What is Shapley Value?

The Shapely Value is a gaming theory that posits that gains and losses (costs) of a game should be distributed fairly amount all the actors who worked collaboratively. This theory is a solution theory used in a context where there is cooperation or coalition amongst all the actors in a particular task. The Shapely Value was introduced in 1951 by Lloyd Shapley, whom the theory was named after. As a solution concept, the Shapely value is used in scenarios when the contributions of the actors that work cooperatively are unequal. The Shapely value aims to assign gains and costs to all actors fairly.

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How is the Shapley Value Used? 

Typically, the Shapely value symbolizes and average or fair distribution of gains and costs to actors in collaborative work. This value considers the contributions of each of the actors and ensures that each of them gets gains and costs equivalent to what they would have received if they had worked independently. Although the Shapely Value is commonly used in the gaming theory, it applies to other industries and sectors. This value assigns a fair distribution to players or actors in every cooperative game. While the Shapely value is not a perfect distribution model, it has proven to be a fair allocation of gains and costs to actors.

Example of Shapely Value in Practice

A good example of the Shapely value in use was during the airport problem, where an airport needed to be constructed to accommodate different aircraft and there was a challenge in the allocation of costs of the airport to all the players (actors). When the Shapely value was used, it paved the way for a solution to the distribution of costs in which the marginal cost of the lengths of the runway was spread across all the actors. This spread also determines the workload of each of the actors, for instance, actors with shorter runway length paid less than actors with longer runway length.