Multi-unit Auctions with Budget Constraints

TL;DR

This paper introduces the Sort-Cut auction mechanism for multi-unit auctions with budget constraints, demonstrating its potential for higher revenue and analyzing its equilibrium properties, inspired by sponsored search auction scenarios.

Contribution

The paper proposes the Sort-Cut mechanism, which weakly dominates truthful bidding on budgets and values, and shows it can significantly increase revenue over traditional mechanisms.

Findings

Sort-Cut's revenue can be much higher than Market Clearing Price mechanisms.

Understating budgets or values is weakly dominated in Sort-Cut.

Efficiency properties of the ex-post Nash equilibrium are discussed.

Abstract

Motivated by sponsored search auctions, we study multi-unit auctions with budget constraints. In the mechanism we propose, Sort-Cut, understating budgets or values is weakly dominated. Since Sort-Cut's revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We show that the revenue of Sort-Cut can be an order of magnitude greater than that of the natural Market Clearing Price mechanism, and we discuss the efficiency properties of its ex-post Nash equilibrium.