Enhancing Affine Maximizer Auctions with Correlation-Aware Payment

TL;DR

This paper introduces Correlation-Aware AMA (CA-AMA), a new auction framework that improves revenue performance in correlated valuation distributions by incorporating correlation-aware payments, while maintaining incentive compatibility.

Contribution

It proposes CA-AMA, a novel correlation-aware auction mechanism that preserves DSIC, formalizes its optimization, and demonstrates improved revenue over classic AMAs in correlated settings.

Findings

CA-AMA can achieve optimal revenue in scenarios where classic AMAs perform poorly.

The proposed training algorithm effectively finds approximate optimal CA-AMA with low IR violation.

Experiments show CA-AMA outperforms traditional AMAs in revenue across various distributions.

Abstract

Affine Maximizer Auctions (AMAs), a generalized mechanism family from VCG, are widely used in automated mechanism design due to their inherent dominant-strategy incentive compatibility (DSIC) and individual rationality (IR). However, as the payment form is fixed, AMA's expressiveness is restricted, especially in distributions where bidders' valuations are correlated. In this paper, we propose Correlation-Aware AMA (CA-AMA), a novel framework that augments AMA with a new correlation-aware payment. We show that any CA-AMA preserves the DSIC property and formalize finding optimal CA-AMA as a constraint optimization problem subject to the IR constraint. Then, we theoretically characterize scenarios where classic AMAs can perform arbitrarily poorly compared to the optimal revenue, while the CA-AMA can reach the optimal revenue. For optimizing CA-AMA, we design a practical two-stage training algorithm. We derive that the target function's continuity and the generalization bound on the degree of deviation from strict IR. Finally, extensive experiments showcase that our algorithm can find an approximate optimal CA-AMA in various distributions with improved revenue and a low degree of violation of IR.