# A Duality-Based Unified Approach to Bayesian Mechanism Design

arXiv: https://arxiv.org/abs/1812.01577 · HTML: https://mlsanity.com/paper/1812.01577/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2018.

## Built on by (most cited first, 9 of 9)

- [Differentiable Economics for Randomized Affine Maximizer Auctions](https://mlsanity.com/paper/2202.02872/) (2022)
- [GemNet: Menu-Based, Strategy-Proof Multi-Bidder Auctions Through Deep Learning](https://mlsanity.com/paper/2406.07428/) (2024)
- [Deep Contract Design via Discontinuous Networks](https://mlsanity.com/paper/2307.02318/) (2023)
- [Recommender Systems meet Mechanism Design](https://mlsanity.com/paper/2110.12558/) (2021)
- [Learning Optimal Posted Prices for a Unit-Demand Buyer](https://mlsanity.com/paper/2506.02284/) (2025)
- [A Robust Multi-Item Auction Design with Statistical Learning](https://mlsanity.com/paper/2302.00941/) (2023)
- [Refined Mechanism Design for Approximately Structured Priors via Active Regression](https://mlsanity.com/paper/2310.07874/) (2023)
- [Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning](https://mlsanity.com/paper/2606.10112/) (2026)
- [Cogentic: Multi-Agent Orchestration for Automated Proof Discovery](https://mlsanity.com/paper/2609.40324/) (2026)

## Abstract (arXiv)

We provide a unified view of many recent developments in Bayesian mechanism design, including the black-box reductions of Cai et al. [CDW13b], simple auctions for additive buyers [HN12], and posted-price mechanisms for unit-demand bidders [CHK07]. Additionally, we show that viewing these three previously disjoint lines of work through the same lens leads to new developments as well. First, we provide a duality framework for Bayesian mechanism design, which naturally accommodates multiple agents and arbitrary objectives/feasibility constraints. Using this, we prove that either a posted-price mechanism or the Vickrey-Clarke-Groves auction with per-bidder entry fees achieves a constant-factor of the optimal revenue achievable by a Bayesian Incentive Compatible mechanism whenever buyers are unit-demand or additive, unifying previous breakthroughs of Chawla et al. [CHMS10] and Yao [Yao15], and improving both approximation ratios (from 30 to 24 and 69 to 8, respectively). Finally, we show that this view also leads to improved structural characterizations in the Cai et al. framework.