Shapley value

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In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs among a group of players who have collaborated. For example, in a team project where each member contributed differently, the Shapley value provides a way to determine how much credit or blame each member deserves. It was named in honor of Lloyd Shapley, who introduced it in 1951. The Shapley value determines each player's contribution by considering how much the overall outcome changes when they join each possible combination of other players, and then averaging those changes. In essence, it calculates each player's average marginal contribution across all possible coalitions. It is the only solution that satisfies four fundamental properties: efficiency, symmetry, additivity, and the dummy player (or null player) property, which are widely accepted as defining a fair distribution. This method is used in many fields, from dividing profits in business partnerships to understanding feature importance in machine learning.