Multi-Unit Auctions: Beyond Roberts

TL;DR

This paper introduces new incentive-compatible multi-unit auctions called Triage auctions that outperform previous affine maximizer auctions in approximating social welfare, establishing fundamental limits for scalable auction design.

Contribution

It demonstrates the existence of non-affine, incentive-compatible auctions that approximate social welfare within a factor of 1+ε and characterizes the uniqueness of Triage auctions for two-item cases.

Findings

Triage auctions are the only scalable, better-than-2 approximation auctions for two-item, two-bidder cases.

No scalable, computationally-efficient incentive-compatible auction can approximate social welfare better than a factor of 2 for multiple items.

Optimal social welfare can be achieved without incentive constraints, but not under scalability and incentive compatibility constraints.

Abstract

We exhibit incentive compatible multi-unit auctions that are not affine maximizers (i.e., are not of the VCG family) and yet approximate the social welfare to within a factor of $1+\epsilon$. For the case of two-item two-bidder auctions we show that these auctions, termed Triage auctions, are the only scalable ones that give an approximation factor better than 2. "Scalable" means that the allocation does not depend on the units in which the valuations are measured. We deduce from this that any scalable computationally-efficient incentive-compatible auction for $m$ items and $n \ge 2$ bidders cannot approximate the social welfare to within a factor better than 2. This is in contrast to arbitrarily good approximations that can be reached under computational constraints alone, and in contrast to the fact that the optimal social welfare can be obtained under incentive constraints alone.