Transferable Utility Cooperative Games Research Articles

Canonical Representation of Set Functions

The representation of a cooperative transferable utility game as a linear combination of unanimity games may be viewed as an isomorphism between no-necessarily additive set functions on the players space and additive ones on the coalitions space. (Or, alternatively, between nonadditive probability measures on a state space and additive ones on the space of events.) We extend the unanimity-basis representation to general (infinite) spaces of players, study spaces of games which satisfy certain properties and provide some conditions for α-additivity of the resulting additive set function (on the space at coalitions). These results also allow us to extend some representations of the Choquet integral from finite to infinite spaces.

Correspondence between social choice functions and solutions of cooperative games

Ordinal solutions of cooperative transferable utility (TU) games are defined as ones that can be represented as social choice functions in a space of the utilities of players and coalitions. We provide an axiomatic characterization of a social choice function of this type. The corresponding solution of a cooperative TU game turns out to be an extended (pre)nucleolus or a set-valued analogue of a (pre)nucleolus.

Solutions of transferable utility cooperative games

Une solution competitive uniforme predit une configuration de vecteurs de paiements associes a certaines coalitions susceptibles de se former dons un jeu cooperatif. Cette configuration est caracterisee par une stabilite interne et externe et les paiements associes repondent a des imperatifs de rationalite individuelle et collective. La solution competitive uniforme est une version modifiee de la solution competitive proposee par R. D. McKelvey, P. C. Ordeshook and M. D. Winer (1978). On fait ici une etude parallele de ces deux notions, en soulignant leurs proprietes communes ainsi que leurs differences. Les theoremes d'existence pour la solution competitive uniforme sont demontres dons des conditions tres generales. D'autre part, on prouve que l'existence d'une solution competitive est restreinte a quelques classes particulieres des jeux cooperatifs a utilites transferables

Study of Division Problems in Nonconvex Games with a Variable Population

In this paper, we investigate some problems about division problems given by transferable utility cooperative games with a variable population of players. First, we set up a unified model format and introduce some new concepts . In theorem 1, we obtain a sufficient and necessary condition for judging core allocation principles in all allocation principles; In theorem 2, we obtain another sufficient condition for distinguishing core allocation principles from the given allocation principles; The conditions given in theorem 3 are easily examined, and theorem 2 is a very usful result for distingushing core allocation principles from the given allocation principles. As an example, we obtain that the Shapley value for certain kind of nonconvex games is a core allocation principle.

A Concept of Egalitarianism Under Participation Constraints

We define a new solution concept for transferable utility cooperative games in characteristic function form, in a framework where individuals believe in equality as a desirable social goal, although private preferences dictate selfish behavior. This latter aspect implies that the solution outcome(s) must satisfy core-like participation constraints while the concern for equality entails choice of Lorenz maximal elements from within the set of payoffs satisfying the participation constraints