Shapley Value

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Definition: Shapley Value

It is a solution proposed by Lloyd Shapley for cooperative game theory introduced in 1953. In a coalition each member collaborates to obtain maximum gain from their efforts.

Each member may not give equal efforts in the outcome and one has to come out with proper distribution of this gain among all the members. Shapley came up with fair allocation of resources based on relative importance of each member.

In this manner one who contributes more would get more gain and relatively the gain would be allocated. Otherwise there will be no incentive for one to contribute in any collaboration work.

Eg: One of the best examples of shapley value is Airport problem where runway cost needs to be distributed to different players. Here each player have different type of aircraft and utilize different length of runway for its takeoff. Thus using Shapley value one which requires maximum runway will have to pay proportionately according his usage. The one which requires very small runway would pay less compared to bigger ones.


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