Iterative Vickrey Auctions via Linear Programming

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 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 novel UCE auctions for multi-unit settings and deriving an iterative UCE 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.