IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/0503007.html
   My bibliography  Save this paper

Cooperative investment games or population games

Author

Listed:
  • Yaron Azrieli

    (Tel Aviv University)

  • Ehud Lehrer

    (Tel Aviv University)

Abstract

The model of a cooperative fuzzy game is interpreted as both a population game and a cooperative investment game. Three types of core- like solutions induced by these interpretations are introduced and investigated. The interpretation of a game as a population game allows us to define sub-games. We show that, unlike the well-known Shapley- Shubik theorem on market games (Shapley-Shubik) there might be a population game such that each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a population game needs to be also homogeneous. We also discuss some special classes of population games such as convex games, exact games, homogeneousgames and additive games.

Suggested Citation

  • Yaron Azrieli & Ehud Lehrer, 2005. "Cooperative investment games or population games," Game Theory and Information 0503007, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0503007
    Note: Type of Document - pdf; pages: 30
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0503/0503007.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
    2. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    3. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    4. Louis J. Billera & David C. Heath, 1982. "Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 32-39, February.
    5. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, University Library of Munich, Germany.
    6. Jean-Pierre Aubin, 1981. "Cooperative Fuzzy Games," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 1-13, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mojmír Sabolovič, 2011. "An alternative methodological approach to value analysis of regions, municipal corporations and clusters," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 59(4), pages 295-300.

    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. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Egalitarianism in convex fuzzy games," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 313-325, May.
    2. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Hypercubes and compromise values for cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 155(3), pages 733-740, June.
    3. Yu-Hsien Liao, 2013. "The Shapley value for fuzzy games: TU games approach," Economics Bulletin, AccessEcon, vol. 33(1), pages 192-197.
    4. Boonen, Tim J., 2017. "Risk Redistribution Games With Dual Utilities," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 303-329, January.
    5. Gerwald Gulick & Henk Norde, 2013. "Fuzzy cores and fuzzy balancedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 131-146, April.
    6. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
    7. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    8. Yu-Hsien Liao, 2017. "Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 257-268, September.
    9. Tsanakas, Andreas, 2009. "To split or not to split: Capital allocation with convex risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 268-277, April.
    10. Yaron Azrieli & Ehud Lehrer, 2007. "On some families of cooperative fuzzy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 1-15, September.
    11. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    12. Philippe Artzner & Claude d'Aspremont & Louis-André Gérard-Varet, 1986. "Envelopes and Geometrical Covers of Side-Payment Games and their Market Representations," Post-Print hal-00950764, HAL.
    13. Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems," Other publications TiSEM 2c502ef8-76f0-47f5-ab45-1, Tilburg University, School of Economics and Management.
    14. Keyzer, Michiel & van Wesenbeeck, Cornelia, 2011. "Optimal coalition formation and surplus distribution: Two sides of one coin," European Journal of Operational Research, Elsevier, vol. 215(3), pages 604-615, December.
    15. Zuofeng Gao & Yongbo Yu & Hongxin Bai & Chunyan Han, 2008. "A Repeated Convex Fuzzy Cooperative Game," Modern Applied Science, Canadian Center of Science and Education, vol. 2(3), pages 1-54, May.
    16. Tijs, S.H. & Brânzei, R. & Ishihara, S. & Muto, S., 2002. "On Cores and Stable Sets for Fuzzy Games," Other publications TiSEM 574e2ed7-34ee-4d97-a289-0, Tilburg University, School of Economics and Management.
    17. Fernández, J.R. & Gallego, I. & Jiménez-Losada, A. & Ordóñez, M., 2016. "Cooperation among agents with a proximity relation," European Journal of Operational Research, Elsevier, vol. 250(2), pages 555-565.
    18. Tijs, S.H. & Brânzei, R. & Ishihara, S. & Muto, S., 2002. "On Cores and Stable Sets for Fuzzy Games," Discussion Paper 2002-116, Tilburg University, Center for Economic Research.
    19. Molina, Elisenda & Tejada, Juan, 2004. "Linear production games with committee control: Limiting behaviour of the core," European Journal of Operational Research, Elsevier, vol. 154(3), pages 609-625, May.
    20. Jiménez-Losada, Andrés & Fernández, Julio R. & Ordóñez, Manuel & Grabisch, Michel, 2010. "Games on fuzzy communication structures with Choquet players," European Journal of Operational Research, Elsevier, vol. 207(2), pages 836-847, December.

    More about this item

    Keywords

    investment game; population game; fuzzy game; core-like solution; market game;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpga:0503007. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.