IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1701.01677.html
   My bibliography  Save this paper

The Shapley Value of Digraph Games

Author

Listed:
  • Krishna Khatri

Abstract

In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation between two adjacent players is established by a directed line segment. Directed path, connecting the initial player with the terminal player, form the coalition among players. A dominance relation is established between players and this relation determines whether or not a player wants to cooperate. To cooperate, we assume that a player joins a coalition where he/she is not dominated by any other players.The Shapley value is defined as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. The Shapley value for cyclic digraph games is calculated and analyzed. For a given family of characteristic functions, a quick way to calculate Shapley values is formulated.

Suggested Citation

  • Krishna Khatri, 2017. "The Shapley Value of Digraph Games," Papers 1701.01677, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1701.01677
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1701.01677
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Anna, Petrenko, 2016. "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(1), March.
    3. Anna Khmelnitskaya & Gerard van der Laan & Dolf Talman, 2016. "Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games," Tinbergen Institute Discussion Papers 16-070/II, Tinbergen Institute.
    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. Ping Sun & Elena Parilina, 2021. "Network Formation with Asymmetric Players and Chance Moves," Mathematics, MDPI, vol. 9(8), pages 1-16, April.
    2. 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.
    3. Vivian Welch & Christine M. Mathew & Panteha Babelmorad & Yanfei Li & Elizabeth T. Ghogomu & Johan Borg & Monserrat Conde & Elizabeth Kristjansson & Anne Lyddiatt & Sue Marcus & Jason W. Nickerson & K, 2021. "Health, social care and technological interventions to improve functional ability of older adults living at home: An evidence and gap map," Campbell Systematic Reviews, John Wiley & Sons, vol. 17(3), September.
    4. Merja Anis & Kati Turtiainen, 2021. "Social Workers’ Reflections on Forced Migration and Cultural Diversity—Towards Anti-Oppressive Expertise in Child and Family Social Work," Social Sciences, MDPI, vol. 10(3), pages 1-18, February.
    5. Ian Parry & Victor Mylonas, 2018. "Canada's Carbon Price Floor," CESifo Working Paper Series 6959, CESifo.
    6. Persson, Petra & Qiu, Xinyao & Rossin-Slater, Maya, 2021. "Family Spillover Effects of Marginal Diagnoses: The Case of ADHD," IZA Discussion Papers 14020, Institute of Labor Economics (IZA).
    7. Menkhoff, Lukas & Miethe, Jakob, 2019. "Tax evasion in new disguise? Examining tax havens' international bank deposits," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 176, pages 53-78.
    8. Sylvain Béal & Marc Deschamps & Catherine Refait-Alexandre & Guillaume Sekli, 2022. "Early contributors, cooperation and fair rewards in crowdfunding," Working Papers hal-04222321, HAL.
    9. Ran Abramitzky & Roy Mill & Santiago Pérez, 2020. "Linking individuals across historical sources: A fully automated approach," Historical Methods: A Journal of Quantitative and Interdisciplinary History, Taylor & Francis Journals, vol. 53(2), pages 94-111, April.
    10. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    11. Uguccioni, James, 2022. "The long-run effects of parental unemployment in childhood," CLEF Working Paper Series 45, Canadian Labour Economics Forum (CLEF), University of Waterloo.
    12. 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.
    13. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    14. Werner Eichhorst & Ulf Rinne, 2017. "Digital Challenges for the Welfare State," CESifo Forum, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 18(04), pages 03-08, December.
    15. Sant'Anna, Ana Claudia & Bergtold, Jason & Shanoyan, Aleksan & Caldas, Marcellus & Granco, Gabriel, 2021. "Deal or No Deal? Analysis of Bioenergy Feedstock Contract Choice with Multiple Opt-out Options and Contract Attribute Substitutability," 2021 Conference, August 17-31, 2021, Virtual 315289, International Association of Agricultural Economists.
    16. Tommaso Colussi & Ingo E. Isphording & Nico Pestel, 2021. "Minority Salience and Political Extremism," American Economic Journal: Applied Economics, American Economic Association, vol. 13(3), pages 237-271, July.
    17. Bruns, Stephan B. & Moneta, Alessio & Stern, David I., 2021. "Estimating the economy-wide rebound effect using empirically identified structural vector autoregressions," Energy Economics, Elsevier, vol. 97(C).
    18. Erkmen Giray Aslim, 2019. "The Relationship Between Health Insurance and Early Retirement: Evidence from the Affordable Care Act," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 45(1), pages 112-140, January.
    19. Rodrigo J. Harrison & Roberto Munoz, 2003. "Stability and Equilibrium Selection in a Link Formation Game," Game Theory and Information 0306004, University Library of Munich, Germany.
    20. Burlig, Fiona & Preonas, Louis & Woerman, Matt, 2020. "Panel data and experimental design," Journal of Development Economics, Elsevier, vol. 144(C).

    More about this item

    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:arx:papers:1701.01677. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.