We discuss the structure of those polytopes in /R/n+ 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...

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

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.

A cephoid is a Minkowski sum of finitely many prisms in R^n. 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 volume is a monograph on the geometric structure of a certain class of ("comprehensive") compact polyhedra called Cephoids. A Cephoid is a Minkowski sum of finitely many standardized simplices. The emphasis rests on the Pareto surface of Cephoids which consists of certain translates of...

We consider a class of comprehensive compact convex polyhedra called Cephoids. A Cephoid is a Minkowski sum of finitely many standardized simplices ("deGua Simplices''). The Pareto surface of Cephoids consists of certain translates of simplices, algebraic sums of subsimplices etc. The peculiar...

We introduce a generalization of the Maschler--Perles bargaining solution to smooth bargaining problems for $n$ players. We proceed by the construction of measures on the Pareto surface of a convex body. The MP surface measure is defined for Cephoids, i.e., Minkowski sums of simplices (see [14]...

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...