The Shapley value without efficiency and additivity

The Shapley value without efficiency and additivity

We provide a new characterization of the Shapley value neither using the e¢ciency axiom nor the additivity axiom. In this characterization, e¢ciency is replaced by the gain-loss axiom (Einy and Haimanko, 2011, Game Econ Behav 73: 615–621), i.e., whenever the total worth generated does not change, a player can only gain at the expense of another one. Additivity and the equal treatment axiom are ...

Another characterization of the Banzhaf value without the additivity axiom

We provide another characterization of the Banzhaf value for TU games without the additivity axiom, which also works within the class of simple games and within the class of superadditive games. Journal of Economic Literature Classification Number: C71.

A characterization of the Owen value without the additivity axiom

We provide a characterization of the Owen value for TU games with a coalition structure without the additivity axiom. Journal of Economic Literature Classi…cation Number: C71.

The Shapley group value

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a priori evaluation of the prospects of a group of players in a coalitional game when acting as a unit. We study its properties and we give an axiomatic charact...

64 The Shapley Value