IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/50073.html
   My bibliography  Save this paper

Graph value for cooperative games

Author

Listed:
  • Hellman, Ziv
  • Peretz, Ron

Abstract

We suppose that players in a cooperative game are located within a graph structure, such as a social network or supply route, that limits coalition formation to coalitions along connected paths within the graph. This leads to a generalisation of the Shapley value that is studied here from an axiomatic perspective. The resulting ‘graph value’ is endogenously asymmetric, with the automorphism group of the graph playing a crucial role in determining the relative values of players.

Suggested Citation

  • Hellman, Ziv & Peretz, Ron, 2013. "Graph value for cooperative games," LSE Research Online Documents on Economics 50073, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:50073
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/50073/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Álvarez-Mozos, Mikel & Hellman, Ziv & Winter, Eyal, 2013. "Spectrum value for coalitional games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 132-142.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, 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. Álvarez-Mozos, Mikel & Hellman, Ziv & Winter, Eyal, 2013. "Spectrum value for coalitional games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 132-142.

    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. Tobias Hiller, 2018. "The Effects of Excluding Coalitions," Games, MDPI, vol. 9(1), pages 1-7, January.
    2. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    3. Ziv Hellman & Ron Peretz, 2015. "Values for Cooperative Games over Graphs and Games With Inadmissible Coalitions," Working Papers 2015-04, Bar-Ilan University, Department of Economics.
    4. Hellman, Ziv & Peretz, Ron, 2018. "Values for cooperative games over graphs and games with inadmissible coalitions," Games and Economic Behavior, Elsevier, vol. 108(C), pages 22-36.
    5. M. Josune Albizuri & Satoshi Masuya & José M. Zarzuelo, 2022. "Characterization of a value for games under restricted cooperation," Annals of Operations Research, Springer, vol. 318(2), pages 773-785, November.
    6. Emilio Calvo & Esther Gutiérrez-López, 2015. "The value in games with restricted cooperation," Discussion Papers in Economic Behaviour 0115, University of Valencia, ERI-CES.
    7. Guang Zhang & Erfang Shan & Liying Kang & Yanxia Dong, 2017. "Two efficient values of cooperative games with graph structure based on $$\tau $$ τ -values," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 462-482, August.
    8. Alexandre Skoda, 2016. "Convexity of Network Restricted Games Induced by Minimum Partitions," Documents de travail du Centre d'Economie de la Sorbonne 16019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    10. H. Andrew Michener & Daniel J. Myers, 1998. "Probabilistic Coalition Structure Theories," Journal of Conflict Resolution, Peace Science Society (International), vol. 42(6), pages 830-860, December.
    11. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    12. Hadas, Yuval & Gnecco, Giorgio & Sanguineti, Marcello, 2017. "An approach to transportation network analysis via transferable utility games," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 120-143.
    13. Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1979. "A group incentive compatible mechanism yielding core allocations," Journal of Economic Theory, Elsevier, vol. 20(1), pages 13-22, February.
    14. Sylvain Béal & Mostapha Diss & Rodrigue Tido Takeng, 2024. "New axiomatizations of the Diversity Owen and Shapley values," Working Papers 2024-09, CRESE.
    15. Tesfatsion, Leigh, 1998. "Ex Ante Capacity Effects in Evolutionary Labor Markets with Adaptive Search," ISU General Staff Papers 199810010700001046, Iowa State University, Department of Economics.
    16. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Sofia Priazhkina & Samuel Palmer & Pablo Martín-Ramiro & Román Orús & Samuel Mugel & Vladimir Skavysh, 2024. "Digital Payments in Firm Networks: Theory of Adoption and Quantum Algorithm," Staff Working Papers 24-17, Bank of Canada.
    18. Sridhar Mandyam & Usha Sridhar, 2017. "DON and Shapley Value for Allocation among Cooperating Agents in a Network: Conditions for Equivalence," Studies in Microeconomics, , vol. 5(2), pages 143-161, December.
    19. Liying Kang & Anna Khmelnitskaya & Erfang Shan & Dolf Talman & Guang Zhang, 2021. "The average tree value for hypergraph games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 437-460, December.
    20. Sjur Didrik Flåm, 2013. "Reaching Market Equilibrium Merely by Bilateral Barters," CESifo Working Paper Series 4504, CESifo.

    More about this item

    Keywords

    Shapley value; network games;

    JEL classification:

    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:ehl:lserod:50073. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.