Cephoids: Duality and reference vectors

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 face and its reference system. The second graph describes the generalized tentacles.

Computing the Minkowski sum of prisms

Within this paper we compute 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.convex analysis, Minkowski sum, polytopes

The Shapley Value for Countably Many Players

Shapley value, invariant measure

Computing the Minkowski sum of prisms

Pallaschke D, Rosenmüller J. Computing the Minkowski sum of prisms. Working Papers. Institute of Mathematical Economics. Vol 362. Bielefeld: Universität Bielefeld; 2005.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

Cephoids. Duality and reference vectors

Pallaschke D, Rosenmüller J. Cephoids. Duality and reference vectors. Working Papers. Institute of Mathematical Economics. Vol 389. Bielefeld: Universität Bielefeld; 2007.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 face and its reference system. The second graph describes the generalized tentacles

Cephoids. Minkowski sums of prisms

Pallaschke D, Rosenmüller J. Cephoids. Minkowski sums of prisms. Working Papers. Institute of Mathematical Economics. Vol 360. Bielefeld: Universität Bielefeld; 2004.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 shape resembles the view of a cephalopod, the polytope obtained is called a "cephoid". The general geometrical and combinatorial aspects of cephoids are exhibited

A superadditive solution

Pallaschke D, Rosenmüller J. A superadditive solution. Working Papers. Institute of Mathematical Economics. Vol 361. Bielefeld: Universität Bielefeld; 2004.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

The Shapley value for countably many players

Pallaschke D, Rosenmüller J. The Shapley value for countably many players. Working Papers. Institute of Mathematical Economics. Vol 240. Bielefeld: Center for Mathematical Economics; 1995