A VALUE FOR PARTIALLY DEFINED COOPERATIVE GAMES

The Shapley value provides a method, which satisfies certain desirable axioms, of allocating benefits to the players of a cooperative game. When there are n players and n is large, the Shapley value requires a large amount of accounting because the number of coalitions grows exponentially with n. This paper proposes a modified value that shares some of the axiomatic properties of the Shapley value yet allows the consideration of games that are defined only for certain coalitions. Two different axiom systems are shown to determine the same modified value uniquely.