Game-Theoretic Approaches to Matching Markets

Game theory has provided foundational insights into the design and analysis of matching markets, where self-interested agents on two or more sides seek mutually beneficial pairings without monetary transfers. Central concepts include stability—ensuring no two agents prefer each other to their assigned matches—and strategy-proofness, which guarantees that truthful revelation of preferences is a dominant strategy. The deferred-acceptance algorithm and its many-to-one and one-to-one variants have dominated theoretical and practical advances, as they produce stable outcomes even in large-scale applications such as school choice, college admissions and organ exchange. Contemporary research extends these classics by incorporating realistic constraints (capacities, diversity requirements, priority structures), fairness metrics (envy-freeness, proportionality) and computational scalability. Recent game-theoretic analyses have characterised how agents with limited foresight or bounded rationality interact with simple mechanisms, illuminating the trade-offs between simplicity, efficiency and robustness. Furthermore, experimental and empirical studies have probed strategic misreporting, learning dynamics and behavioural biases, informing refinements to both centralised and decentralised designs. The interplay between local institutional priorities and global algorithmic standards underscores the real-world impact of this field, which continues to evolve at the intersection of economic theory, operations research and computer science.

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Game-Theoretic Approaches to Matching Markets publication trend

The graph below shows the total number of articles in game-theoretic approaches to matching markets across all publications each year (not limited to Nature Index journals).

Technical terms

Matching market: A setting where two or more groups of agents are paired based on mutual preferences without monetary transfers.

Stable matching: An assignment in which no pair of agents would both prefer to be matched with each other rather than with their current partners.

Deferred-acceptance algorithm: A procedure in which one side proposes to the other and tentative acceptances are held until no further proposals occur, yielding a stable outcome.

Strategy-proofness: A property of a mechanism that makes truthful preference reporting a dominant strategy for all participants.

Fairness constraints: Additional rules—such as capacity limits or diversity requirements—that govern the set of permissible matchings beyond classical preferences.

Envy-freeness: A fairness criterion whereby no agent prefers another agent’s assignment to their own.

References

1. A Theory of Simplicity in Games and Mechanism Design. Econometrica (2023).
2. Fair Matching under Constraints: Theory and Applications. The Review of Economic Studies (2023).
3. Experiments on centralized school choice and college admissions: a survey. Experimental Economics (2021).
4. Mathematical models for stable matching problems with ties and incomplete lists. European Journal of Operational Research (2019).