Shapley Value Examples

Game Theory · Axiom Academy

EXAMPLE Shapley Value Examples Unit 6 - Cooperative Game Theory: Computing fair payoff distributions Excellent work! You've completed a full Shapley value calculation. Here's what we learned: Systematic enumeration: The Shapley value requires considering all n! orderings of players (6 orderings for 3 players). Marginal contributions: For each ordering, a player's contribution is v(S ∪ i ) - v(S), where S is the set of players who come before them. Fairness through averaging: By averaging marginal contributions across all orderings, we ensure each player is credited fairly for their contribution in all possible scenarios. Efficiency property: The Shapley values always sum to v(N), ensuring the entire coalition value is distributed. Uniqueness: The Shapley value is the unique payoff distribution satisfying efficiency, symmetry, null player, and additivity axioms. This calculation method extends to any number of players, though computational complexity grows as n! Practice with different characteristic functions to build intuition for cooperative game theory!

This is the written version of the interactive lesson above. See the full Game Theory course.