MenuNet: A Strategy-Proof Mechanism for Matching Markets

2026-05-04

AI Summary

In matching markets subject to complex constraints such as diversity quotas, stable matchings often fail to exist, making it a central challenge to manage instability while preserving strategyproofness. This work proposes MenuNet, a novel framework that, for the first time, decomposes stability into two differentiable vector objectives: envy-freeness and non-wastefulness. By leveraging neural networks to learn personalized probabilistic menus for participants and integrating them with a structured sequential choice rule, MenuNet yields a strategyproof, learnable assignment mechanism. The approach remains computationally efficient and scalable, significantly outperforming classical mechanisms: it substantially reduces envy compared to Random Serial Dictatorship (RSD) and markedly decreases resource wastefulness relative to Deferred Acceptance (DA).

Abstract

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 \texttt{MenuNet}, a strategy-proof mechanism design framework based on a neural representation of menus. Rather than directly constructing assignments, \texttt{MenuNet} 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, \texttt{MenuNet} 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.

Problem

• strategy-proofness
• matching markets
• stability
• distributional constraints
• instability

Innovation

• strategy-proofness
• matching markets
• probabilistic menus
• differentiable optimization
• stability decomposition