Pareto optimal budgeted combinatorial auctions

This paper studies the possibility of implementing Pareto optimal outcomes in the combinatorial auction setting where bidders may have budget constraints. I show that when the setting involves a single good, or multiple goods but with single-minded bidders, there is a unique mechanism, called truncation Vickrey-Clarke-Groves (VCG), that is individually rational, incentive compatible, and Pareto optimal. Truncation VCG works by first truncating valuations at budgets, and then implementing standard VCG on the truncated valuations. I also provide maximal domain results, characterizing when it is possible to implement Pareto optimal outcomes and, if so, providing an implementing mechanism. Whenever there is at least one multi-minded constrained bidder and another multi-minded bidder, implementation is impossible. For any other domain, however, implementation is possible.