Shapleyérték

Shapleyérték, often translated as Shapley value, is a concept in cooperative game theory that provides a unique and fair distribution of the total surplus generated by a coalition of players. Developed by Lloyd Shapley in 1953, it's a method for assigning a payment or benefit to each player based on their individual contribution to the coalition. The core idea is to consider every possible order in which players could join a coalition and then average their marginal contributions across all these permutations. This ensures that each player receives a payoff that reflects their average impact on the group's success, regardless of the order in which they joined.

The Shapley value possesses several desirable properties, including efficiency (the sum of Shapley values equals the total surplus), symmetry (players with identical contributions receive identical payoffs), and dummy player (a player who adds nothing to any coalition receives zero payoff). These properties make it a widely accepted and robust solution concept for fair resource allocation in various fields, such as economics, political science, and even machine learning for feature attribution. Calculating Shapley values can be computationally intensive for large numbers of players, but it remains a fundamental tool for understanding and implementing fair cooperative outcomes.