items that can be seen as in- distinguishable. Although the mechanism can be applied to dynamic electricity auctions and various purposes, it is difficult to apply to large-scale auction problems due to its computational intractability. In this paper, I present an idea and an analysis about an approximate allocation and pricing algorithm that is capable of handling multi-unit auctions. The analysis shows that the algorithm effectively produces approximation allocations that are necessary in pricing. Furthermore, the algorithm can be seen as an approximation of VCG (Vickrey-Clarke-Groves) mechanism satisfying budget balance condition and bidders' individual rationality without having unrealistic assumptions on bidders' be- haviors. I show that the proposed allocation algorithm successfully produced good allocations for those problems that could not be easily solved by ordinary LP solvers due to hard time constraints.

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