# A Permutation-Equivariant Neural Network Architecture For Auction Design

arXiv: https://arxiv.org/abs/2003.01497 · HTML: https://mlsanity.com/paper/2003.01497/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2020.

## Built on by (most cited first, 30 of 32)

- [Optimal-er Auctions through Attention](https://mlsanity.com/paper/2202.13110/) (2022)
- [A Scalable Neural Network for DSIC Affine Maximizer Auction Design](https://mlsanity.com/paper/2305.12162/) (2023)
- [PreferenceNet: Encoding Human Preferences in Auction Design with Deep Learning](https://mlsanity.com/paper/2106.03215/) (2021)
- [Differentiable Economics for Randomized Affine Maximizer Auctions](https://mlsanity.com/paper/2202.02872/) (2022)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [Deep Learning for Two-Sided Matching](https://mlsanity.com/paper/2107.03427/) (2021)
- [Learning Revenue-Maximizing Auctions With Differentiable Matching](https://mlsanity.com/paper/2106.07877/) (2021)
- [GemNet: Menu-Based, Strategy-Proof Multi-Bidder Auctions Through Deep Learning](https://mlsanity.com/paper/2406.07428/) (2024)
- [Learning to Mitigate AI Collusion on Economic Platforms](https://mlsanity.com/paper/2202.07106/) (2022)
- [Principal-Agent Reinforcement Learning: Orchestrating AI Agents with Contracts](https://mlsanity.com/paper/2407.18074/) (2024)
- [Benefits of Permutation-Equivariance in Auction Mechanisms](https://mlsanity.com/paper/2210.05579/) (2022)
- [Data Market Design through Deep Learning](https://mlsanity.com/paper/2310.20096/) (2023)
- [Representing and Learning Functions Invariant Under Crystallographic Groups](https://mlsanity.com/paper/2306.05261/) (2023)
- [The Bandit Whisperer: Communication Learning for Restless Bandits](https://mlsanity.com/paper/2408.05686/) (2024)
- [Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetries](https://mlsanity.com/paper/2210.06741/) (2022)
- [Are Equivariant Equilibrium Approximators Beneficial?](https://mlsanity.com/paper/2301.11481/) (2023)
- [Automated Deterministic Auction Design with Objective Decomposition](https://mlsanity.com/paper/2402.11904/) (2024)
- [An Interpretable Automated Mechanism Design Framework with Large Language Models](https://mlsanity.com/paper/2502.12203/) (2025)
- [Optimal Automated Market Makers: Differentiable Economics and Strong Duality](https://mlsanity.com/paper/2402.09129/) (2024)
- [Deep Reinforcement Learning for Sequential Combinatorial Auctions](https://mlsanity.com/paper/2407.08022/) (2024)
- [Bridging the Gap Between Estimated and True Regret Towards Reliable Regret Estimation in Deep Learning based Mechanism Design](https://mlsanity.com/paper/2601.13489/) (2026)
- [Incentive-Aware Multi-Fidelity Optimization for Generative Advertising in Large Language Models](https://mlsanity.com/paper/2604.06263/) (2026)
- [Statistically Truthful Auctions via Acceptance Rule](https://mlsanity.com/paper/2405.12016/) (2024)
- [Large-Scale Contextual Market Equilibrium Computation through Deep Learning](https://mlsanity.com/paper/2406.15459/) (2024)
- [Learning Fair and Preferable Allocations through Neural Network](https://mlsanity.com/paper/2410.17500/) (2024)
- [Learning Neural Strategy-Proof Matching Mechanism from Examples](https://mlsanity.com/paper/2410.19384/) (2024)
- [Deep Learning for Double Auction](https://mlsanity.com/paper/2504.05355/) (2025)
- [Optimal Auction Design in the Joint Advertising](https://mlsanity.com/paper/2507.07418/) (2025)
- [Strategic Cyber Defense via Reinforcement Learning-Guided Combinatorial Auctions](https://mlsanity.com/paper/2509.10983/) (2025)
- [Open Problems in Differentiable Social Choice: Learning Mechanisms, Decisions, and Alignment](https://mlsanity.com/paper/2602.03003/) (2026)

## Abstract (arXiv)

Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. Theoretical approaches to the problem have hit some limits in the past decades and analytical solutions are known for only a few simple settings. Computational approaches to the problem through the use of LPs have their own set of limitations. Building on the success of deep learning, a new approach was recently proposed by Duetting et al. (2019) in which the auction is modeled by a feed-forward neural network and the design problem is framed as a learning problem. The neural architectures used in that work are general purpose and do not take advantage of any of the symmetries the problem could present, such as permutation equivariance. In this work, we consider auction design problems that have permutation-equivariant symmetry and construct a neural architecture that is capable of perfectly recovering the permutation-equivariant optimal mechanism, which we show is not possible with the previous architecture. We demonstrate that permutation-equivariant architectures are not only capable of recovering previous results, they also have better generalization properties.