IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/bab30745-01b4-480b-a8ac-48a347ed9d9d.html
   My bibliography  Save this paper

Cooperative Games in Graph Structure

Author

Listed:
  • Herings, P.J.J.

    (Tilburg University, School of Economics and Management)

  • van der Laan, G.
  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

Abstract

In this paper we generalize the concept of coalitional games by allowingfor any organizational structure within coalitions represented by a graphon the set of players ot the coalition. A, possibly empty, set of payoffvectors is assigned to any graph on every subset of players. Such a gamewill be called a graph game. For each graph a power vector is determinedthat depends on the relative positions of the players within the graph.A collection of graphs will be called balanced if to any graph in the collection apositive weight can be assigned such that the weighted power vectorssum up to the vector of ones. We then define the balanced-core as a refinement ofthe core. A payoff vector lies in the balanced-core if it lies in the core andthe payoff vector is an element of payoff sets of all graphs in some balanced collection ofgraphs. We prove that any balanced graph game has a nonempty balanced-core.We conclude by some examples showing the usefulness of the conceptsof graph games and balanced-core. In particular these examples show a closerelationship between solutions to noncooperative games andbalanced-core elements of a well-defined graph game.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2000. "Cooperative Games in Graph Structure," Other publications TiSEM bab30745-01b4-480b-a8ac-4, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:bab30745-01b4-480b-a8ac-48a347ed9d9d
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/536826/90.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Kamiya, K. & Talman, D., 1990. "Variable Dimension Simplicial Algorithm For Balanced Games," Papers 9025, Tilburg - Center for Economic Research.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. Doup, T.M. & Talman, A.J.J., 1987. "A new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices," Other publications TiSEM 398740e7-fdc2-41b6-968f-4, Tilburg University, School of Economics and Management.
    5. Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998. "Cooperative games in permutational structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 427-442.
    6. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
    7. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    8. Bouyssou, Denis, 1992. "Ranking methods based on valued preference relations: A characterization of the net flow method," European Journal of Operational Research, Elsevier, vol. 60(1), pages 61-67, July.
    9. van der Laan, G. & Talman, A.J.J. & Yang, Z., 1994. "Intersection theorems on polytopes," Discussion Paper 1994-20, Tilburg University, Center for Economic Research.
    10. P. Jean-Jacques Herings, 1997. "An extremely simple proof of the K-K-M-S Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 361-367.
    11. Ichiishi, Tatsuro & Idzik, Adam, 1991. "Closed Covers of Compact Convex Polyhedra," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 161-169.
    12. D. Bouyssou & P. Perny, 1992. "Ranking methods for valued preference relations," Post-Print hal-02920156, HAL.
    13. Bouyssou, D. & Perny, P., 1992. "Ranking methods for valued preference relations : A characterization of a method based on leaving and entering flows," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 186-194, August.
    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. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2001. "Measuring the Power of Nodes in Digraphs," Other publications TiSEM 8ad1bdb1-a602-4674-b737-2, Tilburg University, School of Economics and Management.
    2. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.

    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. P. Herings & A. Predtetchinski & A. Perea, 2006. "The Weak Sequential Core for Two-Period Economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 55-65, April.
    2. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2003. "Socially Structured Games and their Applications," Other publications TiSEM 271c701e-4489-41b3-8d9e-f, Tilburg University, School of Economics and Management.
    3. Clemens J. M. Kool, 2000. "International bond markets and the introduction of the Euro," Review, Federal Reserve Bank of St. Louis, vol. 82(Sep), pages 41-56.
    4. Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998. "Cooperative games in permutational structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 427-442.
    5. P. Herings & Gerard Laan & Dolf Talman, 2007. "Socially Structured Games," Theory and Decision, Springer, vol. 62(1), pages 1-29, February.
    6. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592181, HAL.
    7. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    8. van den Brink, René & Gilles, Robert P., 2009. "The outflow ranking method for weighted directed graphs," European Journal of Operational Research, Elsevier, vol. 193(2), pages 484-491, March.
    9. Rene van den Brink & Agnieszka Rusinowska, "undated". "The Degree Ratio Ranking Method for Directed Networks," Tinbergen Institute Discussion Papers 19-026/II, Tinbergen Institute.
    10. László Csató, 2019. "An impossibility theorem for paired comparisons," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 497-514, June.
    11. G Özerol & E Karasakal, 2008. "Interactive outranking approaches for multicriteria decision-making problems with imprecise information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1253-1268, September.
    12. Chen, Xuqi & Gao, Zhifeng & House, Lisa, 2015. "Willingness to Pay for Niche Fresh Produce across the States: Why Are Consumers Willing to Pay More for the Less Favorite?," 2015 Annual Meeting, January 31-February 3, 2015, Atlanta, Georgia 196901, Southern Agricultural Economics Association.
    13. Zhiwei Cui & Yan-An Hwang & Ding-Cheng You, 2021. "Axiomatizations of the $$\beta $$ β and the score measures in networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 399-418, June.
    14. Csató, László, 2013. "Rangsorolás páros összehasonlításokkal. Kiegészítések a felvételizői preferencia-sorrendek módszertanához [Paired comparisons ranking. A supplement to the methodology of application-based preferenc," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1333-1353.
    15. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2001. "Measuring the Power of Nodes in Digraphs," Other publications TiSEM 8ad1bdb1-a602-4674-b737-2, Tilburg University, School of Economics and Management.
    16. Vincke, Ph., 1999. "Robust and neutral methods for aggregating preferences into an outranking relation," European Journal of Operational Research, Elsevier, vol. 112(2), pages 405-412, January.
    17. Yazidi, Anis & Ivanovska, Magdalena & Zennaro, Fabio M. & Lind, Pedro G. & Viedma, Enrique Herrera, 2022. "A new decision making model based on Rank Centrality for GDM with fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1030-1041.
    18. Monsuur, Herman, 2005. "Characterizations of the 3-cycle count and backward length of a tournament," European Journal of Operational Research, Elsevier, vol. 164(3), pages 778-784, August.
    19. Mario Martín-Gamboa & Luis C. Dias & Paula Quinteiro & Fausto Freire & Luís Arroja & Ana Cláudia Dias, 2019. "Multi-Criteria and Life Cycle Assessment of Wood-Based Bioenergy Alternatives for Residential Heating: A Sustainability Analysis," Energies, MDPI, vol. 12(22), pages 1-17, November.
    20. Fernandez, Eduardo & Leyva, Juan Carlos, 2004. "A method based on multiobjective optimization for deriving a ranking from a fuzzy preference relation," European Journal of Operational Research, Elsevier, vol. 154(1), pages 110-124, April.

    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:tiu:tiutis:bab30745-01b4-480b-a8ac-48a347ed9d9d. 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: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    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.