  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.
