Linear Consistency of Values for TU-Games

摘要

The paper presents necessary and sufficient conditions for an efficient value to211u001ebe consistent with respect to a linear type of reduced game. In the framework of 211u001etransferable utility (TU-) games, the reduced game is said to be linear in that 211u001ethe worth of a coalition is a weighted sum of what the coalition can gain by 211u001eforming partnerships with players who are removed from the initial TU-game. The 211u001enecessary and sufficient conditions concern the linearity and anonymity of the 211u001evalue as well as another fundamental constraint upon the coefficients that 211u001edescribe the value. A second main result states that this linear consistency, 211u001etogether with some kind of standardness for two-person games, fully characterize 211u001ethe value. This unified axiomatic approach to linearly consistent values for TU-211u001egames includes Ruiz' axiomatization of some type of least square values and 211u001eSobolev's axiomatization of the Shapley value in particular. A basic tool in our 211u001eunified consistency treatment is the invariance of the linearly reduced game with 211u001erespect to the order of consecutive elimination of two (or more) players from the 211u001einitial game.