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.
This paper proposes a computationally efficient mechanism for multi-dimensional matching markets where agents report preferences over object features rather than complete utility assessments. We use Singular Value Decomposition (SVD) to identify the principal direction of variation in feature space and match agents to objects along this dimension, reducing a complex multi-dimensional problem to an effectively one-dimensional problem solvable in O(NlogN) time. We show that when data exhibit low effective dimensionality, our mechanism approximately maximizes Nash Social Welfare, satisfies distributional truthfulness, and achieves symmetry. We establish a novel connection between Nash Social Welfare and Geometric Distributionally Robust Optimization, providing robustness guaranties. Numerical experiments demonstrate that our approach achieves 99% optimal welfare while running three orders of magnitude faster than direct optimization. The framework applies naturally to school choice, labor markets, and course allocation, where feature-based elicitation reduces the cognitive burden on agents.
We study a sequential learning problem for stable matchings in two-sided markets where preferences on both sides are initially unknown. We focus on a centralized setting where an algorithm matches agents at each time step and receives noisy rewards that reflect the preferences of the matched agents, following a semi-bandit feedback structure. We adopt a pure exploration perspective, aiming to efficiently identify the optimal stable matching with high probability. Our work extends prior results by handling \emph{two-sided uncertainty} and by exploiting \emph{partial preference} information. A central ingredient is the notion of \textbf{pervasive stable matching}, which enables the identification of optimal stable matchings under partial preferences. We propose elimination-based algorithms whose stopping criteria exploit the structure of the learned partial preferences, and provide a refined sample-complexity analysis. Beyond pure exploration, we extend our approach to regret minimization and establish regret bounds with respect to the \emph{optimal} stable matching that avoid dependence on the minimum reward gap Δmin.
Andreas Athanasopoulos, Anne-Marie George, Christos Dimitrakakis
Two-sided matching markets often involve information that unfolds over time through interviews, repeated interaction, learning, and separation. Existing matching models typically reduce this process to immediate sub-Gaussian feedback about fixed preferences, missing settings where payoff-relevant information is revealed gradually and changes future matching decisions. We introduce a framework with temporally extended feedback, that formulates two-sided matching as a partially observable Markov game with costly pre-match screening, noisy post-match observations, evolving latent profiles, and endogenous continuation or dissolution. We instantiate this framework in Learn2Match, a multi-agent reinforcement-learning benchmark for dynamic matching markets. Learn2Match supports decentralized decision making over whom to interview, whom to match with, and when to dissolve a match, while evaluating policies using regret, social welfare, and an information-friction loss that measures the welfare gap caused by incomplete revelation of latent preferences. We find that independent PPO achieves higher cumulative social welfare and lower cumulative regret than the bandit-style CA-ETC baseline under temporally extended feedback, demonstrating the promise of MARL for dynamic matching markets. However, PPO still incurs higher information-friction loss, revealing that end-to-end MARL does not yet provide the coordinated exploration structure of matching-bandit methods. These results position Learn2Match as a benchmark for developing the next generation of matching-market algorithms: methods that are adaptive like RL agents, statistically disciplined like bandit algorithms, and structurally aware like stable-matching mechanisms. Please refer to https://sites.google.com/view/learn-to-match/home for the official website and the code link.