Pareto optimal budgeted combinatorial auctions

Abstract

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 singleminded 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.

Pareto efficient combinatorial auctions: dichotomous preferences without quasilinearity

“…For combinatorial auctions with single-minded and quasilinear preferences, Le (2018) shows that these impossibilities with budget-constrained agents can be overcome in a generic sense -he defines a "truncated" VCG mechanism and shows that it is desirable almost everywhere.…”