# Duality and Optimality of Auctions for Uniform Distributions

arXiv: https://arxiv.org/abs/1404.2329 · HTML: https://mlsanity.com/paper/1404.2329/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2014.

## Built on by (most cited first, 12 of 12)

- [PreferenceNet: Encoding Human Preferences in Auction Design with Deep Learning](https://mlsanity.com/paper/2106.03215/) (2021)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [GemNet: Menu-Based, Strategy-Proof Multi-Bidder Auctions Through Deep Learning](https://mlsanity.com/paper/2406.07428/) (2024)
- [Mode Connectivity in Auction Design](https://mlsanity.com/paper/2305.11005/) (2023)
- [Learning Payment-Free Resource Allocation Mechanisms](https://mlsanity.com/paper/2311.10927/) (2023)
- [Recommender Systems meet Mechanism Design](https://mlsanity.com/paper/2110.12558/) (2021)
- [Optimal Automated Market Makers: Differentiable Economics and Strong Duality](https://mlsanity.com/paper/2402.09129/) (2024)
- [Learning Truthful Mechanisms without Discretization](https://mlsanity.com/paper/2506.22911/) (2025)
- [How to Sell High-Dimensional Data Optimally](https://mlsanity.com/paper/2510.15214/) (2025)
- [Regularized Proportional Fairness Mechanism for Resource Allocation Without Money](https://mlsanity.com/paper/2501.01111/) (2025)
- [Universal Representation of Generalized Convex Functions and their Gradients](https://mlsanity.com/paper/2509.04477/) (2025)
- [Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning](https://mlsanity.com/paper/2606.10112/) (2026)

## Abstract (arXiv)

We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. We demonstrate the power of the framework by applying it to a multiple-good monopoly setting where the buyer has uniformly distributed valuations for the items, the canonical long-standing open problem in the area. We propose a deterministic selling mechanism called Straight-Jacket Auction (SJA), which we prove to be exactly optimal for up to 6 items, and conjecture its optimality for any number of goods. The duality framework is used not only for proving optimality, but perhaps more importantly for deriving the optimal mechanism itself; as a result, SJA is defined by natural geometric constraints.