Time Bounds for Iterative Auctions: A Unified Approach by Discrete Convex Analysis

We examine an auction model where there are many different goods, each good has multiple units, and bidders have gross substitutes valuations over the goods. We analyze the number of iterations in iterative auction algorithms for the model based on the theory of discrete convex analysis. By making use of L♮-convexity of the Lyapunov function we derive exact bounds on the number of iterations in terms of the ℓ∞-distance between the initial price vector and the found equilibrium. Our results extend and unify the price adjustment algorithms of Ausubel (2006) and other existing algorithmsfor the unit-demand auction models, offering computational complexity results for these algorithms, and reinforcing the connection between auction theory and discrete convex analysis.