Following the original interpretation of the Shapley value as a priori evaluation of the prospects of a player in a multi-person interaction situation, we intend to apply the Shapley generalized value (introduced formally in Marichal et al. in Discrete Appl Math 155:26-43, 2007) as a tool for the assessment of a group of players that act as a unit in a coalitional game. We propose an alternative axiomatic characterization which does not use a direct formulation of the classical efficiency property. Relying on this valuation, we also analyze the profitability of a group. We motivate this use of the Shapley generalized value by means of two relevant applications in which it is used as an objective function by a decision maker who is trying to identify an optimal group of agents in a framework in which agents interact and the attained benefit can be modeled by means of a transferable utility game.
game theory; tu games; shapley value; generalized values; group values;axiomatic characterizations; game; model