Fair Payments for Efficient Allocations in Public Sector Combinatorial Auctions

Abstract

Motivated by the increasing use of auctions by government
agencies, we consider the problem of fairly pricing public goods in a combinatorial
auction. A well-known problem with the incentive-compatible Vickrey-Clarke-Groves
(VCG) auction mechanism is that the resulting prices may not be in the core. Loosely
speaking, this means the payments of the winners could be so low, that there are losing
bidders who would have been willing to pay more than the payments of the winning bidders.
Clearly, this ``unfair'' outcome is unacceptable for a public-sector auction. Proxy-based
combinatorial auctions,
in which each bidder submits several package bids to a proxy, result in efficient outcomes
and bidder-Pareto-optimal core-payments by winners, thus offering a viable practical alternative
to address this problem. 

This paper confronts two critical issues facing the proxy-auction. First, motivated to
minimize a bidder's ability to benefit through strategic manipulation (through collusive
agreement or unilateral action), we demonstrate the strength of a mechanism that minimizes
total payments among all possible proxy auction outcomes, narrowing the previously broad
solution concept. Secondly, we address the computational difficulties of achieving these outcomes
with a constraint-generation approach, promising to broaden the range of applications for which the
proxy-auction achieves a comfortably rapid solution.