The Consensus Value for Games in Partition Function Form

This paper studies a generalization of the consensus value (cf.Ju, Borm and Ruys (2004)) to the class of partition function form games. The concepts and axioms, related to the consensus value, are extended. This value is characterized as the unique function that satisfies efficiency, complete symmetry, the quasi null player property and additivity. By means of the transfer property, a second characterization is provided. Moreover, it is shown that this value satisfies the individual rationality under a certain condition, and well balances the trade-off between coalition effects and externality effects. By modifying the stand-alone reduced game, a recursive formula for the value is established. A further generalization of the consensus value is discussed. Finally, two applications of the consensus value are given: one is for oligopoly games in partition function form and the other is about participation incentives in free-rider situations