The balanced solutionfor cooperative transferable utility games

The Shapley value of a cooperative transferable utility game distributes the dividendof each coalition in the game equally among its members. Given exogenous weightsfor all players, the corresponding weighted Shapley value distributes the dividendsproportionally to their weights. In this contribution we de¯ne the balanced solutionwhich assigns weights to players such that the corresponding weighted Shapley valueof each player is equal to her weight. We prove its existence for all monotonetransferable utility games, discuss other properties of this solution, and deal withits characterization through a reduced game consistency.