Efficient Iterative Auctions for Multi-Featured Items: A Network Flow Approach

Abstract

We develop a methodology for the design of efficient iterative auctions for heterogeneous items whose values are expressed in terms of a finite set of features they possess. Bidders have decreasing marginal values for each feature, and their value for a bundle is the sum of individual feature valuations associated with this bundle. This feature-driven representation of valuations allows us to formulate a novel (multicommodity) network flow representation of the efficient allocation problem. Using the integrality of the optimal solutions to the min-cost flow problem, we establish the existence of a Walrasian equilibrium for F-feature valuations (first with F = 2, and subsequently with F > 2 under additional structural assumptions). We also show that F-feature valuations might not exhibit substitutability even for F = 2, thereby revealing a new class of valuations for which a Walrasian equilibrium exists. By analyzing the structural properties of the optimal solutions to the network flow problem for 2-feature valuations, we develop an iterative algorithm that finds the efficient allocation in this setting. Furthermore, a single run of the procedure collects sufficient information to compute VCG payments. Thus, complementing the algorithm with this payment rule, we obtain a new iterative auction in which it is an (ex-post) equilibrium to bid truthfully, and the equilibrium is efficient. Our approach suggests that analyzing (i) alternative valuation representations, and (ii) network flow formulation of the efficient allocation problem, could potentially reveal other valuation classes for which a Walrasian equilibrium exists, and simple iterative auctions which implement an efficient outcome.