van den Brink, René Levinsky, René Zeleny, Miroslav
Year of Publication:
Tinbergen Institute Discussion Paper 07-073/1
The Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. In this contribution we define the balanced solution which assigns weights to players such that the corresponding weighted Shapley value of each player is equal to her weight. We prove its existence for all monotone transferable utility games, discuss other properties of this solution, and deal with its characterization through a reduced game consistency.
Balanced solution Proportionality Reduced game consistency Weighted Shapley value