Enhancing Affine Maximizer Auctions with Correlation-Aware Payment

TL;DR

This work addresses revenue extraction under bidder correlation by extending Affine Maximizer Auctions with a correlation-aware payment (CA-AMA) that preserves DSIC and IR. CA-AMA is optimized under an IR constraint via a loss that blends revenue with Regret$_{\mathrm{IR}}$, and a two-stage training procedure plus a post-processing step enables approximate or strict IR as needed. The authors prove that CA-AMA can attain optimal revenue in single-item correlated settings where classic AMAs fail, and they provide continuity and generalization guarantees for the learned core payments. Empirically, CA-AMA outperforms baselines across multi-item and perfectly correlated valuation distributions while maintaining comparable computational efficiency, demonstrating practical impact for automated mechanism design under correlation.

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.

Figures (5)

• Figure 1: The comparison between the optimization for classic Affine Maximizer Auctions (AMAs) and our proposed Correlation Aware AMA (CA-AMA). In classic AMA-based methods VVCA2015LotteryAMAAMenuNetODVVCA, we only optimize the AMA parameters to improve the revenue. To enhance AMA's performance under bidder-correlated distributions, we introduce a correlation-aware payment $p^\text{Cor}$ and hence add a $\text{Regret}_{\text{IR}}$ term in our loss function.
• Figure 2: The revenue results and training curves of CA-AMA and Randomized AMA (implemented by AMenuNet AMenuNet) in auctions with the first bidder's valuation $v_1$ following equal revenue distribution on $[\epsilon, 1]$ and the second bidder's valuation $v_2 = \frac{\epsilon}{1 - \epsilon} (1 - v_1)$. As the final $\text{Regret}_{\text{IR}}$ in all cases is less than $1e-5$, it is not plotted in the figure.
• Figure 3: Revenue surfaces of learned CA-AMA and Randomized AMA in a 2-bidder, 2-item perfectly negative linear scenario ($v_{21} = 1 - v_{11}$ and $v_{22} = 1 - v_{12}$). Bidder 1's valuations ($v_{11}, v_{12}$) are on the x-y axes; revenue is on the z-axis. CA-AMA closely approximates the optimal revenue surface, while Randomized AMA often reserves items and has sub-optimal revenue.
• Figure 4: The revenue results and training curves of CA-AMA and Randomized AMA (implemented by AMenuNet AMenuNet) in auctions with the first bidder's valuation $v_1$ following equal revenue distribution on $[\epsilon, 1]$ and the second bidder's valuation $v_2 = \frac{\epsilon}{1 - \epsilon} (1 - v_1)$. As the $\text{Regret}_{\text{IR}}$ in all cases is less than $1e-5$, it is not plotted in the figure.
• Figure 5: Average revenue vs. achieved IR regret for the optimized CA-AMA under different target IR regret ($R_{\text{target}}$). Results are averaged over $5$ test runs in a $2$-bidder, $2$-item auction setting with irregular multivariate normal value distributions. Revenue obtained by Randomized AMA, VCG, and Item-CAN is included for comparison.

Theorems & Definitions (25)

• Example 1.1
• Definition 2.1: DSIC
• Definition 2.2: IR
• Proposition 3.0
• Proposition 3.0
• Theorem 3.1
• Theorem 4.1
• Theorem 4.2: Informal version of Theorem \ref{['thm:gen-bound']}
• Proposition 2.0
• proof