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Cephoids. Minkowski Sums of DeGua Simplices. Theory and Applications

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  • Rosenmüller, Joachim

    (Center for Mathematical Economics, Bielefeld University)

Abstract

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 simplices, algebraic sums of subsimplices etc. Cephoids appear in Operations Research (Optimization), in Mathematical Economics (Free Trade theory), and in Cooperative Game Theory. In particular, in the context of Cooperative Game Theory the notions of a Cephoid serves to construct “solutions” or “values” for bargaining problems and non–side payment games.

Suggested Citation

  • Rosenmüller, Joachim, 2019. "Cephoids. Minkowski Sums of DeGua Simplices. Theory and Applications," Center for Mathematical Economics Working Papers 629, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:629
    as

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    File URL: https://pub.uni-bielefeld.de/download/2939557/2939558
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    References listed on IDEAS

    as
    1. Wolfram F. Richter & Joachim Rosenmüller, 2012. "Efficient Specialization in Ricardian Production," German Economic Review, Verein für Socialpolitik, vol. 13(2), pages 117-126, May.
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    3. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    4. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    5. Geoffroy de Clippel & Hans Peters & Horst Zank, 2004. "Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 145-158, January.
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