Greedy Algorithms make Efficient Mechanisms

TL;DR

This paper demonstrates that greedy mechanisms with pay-your-bid pricing under matroid constraints guarantee a constant fraction of optimal welfare at equilibrium, unifying various auction efficiency results.

Contribution

It proves that all greedy, pay-your-bid mechanisms under matroid constraints achieve a constant welfare approximation at equilibrium, extending to polymatroid and matching constraints.

Findings

Greedy mechanisms guarantee a constant welfare fraction at equilibrium.

Results unify recent auction efficiency bounds.

Extensions to polymatroid and matching constraints are provided.

Abstract

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.