Greedy Algorithms make Efficient Mechanisms

We study mechanisms that use greedy allocation rules and pay-your-bid pricing to allocate resources subject to a matroid constraint. We show that all such mechanisms obtain a constant fraction of the optimal welfare at any equilibrium of bidder behavior, via a smoothness argument. This unifies numerous recent results on the price of anarchy of simple auctions. Our results extend to polymatroid and matching constraints, and we discuss extensions to more general matroid intersections.