Iterative Vickrey Auctions via Linear Programming

TL;DR

This paper introduces a linear programming-based method for designing iterative Vickrey auctions that achieve VCG outcomes, improving transparency and incentive compatibility in complex auction settings.

Contribution

It develops a novel transformation of linear programs to construct iterative Vickrey auctions with a single price path, applicable to multi-unit and product-mix auctions.

Findings

Achieves VCG outcomes through iterative auctions with a single price path

Extends the method to multi-unit and product-mix auction settings

Maintains transparency and incentive properties of VCG mechanisms

Abstract

Building on the linear programming approach to competitive equilibrium pricing, we develop a general method for constructing iterative auctions that achieve Vickrey-Clarke-Groves (VCG) outcomes. We show how to transform a linear program characterizing competitive equilibrium prices into one that characterizes universal competitive equilibrium (UCE) prices, which elicit precisely the information needed to compute VCG payments. By applying a primal-dual algorithm to these transformed programs, we derive iterative Vickrey auctions that maintain a single price path, eliminating the overhead and incentive problems associated with multiple price paths used solely for payment calculations. We demonstrate the versatility of our method by developing a novel iterative Vickrey auction for the multi-unit setting and an iterative variant of the Product-Mix auction. The resulting auctions combine the transparency of iterative price discovery with the efficiency and incentive properties of the VCG mechanism.