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Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person iteraction 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 characterization. We motivate our proposal by means of some relevant applications of the Shapley group value, when 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. As an illustrative example we analyze the problem of identifying the set of key agents in a terrorist network. ; This research has been supported by I+D+i research project MTM2011-27892 from the Government of Spain

We propose a new type of values for cooperative TU-games, which we call pyramidal values. Assuming that the grand coalition is sequentially formed, and all orderings are equally likely, we define a pyramidal value to be any expected payoff in which the entrant player receives a salary and the right to get part of the benefits derived from subsequent incorporations to the just formed coalition, whereas the remaining benefit is distributed among the incumbent players. To be specific, we consider some parametric families of pyramidal values: the egalitarian pyramidal family, which coincides with the a-consensus value family introduced by Ju et al. in (2007), the proportional pyramidal family, and the weighted pyramidal family, which in turn includes the other two families as special cases. We also analyze the properties of these families, as well as their relationships with other previously defined values. ; This research has been supported by I+D+i research project MTM2011-27892 from the Government of Spain.

This paper is centered in the valuation of the centrality of groups following aproblem-specific approach (Friedkin, 1991). Assuming a TU-game that reflects theinterests which motivate the interactions among individuals in a network, we extend thegame theoretic centrality measure of Gomez et al. (2003) to the case of groups, anddefine the game theoretic group centrality of a group as the variation of its value orpower due to their social relations. We rely on the Shapley group value (Flores et al.,2014) for measuring the value of a group in a game without any restriction, and weintroduce the Myerson group value in order to measure the value when the socialstructure is considered. ; This research has been supported by I+D+i research project MTM2011-27892 from the Government of Spain