Economics, Illustrated: Shapley Values

Shapley Values is a widely-used concept in game theory that provides a fair way to distribute the total payoff of a cooperative game among its players. Introduced by Lloyd Shapley in 1953, the concept is based on the idea that each player should be compensated for their marginal contribution to the game.

Essentially, Shapley Values help answer the question: how important is each player to the overall cooperation, and consequently what payoff can each player expect?

Let’s work through an example to understand the math behind them.

Math Behind Shapley Values

Suppose we have a cooperative game with four players: Alice, Bob, Cooper, and Diana.

They have decided to join forces and play the game together as a coalition. They win a total of $1000.

Now the players are faced with the task of dividing the $1000 prize money fairly among themselves. To determine each player’s share, we need to calculate their individual Shapley Values, which measures their contribution to the total prize money.