IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v14y2023i5p64-d1247926.html
   My bibliography  Save this article

Game Theoretic Foundations of the Gately Power Measure for Directed Networks

Author

Listed:
  • Robert P. Gilles

    (Department of Economics, The Queen’s University of Belfast, Riddel Hall, 185 Stranmillis Road, Belfast BT9 5EE, UK)

  • Lina Mallozzi

    (Department of Mathematics and Applications, University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy)

Abstract

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can be represented through appropriate TU-games. We investigate the properties of these TU-representations and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a core power gauge, investigate the relationship of the Gately with the β -measure, and construct an axiomatisation of the Gately measure.

Suggested Citation

  • Robert P. Gilles & Lina Mallozzi, 2023. "Game Theoretic Foundations of the Gately Power Measure for Directed Networks," Games, MDPI, vol. 14(5), pages 1-19, September.
    • Handle: RePEc:gam:jgames:v:14:y:2023:i:5:p:64-:d:1247926
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/14/5/64/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/14/5/64/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert P. Gilles & Lina Mallozzi, 2022. "Gately Values of Cooperative Games," Papers 2208.10189, arXiv.org, revised Jul 2023.
    2. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, March.
    3. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    4. Smita Shandilya & Zdzislaw Szymanski & Shishir Kumar Shandilya & Ivan Izonin & Krishna Kant Singh, 2022. "Modeling and Comparative Analysis of Multi-Agent Cost Allocation Strategies Using Cooperative Game Theory for the Modern Electricity Market," Energies, MDPI, vol. 15(7), pages 1-14, March.
    5. Gately, Dermot, 1974. "Sharing the Gains from Regional Cooperation: A Game Theoretic Application to Planning Investment in Electric Power," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 195-208, February.
    6. 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.
    7. van den Brink, J.R. & Borm, P.E.M., 2002. "Digraph competitions and cooperative games," Other publications TiSEM 262e8724-0bc0-49da-99c5-f, Tilburg University, School of Economics and Management.
    8. Jochen Staudacher & Johannes Anwander, 2019. "Conditions for the uniqueness of the Gately point for cooperative games," Papers 1901.01485, arXiv.org.
    9. van den Brink, J.R. & Borm, P.E.M., 1994. "Digraph competitions and cooperative games," Other publications TiSEM 1b98a76d-ab49-4f5c-975c-c, Tilburg University, School of Economics and Management.
    10. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
    11. van den Brink, René & He, Simin & Huang, Jia-Ping, 2018. "Polluted river problems and games with a permission structure," Games and Economic Behavior, Elsevier, vol. 108(C), pages 182-205.
    12. Jicheng Liu & Dandan He, 2018. "Profit Allocation of Hybrid Power System Planning in Energy Internet: A Cooperative Game Study," Sustainability, MDPI, vol. 10(2), pages 1-19, February.
    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. Robert P. Gilles & Lina Mallozzi, 2022. "Gately Values of Cooperative Games," Papers 2208.10189, arXiv.org, revised Jul 2023.
    2. Gilles, Robert P. & Mallozzi, Lina, 2022. "Generalised Gately Values of Cooperative Games," QBS Working Paper Series 2022/06, Queen's University Belfast, Queen's Business School.
    3. Hao Wu & Rene van den Brink & Arantza Estevez-Fernandez, 2022. "The locally partial permission value for games with a permission structure," Tinbergen Institute Discussion Papers 22-037/II, Tinbergen Institute.
    4. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    5. Robert P. Gilles & Lina Mallozzi, 2023. "Game theoretic foundations of the Gately power measure for directed networks," Papers 2308.02274, arXiv.org.
    6. Borm, P.E.M. & van den Brink, J.R. & Levinsky, R. & Slikker, M., 2000. "On Two New Social Choice Correspondences," Other publications TiSEM 71885704-e24b-43ef-a029-8, Tilburg University, School of Economics and Management.
    7. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    8. Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2004. "The Consensus Value : A New Solution Concept for Cooperative Games," Other publications TiSEM ff51992e-6683-4596-a613-9, Tilburg University, School of Economics and Management.
    9. Borm, P.E.M. & van den Brink, J.R. & Slikker, M., 2000. "An Iterative Procedure for Evaluating Digraph Competitions," Other publications TiSEM 03637fc0-696b-4b91-b292-d, Tilburg University, School of Economics and Management.
    10. Rafael Amer & José Giménez & Antonio Magaña, 2012. "Accessibility measures to nodes of directed graphs using solutions for generalized cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 105-134, February.
    11. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    12. Peter Borm & René van den Brink & Marco Slikker, 2002. "An Iterative Procedure for Evaluating Digraph Competitions," Annals of Operations Research, Springer, vol. 109(1), pages 61-75, January.
    13. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.
    14. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    15. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & Voorneveld, M., 2003. "On a compromise social choice correspondence," Other publications TiSEM 07d3e06d-241b-4aa2-b59d-d, Tilburg University, School of Economics and Management.
    16. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & Voorneveld, M., 2002. "Characterizations of Solutions in Digraph Competitions," Other publications TiSEM f8406395-a31f-47b0-ab62-d, Tilburg University, School of Economics and Management.
    17. Encarnación Algaba & René Brink & Chris Dietz, 2017. "Power Measures and Solutions for Games Under Precedence Constraints," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 1008-1022, March.
    18. Marieke Quant & Peter Borm & Hans Reijnierse & Mark Voorneveld, 2003. "On a compromise social choice correspondence," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 311-324, December.
    19. René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, vol. 76(3), pages 343-361, March.
    20. Borm, Peter & van den Brink, Rene & Levinsky, Rene & Slikker, Marco, 2004. "On two new social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 51-68, January.

    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:gam:jgames:v:14:y:2023:i:5:p:64-:d:1247926. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.