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	トップ・トレーディング・サイクル	Gale-Shapleyアルゴリズム
分野	ゲーム理論	ゲーム理論
系統	Machine learning	Machine learning
提唱年	1974	1962
提唱者	Lloyd Shapley, Herbert Scarf	David Gale, Lloyd Shapley
種類	algorithm	algorithm
原典	Shapley, L. S., & Scarf, H. (1974). On cores and indivisibility. Journal of Mathematical Economics, 1(1), 23-37.	Gale, D., & Shapley, L. S. (1962). College admissions and the stability of marriage. The American Mathematical Monthly, 69(1), 9-15.
別名	TTC, Shapley-Scarf Algorithm, Efficient Exchange	Stable Marriage Problem, Deferred Acceptance, Two-Sided Matching
関連	4	4
概要	Top Trading Cycles (TTC) is an algorithm for allocating indivisible goods to agents such that the allocation is Pareto efficient and individually rational. Developed by Lloyd Shapley and Herbert Scarf in 1974, the algorithm identifies cycles of trades in a preference digraph, executes those trades, and iteratively repeats until no further trades are beneficial. TTC is widely used in kidney exchange and housing allocation due to its efficiency and implementation simplicity.	The Gale-Shapley algorithm solves the stable marriage problem: how to match two groups (e.g., medical residents to hospitals, students to schools) such that no pair prefers each other to their assigned partners. Introduced by David Gale and Lloyd Shapley in 1962, the algorithm guarantees a stable matching in polynomial time through a deferred acceptance process where one side proposes sequentially and the other side responds, revising choices as better options arrive.