We introduce the Maschler-Perles-Shapley value for NTU games composed by smooth bodies. This waywe extend the M-P-S value established for games composed by Cephoids ("sums of deGua Simplices"). The development is parallel to the one of the (generalized) Maschler-Perles bargaining solution. For...

We consider (cooperative) linear production games with a continuum of players. The coalitional function is generated by r + 1 production factors that is, non atomic measures defined on an interval. r of these are orthogonal probabilities which, economically, can be considered as cornered...

We discuss the structure of those polytopes in Rⁿ+ that are Minkowski sums of prisms. A prism is the convex hull of the origin and n positive multiples of the unit vectors. We characterize the defining outer surface of such polytopes by describing the shape of all maximal faces. As this shape...

Game Theory describes human interaction involving conflict, cooperation and competition, the term Interpersonal Decision Theory is synonymous. The term reflects the fact that most essential features of this field are manifested in parlor games. This topic-level treatment covers large parts of...

Within this paper we study the Minkowski sum of prisms ('Cephoids') in a finite dimensional vector space. We provide a representation of a finite sum of prisms in terms of inequalities.

We present a superadditive bargaining solution defined on a class of polytopes in Rⁿ. The solution generalizes the superadditive solution exhibited by MASCHLER and PERLES.

A cephoid is a Minkowski sum of finitely many prisms in Rⁿ. We discuss the concept of duality for cephoids. Also, we show that the reference number uniquely defines a face. Based on these results, we exhibit two graphs on the outer surface of a cephoid. The first one corresponds to a maximal...

A cephoid is an algebraic ('Minkowski') sum of finitely many prisms in R^n. A cephoidal game is an NTU game the feasible sets of which are cephoids. We provide a version of the Shapley NTU value for such games based on the bargaining solution of Maschler-Perles.

We characterize convex vNM-Stable Sets according to von Neumann and Morgenstern for orthogonal linear production games with a continuum of players. The results of Rosenmüller & Shitovitz [International journal of game theory 29 (2000), pp. 39-61] are thereby substantially improved....

This paper constitutes the second part in a series dealing with vNM-Stable sets for (cooperative) linear production games with a continuum of players, see [2]. The coalitional function is generated by r + 1 production factors (non atomic measures). R factors are given by orthogonal probabilities...