手法を比較

	シャープレイ値	トップ・トレーディング・サイクル
分野	ゲーム理論	ゲーム理論
系統	Machine learning	Machine learning
提唱年	1953	1974
提唱者	Lloyd Shapley	Lloyd Shapley, Herbert Scarf
種類	algorithm	algorithm
原典	Shapley, L. S. (1953). A value for n-person games. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the Theory of Games II (pp. 307-317). Princeton University Press.	Shapley, L. S., & Scarf, H. (1974). On cores and indivisibility. Journal of Mathematical Economics, 1(1), 23-37.
別名	Fair Division, Cooperative Game Solution, Dividend Vector	TTC, Shapley-Scarf Algorithm, Efficient Exchange
関連	4	4
概要	The Shapley Value is a solution concept for coalition games that distributes total payoff fairly among players based on their marginal contributions to coalitions. Introduced by Lloyd Shapley in 1953, the Shapley Value is the unique payoff distribution that satisfies four intuitive axioms: efficiency (total payoff is distributed), symmetry (identical players receive equal payoff), null player (players contributing nothing receive nothing), and additivity across games.	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.