Budget Feasible Mechanisms

TL;DR

This paper investigates budget-constrained procurement auctions with private costs, demonstrating that for submodular utility functions, effective mechanisms with bounded approximation ratios can be designed, unlike the general case.

Contribution

It introduces the study of budget feasible mechanisms in procurement auctions and provides approximation algorithms for submodular utility functions, a previously unexplored area.

Findings

Budget constraints can cause mechanisms to perform arbitrarily poorly in general.

For submodular functions, mechanisms with bounded approximation ratios are achievable.

Improved results are obtained for subclasses of submodular functions.

Abstract

We study a novel class of mechanism design problems in which the outcomes are constrained by the payments. This basic class of mechanism design problems captures many common economic situations, and yet it has not been studied, to our knowledge, in the past. We focus on the case of procurement auctions in which sellers have private costs, and the auctioneer aims to maximize a utility function on subsets of items, under the constraint that the sum of the payments provided by the mechanism does not exceed a given budget. Standard mechanism design ideas such as the VCG mechanism and its variants are not applicable here. We show that, for general functions, the budget constraint can render mechanisms arbitrarily bad in terms of the utility of the buyer. However, our main result shows that for the important class of submodular functions, a bounded approximation ratio is achievable. Better approximation results are obtained for subclasses of the submodular functions. We explore the space of budget feasible mechanisms in other domains and give a characterization under more restricted conditions.