The Shapley valuation function for strategic games in which players cooperate

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these playersÂ’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lowervalue based method to associate coalitional games with strategic games that was introduced in Carpente et al. (2003). We discuss axiomatic characterizations of the Shapley valuation function.