Rate of Price Discovery in Iterative Combinatorial Auctions

TL;DR

This paper analyzes the convergence rates of iterative combinatorial auctions modeled as subgradient descent, showing how different pricing schemes and bidder behaviors affect the speed of reaching market-clearing prices.

Contribution

It provides concrete convergence bounds for various auction pricing schemes and models of bidder behavior, including stochastic and adversarial scenarios.

Findings

More expressive pricing schemes slow convergence.

Convergence bounds depend on bidder behavior model.

Proper activity rules are essential for convergence under adversarial behavior.

Abstract

We study a class of iterative combinatorial auctions which can be viewed as subgradient descent methods for the problem of pricing bundles to balance supply and demand. We provide concrete convergence rates for auctions in this class, bounding the number of auction rounds needed to reach clearing prices. Our analysis allows for a variety of pricing schemes, including item, bundle, and polynomial pricing, and the respective convergence rates confirm that more expressive pricing schemes come at the cost of slower convergence. We consider two models of bidder behavior. In the first model, bidders behave stochastically according to a random utility model, which includes standard best-response bidding as a special case. In the second model, bidders behave arbitrarily (even adversarially), and meaningful convergence relies on properly designed activity rules.