IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/629.html
   My bibliography  Save this paper

Cephoids. Minkowski Sums of DeGua Simplices. Theory and Applications

Author

Listed:
  • 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

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2939557/2939558
    File Function: First Version, 2019
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Richter Wolfram F. & Rosenmüller Joachim, 2012. "Efficient Specialization in Ricardian Production," German Economic Review, De Gruyter, vol. 13(2), pages 117-126, May.
    2. 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.
    3. 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.
    4. Calvo, Emilio & Gutierrez, Esther, 1994. "Extension of the Perles-Maschler Solution to N-Person Bargaining Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(4), pages 325-346.
    5. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gustavo Bergantiños & Balbina Casas- Méndez & Gloria Fiestras- Janeiro & Juan Vidal-Puga, 2005. "A Focal-Point Solution for Bargaining Problems with Coalition Structure," Game Theory and Information 0511006, University Library of Munich, Germany.
    2. Bergantinos, G. & Casas-Mendez, B. & Fiestras-Janeiro, M.G. & Vidal-Puga, J.J., 2007. "A solution for bargaining problems with coalition structure," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 35-58, July.
    3. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers 2007-11, Brown University, Department of Economics.
    4. Laruelle, Annick & Valenciano, Federico, 2007. "Bargaining in committees as an extension of Nash's bargaining theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 291-305, January.
    5. Dietzenbacher, Bas & Yanovskaya, Elena, 2023. "The equal split-off set for NTU-games," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 61-67.
    6. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers 2007-11, Brown University, Department of Economics.
    7. M. Hinojosa & E. Romero-Palacios & J. Zarzuelo, 2015. "Consistency of the Shapley NTU value in G-hyperplane games," Review of Economic Design, Springer;Society for Economic Design, vol. 19(4), pages 259-278, December.
    8. Bhattacharya, Anindya & Ziad, Abderrahmane, 2006. "The core as the set of eventually stable outcomes: A note," Games and Economic Behavior, Elsevier, vol. 54(1), pages 25-30, January.
    9. de Clippel, Geoffroy, 2005. "Values for cooperative games with incomplete information: An eloquent example," Games and Economic Behavior, Elsevier, vol. 53(1), pages 73-82, October.
    10. Salamanca, Andrés, 2020. "On the values of Bayesian cooperative games with sidepayments," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 38-49.
    11. Gustavo Bergantiños & Juan Vidal-Puga, 2003. "The NTU consistent coalitional value," Game Theory and Information 0303007, University Library of Munich, Germany.
    12. Gustavo Bergantiños & Juan Vidal-Puga, 2005. "The Consistent Coalitional Value," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 832-851, November.
    13. Sudhölter, Peter & Zarzuelo, José M., 2013. "Extending the Nash solution to choice problems with reference points," Games and Economic Behavior, Elsevier, vol. 80(C), pages 219-228.
    14. Chaowen Yu, 2022. "Hyperplane games, prize games and NTU values," Theory and Decision, Springer, vol. 93(2), pages 359-370, September.
    15. Vidal-Puga, Juan J., 2008. "Forming coalitions and the Shapley NTU value," European Journal of Operational Research, Elsevier, vol. 190(3), pages 659-671, November.
    16. Hinojosa, M.A. & Romero, E. & Zarzuelo, J.M., 2012. "Consistency of the Harsanyi NTU configuration value," Games and Economic Behavior, Elsevier, vol. 76(2), pages 665-677.
    17. Perez-Castrillo, David & Wettstein, David, 2006. "An ordinal Shapley value for economic environments," Journal of Economic Theory, Elsevier, vol. 127(1), pages 296-308, March.
    18. Emililo Calvo, 2004. "Single NTU-value solutions," Game Theory and Information 0405004, University Library of Munich, Germany, revised 10 Jun 2004.
    19. Sergei Pechersky, 2001. "On Proportional Excess for NTU Games," EUSP Department of Economics Working Paper Series 2001/02, European University at St. Petersburg, Department of Economics, revised 30 Oct 2001.
    20. Hwang, Yan-An, 2010. "Marginal monotonicity solution of NTU games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 502-508, November.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:629. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.