A Scalable Neural Network for DSIC Affine Maximizer Auction Design

TL;DR

The paper tackles automated auction design by enforcing dominant strategy incentive compatibility and individual rationality while seeking high revenue. It introduces AMenuNet, a permutation-equivariant neural network that constructs AMA parameters including a predefined allocation menu, bidder weights, and boosts from bidder and item representations, ensuring DSIC/IR by design. The approach significantly improves scalability over traditional AMA methods by learning a compact menu and relying on a transformer-based architecture, and it demonstrates strong revenue performance, generalization to unseen scales, and the ability to identify useful deterministic allocations. The practical impact lies in providing a data-driven, scalable tool for DSIC auction design that can adapt to contextual and non-contextual auction settings and generalize beyond training configurations. The work also outlines limitations and future directions such as online learning and making the allocation menu size itself learnable.

Abstract

Automated auction design aims to find empirically high-revenue mechanisms through machine learning. Existing works on multi item auction scenarios can be roughly divided into RegretNet-like and affine maximizer auctions (AMAs) approaches. However, the former cannot strictly ensure dominant strategy incentive compatibility (DSIC), while the latter faces scalability issue due to the large number of allocation candidates. To address these limitations, we propose AMenuNet, a scalable neural network that constructs the AMA parameters (even including the allocation menu) from bidder and item representations. AMenuNet is always DSIC and individually rational (IR) due to the properties of AMAs, and it enhances scalability by generating candidate allocations through a neural network. Additionally, AMenuNet is permutation equivariant, and its number of parameters is independent of auction scale. We conduct extensive experiments to demonstrate that AMenuNet outperforms strong baselines in both contextual and non-contextual multi-item auctions, scales well to larger auctions, generalizes well to different settings, and identifies useful deterministic allocations. Overall, our proposed approach offers an effective solution to automated DSIC auction design, with improved scalability and strong revenue performance in various settings.

Figures (5)

• Figure 1: A schematic view of AMenuNet, which takes the bidder representations $X$ (including the dummy bidder) and item representations $Y$ as inputs. These representations are assembled into a tensor $E \in \mathbb{R}^{(n+1) \times m \times (d_x + d_y)}$. Two $1\times 1$ convolution layers are then applied to obtain the tensor $L$. Following $L$, multiple transformer-based interaction modules are used to model the mutual interactions among all bidders and items. The output tensor after these modules is denoted as $J$. $J$ is further split into three parts: $J^\mathcal{A} \in \mathbb{R}^{(n+1)\times m\times s}$, $J^{\bm{w}}\in \mathbb{R}^{(n+1)\times m}$ and $J^{\bm\lambda}\in \mathbb{R}^{(n+1)\times m\times s}$. These parts correspond to the allocation menu $\mathcal{A}$, bidder weights ${\bm{w}}$, and boosts $\bm\lambda$, respectively. Finally, based on the induced AMA parameters and the submitted bids, the allocation and payment results are computed according to the AMA mechanism.
• Figure 2: Out-of-setting generalization results. We use the notation $n\times m$ to represent the number of bidders $n$ and the number of items $m$. We train AMenuNet and evaluate it on the same auction setting, excepts for the number of bidders or items. For detailed numerical results, please refer to \ref{['app:experiments']}.
• Figure 3: The top-$10$ allocations (with respect to winning rate) and the corresponding boosts among $100,000$ test samples.
• Figure 4: Revenue results of AMenuNet under different menu sizes.
• Figure 5: The top-10 allocations (with respect to winning rate) and the corresponding boosts among $100,000$ test samples in $3\times 10$\ref{['settingC']}, with menu size $s=1024$.

Theorems & Definitions (4)

• Theorem 4.1
• Definition 4.2: Permutation Equivariance
• Theorem A.1
• proof