# MenuNet: A Strategy-Proof Mechanism for Matching Markets

arXiv: https://arxiv.org/abs/2605.03216 · HTML: https://mlsanity.com/paper/2605.03216/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 10 of 10)

- [Competing Bandits in Matching Markets](https://mlsanity.com/paper/1906.05363/) (2019)
- [Bandit Learning in Decentralized Matching Markets](https://mlsanity.com/paper/2012.07348/) (2020)
- [Optimal Auctions through Deep Learning: Advances in Differentiable Economics](https://mlsanity.com/paper/1706.03459/) (2017)
- [A Permutation-Equivariant Neural Network Architecture For Auction Design](https://mlsanity.com/paper/2003.01497/) (2020)
- [Optimal-er Auctions through Attention](https://mlsanity.com/paper/2202.13110/) (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)
- [Competing Bandits in Matching Markets via Super Stability](https://mlsanity.com/paper/2506.15926/) (2025)
- [Daycare Matching in Japan: Transfers and Siblings](https://mlsanity.com/paper/2212.02751/) (2022)
- [Stable Matchings in Practice: A Constraint Programming Approach](https://mlsanity.com/paper/2401.07761/) (2024)

## Abstract (arXiv)

Strategy-proofness is a fundamental desideratum in mechanism design, ensuring truthful reporting and robust participation. Stability is another central requirement in matching markets, widely adopted in applications such as school choice and labor market clearing. In practice, however, these markets are invariably governed by complex distributional constraints, ranging from diversity quotas and regional balance to global capacity slacks, under which stable matchings often fail to exist. This raises a fundamental question: how to distribute unavoidable instability across agents while preserving strategy-proofness? To address this, we propose textttMenuNet, a strategy-proof mechanism design framework based on a neural representation of menus. Rather than directly constructing assignments, textttMenuNet learns to generate personalized probabilistic menus, from which assignments are realized via a structured sequential choice rule that guarantees strategy-proofness by construction. By decomposing stability into fairness (no envy) and non-wastefulness, our approach models these properties as vector-valued quantities and optimizes their distribution through differentiable objectives, providing a principled trade-off between competing axioms. Empirically, textttMenuNet navigates this trade-off effectively: it consistently outperforms Random Serial Dictatorship (RSD) in terms of envy and Deferred Acceptance (DA) in terms of waste, while maintaining scalability and computational efficiency. These results suggest that learning-based menu mechanisms provide a flexible and scalable paradigm for mechanism design in highly constrained, real-world environments.