Fair Payments for Efficient Allocations in Public Sector Combinatorial Auctions

Abstract

M otivated 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 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. Recent advances in auction theory suggest that combinatorial auctions resulting in efficient outcomes and bidder-Pareto-optimal core payments offer a viable practical alternative to address this problem.This paper confronts two critical issues facing the bidder-Pareto-optimal core payment. 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 such auction outcomes, narrowing the previously broad solution concept. Second, we address the computational difficulties of achieving these outcomes with a constraint-generation approach, promising to broaden the range of applications for which bidder-Pareto-optimal core pricing achieves a comfortably rapid solution.

Algorithmic Cost Allocation Games: Theory and Applications

“…Just a few constraints influence the optimal solutions of the linear program, while the remainders are just redundant. An usual idea to overcome the difficulty is using a constraint generation approach [30,15,11]. We start with a simplified version of the original linear program formed by a few of its constraints.…”

“…However, it is not necessary to evaluate the cost of every possible coalition. Using the constraint generation technique [30,15,11], we only have to calculate the costs of several coalitions and therefore are able to solve large applications of the cost allocation problem in practice.…”

Core Deviation Minimizing Auctions

“…Motivated by this observation, Day and Raghavan (2007) and Day and Milgrom (2008) introduced core-selecting auctions (CSAs) as alternatives to VCG. 2 Since then di¤erent forms of CSAs have been proposed, but they all share the main features that the allocation is e¢ cient and the payo¤ vector associated with the auction outcome is always in the core given that buyers' reports are their true valuations.…”

A New Payment Rule for Core-Selecting Package Auctions

“…Finding the "optimal" rule in any more realistic environment seems an intractable problem. 8 Furthermore, no real-world regulator could use any rule that depends on detailed information about priors about distributions of bidders' values, and relying on Bayesian-Nash equilibrium responses in these extremely complex many-object environments is in any case questionable. 9 The logic that proponents of core-selecting auctions espouse is not, therefore, a simple equilibrium one.…”