The main goal is to illustrate that the so-called indirect function of a cooperative game in characteristic function form is applicable to determine the nucleolus for a subclass of coalitional games called compromise stable TU games. In accordance with the Fenchel-Moreau theory on conjugate functions, the indirect function is known as the dual representation of the characteristic function of th...

A partially de ned cooperative game is a coalition function form game in which some of the coalitional worths are not known. An application would be cost allocation of a joint project among so many players that the determination of all coalitional worths is prohibitive. This paper generalizes the concept of the Shapley value for cooperative games to the class of partially de ned cooperative gam...

Deontic logic has extensively been used to reason about what a player (or coalition) should do when confronted with several choices at its disposal while being aware of its opponents’ possibilities. So far this line of research, inspired by Horty’s utilitarian account of obligations, has been focused on interpreting coalitional oughts as rational choices, going on to characterizing game-theoret...

A partially defined cooperative game is a coalition function form game in which some of the coalitional worths are not known. An application would be cost allocation of a joint project among so many players that the determination of all coalitional worths is prohibitive. This paper generalizes the concept of the Shapley value for cooperative games to the class of partially defined cooperative g...

Hamiache’s recent axiomatization of the well-known Shapley value for TU games states that the Shapley value is the unique solution verifying the following three axioms: the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values, of which the Shapley value is the most important...

We provide axiomatizations for six variants of the Public Good Index for games with a priori unions. Two such coalitional PGIs have been introduced and alternatively axiomatized in Alonso-Meijide et al. (2008b). They assign power in two steps. In the first step, power is distributed between unions according to the PGI of the quotient game. In a second step, the Solidarity PGI splits power equal...

In most previous models of coalition structure generation, it is assumed that agents may partition themselves into any coalition structure. In practice, however, there may be physical and organizational constraints that limit the number of co-existing coalitions. In this paper, we introduce k-coalitional games: a type of partition function game especially designed to model such situations. We p...

Computational social choice literature has successfully studied the complexity of manipulation in various voting systems. However, the existing models of coalitional manipulation view the manipulating coalition as an exogenous input, ignoring the question of the coalition formation process. While such analysis is useful as a first approximation, a richer framework is required to model voting ma...

We treat a class of multi-person bargaining mechanisms based on games in coalitional form. For this class of games we identify properties of non-cooperative solution concepts, which are necessary and sufficient for the equilibrium outcomes to coincide with the core of the underlying coalitional form game. We view this result as a non-cooperative axiomatization of the core. In contrast to most o...

McGarvey (1953) has shown that any irreflexive and anti-symmetric relation can be obtained as a relation induced by majority rule. We address the analogous issue for dominance relations of finite cooperative games with non-transferable utility (coalitional NTU games). We find any irreflexive relation over a finite set can be obtained as the dominance relation of some finite coalitional NTU game...