26 interactive visualizations exploring Gale-Shapley's landmark 1962 paper and 60 years of derivative algorithms, from hospital matching to kidney exchange — the mathematics behind the 2012 Nobel Prize in Economics.
🏆 2012 Nobel Prize in EconomicsGale and Shapley's foundational algorithms: deferred acceptance for marriage and college admissions, plus the stable roommates problem and blocking pairs.
Step-by-step Gale-Shapley where men propose, producing the men-optimal stable matching
Core Algorithm Demo 02Women propose instead — compare both algorithms side by side to see the duality
Core Algorithm Demo 03The many-to-one extension from Section 4: students apply to colleges with quotas
Core Algorithm Demo 04Why non-bipartite matching is fundamentally harder — the classic counterexample
Core Theory Demo 05Build your own matching and discover blocking pairs that make it unstable
Interactive Demo 06Enumerate every stable matching for a small instance and explore the lattice structure
Core Theory Demo 07The elegant two-phase algorithm for stable roommates — detects when none exist
AlgorithmHow the original model was extended to handle hospitals, quotas, ties, couples, and incomplete information for deployment in real matching markets.
The 2012 Nobel application: matching 40,000 medical residents to hospitals annually since 1952
Application Demo 09Roth's 1986 proof that no algorithm can help underdemanded programs fill more seats
Core Theory Demo 10When preferences have ties: super-stable, strong-stable, and weakly-stable compared
Algorithm Demo 11When applicants only rank acceptable options — some may remain unmatched by design
Algorithm Demo 12Workers take multiple jobs, firms hire multiple workers — extended DA for both sides
Algorithm Demo 13Couples in the NRMP submit joint rankings — stable matchings may not exist!
ApplicationOther assignment algorithms with different trade-offs between stability, efficiency, strategy-proofness, and fairness.
Immediate acceptance (used until 2005) — why it rewards strategic manipulation
Algorithm Demo 15Shapley & Scarf's 1974 elegant cycle-finding algorithm: Pareto-efficient and strategy-proof
Algorithm Demo 16Run DA, Boston, and TTC on identical data — compare welfare outcomes side by side
Comparison Demo 17Fair assignment via randomized priority — the lottery-based approach to matching
Algorithm Demo 18Bogomolnaia-Moulin's 2001 "eating algorithm" — ordinally efficient and envy-free
Algorithm Demo 19Efficiency-adjusted DA that Pareto-improves on standard DA — deployed in Belgium 2024
Application Demo 20Optimal weight matching with cardinal utilities — maximizing total welfare, not stability
AlgorithmStrategic behavior, mathematical structure, modern extensions, and the remarkable history of market design in practice.
Interactive game: try to manipulate Boston mechanism, then see why it fails under DA
Game Theory Demo 22Conway's theorem: stable matchings form a distributive lattice connected by rotations
Mathematics Demo 23Roth's 2004 application: finding compatible 2-cycles and 3-cycles among incompatible pairs
Application Demo 24When agents arrive over time — rideshare matching and competitive ratio bounds
Modern Demo 25Hatfield & Milgrom's 2005 unification: salary negotiations in matching markets
Mathematics Demo 2660 years of stable matching: from the 1962 paper to real-world deployments worldwide
History