# Strong Duality for a Multiple-Good Monopolist

arXiv: https://arxiv.org/abs/1409.4150 · HTML: https://mlsanity.com/paper/1409.4150/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2014.

## Built on by (most cited first, 17 of 17)

- [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)
- [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)
- [Benefits of Permutation-Equivariance in Auction Mechanisms](https://mlsanity.com/paper/2210.05579/) (2022)
- [Mode Connectivity in Auction Design](https://mlsanity.com/paper/2305.11005/) (2023)
- [Recommender Systems meet Mechanism Design](https://mlsanity.com/paper/2110.12558/) (2021)
- [Neural Auctions Compromise Bidder Information](https://mlsanity.com/paper/2303.00116/) (2023)
- [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)
- [Refined Mechanism Design for Approximately Structured Priors via Active Regression](https://mlsanity.com/paper/2310.07874/) (2023)
- [Statistically Truthful Auctions via Acceptance Rule](https://mlsanity.com/paper/2405.12016/) (2024)
- [Deep Learning for Double Auction](https://mlsanity.com/paper/2504.05355/) (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 characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure μ derived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand-bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism for n independent uniform items each supported on [c,c+1] is a grand-bundling mechanism, as long as c is sufficiently large, extending Pavlov's result for 2 items [Pavlov'11]. At the same time, our characterization also implies that, for all c and for all sufficiently large n, the optimal mechanism for n independent uniform items supported on [c,c+1] is not a grand bundling mechanism.