IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v79y2025i3d10.1007_s00199-024-01612-6.html
   My bibliography  Save this article

Gately values of cooperative games

Author

Listed:
  • Robert P. Gilles

    (The Queen’s University of Belfast)

  • Lina Mallozzi

    (University of Naples Federico II)

Abstract

We investigate Gately’s solution concept for cooperative games with transferable utilities. Gately’s conception introduced a bargaining solution that minimises the maximal quantified “propensity to disrupt” the negotiation process of the players over the allocation of the generated collective payoffs. We show that Gately’s solution concept is well-defined for a broad class of games and that it can be interpreted as a compromise solution. We also consider a generalisation based on a parameter-based quantification of the propensity to disrupt. We provide an axiomatic characterisation of the original Gately value as well as these generalised Gately values. Furthermore, we investigate the relationship of these Gately values with the Core and the Nucleolus and show that Gately’s solution is in the Core for all regular 3-player games, but is fundamentally different from the Nucleolus. We identify exact conditions under which these Gately values are Core imputations for arbitrary regular cooperative games. Finally, we investigate the relationship of the Gately value with the Shapley value.

Suggested Citation

  • Robert P. Gilles & Lina Mallozzi, 2025. "Gately values of cooperative games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(3), pages 723-758, May.
  • Handle: RePEc:spr:joecth:v:79:y:2025:i:3:d:10.1007_s00199-024-01612-6
    DOI: 10.1007/s00199-024-01612-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-024-01612-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00199-024-01612-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yannelis, Nicholas C., 1983. "Existence and fairness of value allocation without convex preferences," Journal of Economic Theory, Elsevier, vol. 31(2), pages 283-292, December.
    2. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
    3. van den Brink, René & Chun, Youngsub & Funaki, Yukihiko & Zou, Zhengxing, 2023. "Balanced externalities and the proportional allocation of nonseparable contributions," European Journal of Operational Research, Elsevier, vol. 307(2), pages 975-983.
    4. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    5. Aumann, Robert J, 1975. "Values of Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 43(4), pages 611-646, July.
    6. Kalyan Chatterjee & Bhaskar Dutia & Debraj Ray & Kunal Sengupta, 2013. "A Noncooperative Theory of Coalitional Bargaining," World Scientific Book Chapters, in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 5, pages 97-111, World Scientific Publishing Co. Pte. Ltd..
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. A. van den Nouweland & P. Borm & W. van Golstein Brouwers & R. Groot Bruinderink & S. Tijs, 1996. "A Game Theoretic Approach to Problems in Telecommunication," Management Science, INFORMS, vol. 42(2), pages 294-303, February.
    9. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 505-538, November.
    10. 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.
    11. Tijs, S.H., 1987. "An axiomatization of the ô-value," Other publications TiSEM 5536ac66-86f3-49fb-9e7d-2, Tilburg University, School of Economics and Management.
    12. repec:hal:pseose:halshs-00749950 is not listed on IDEAS
    13. Robert P. Gilles & Lina Mallozzi, 2023. "Game theoretic foundations of the Gately power measure for directed networks," Papers 2308.02274, arXiv.org.
    14. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Other publications TiSEM 4f162187-3069-4cb5-8353-5, Tilburg University, School of Economics and Management.
    16. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2023. "Core and stable sets of exchange economies with externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 27-44, April.
    17. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    18. E. Calvo & S. Tijs & F. Valenciano & J. Zarzuelo, 1995. "On the axiomatization of the τ-value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 35-46, June.
    19. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    20. 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.
    21. Gilles, R.P. & Owen, G., 1999. "Cooperative Games and Disjunctive Permission Structures," Discussion Paper 1999-20, Tilburg University, Center for Economic Research.
    22. Julio González-Díaz & Estela Sánchez-Rodríguez, 2007. "A natural selection from the core of a TU game: the core-center," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 27-46, September.
    23. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-476, March.
    24. Vincenzo Scalzo, 2022. "Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 1-12, May.
    25. Mingming Leng & Mahmut Parlar, 2010. "Analytic solution for the nucleolus of a three‐player cooperative game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 667-672, October.
    26. Jochen Staudacher & Johannes Anwander, 2019. "Conditions for the uniqueness of the Gately point for cooperative games," Papers 1901.01485, arXiv.org.
    27. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
    28. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    29. Tijs, Stef H., 1987. "An axiomatization of the [tau]-value," Mathematical Social Sciences, Elsevier, vol. 13(2), pages 177-181, April.
    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. Churkin, Andrey & Bialek, Janusz & Pozo, David & Sauma, Enzo & Korgin, Nikolay, 2021. "Review of Cooperative Game Theory applications in power system expansion planning," Renewable and Sustainable Energy Reviews, Elsevier, vol. 145(C).
    2. Slikker, M. & Gilles, R.P. & Norde, H.W. & Tijs, S.H., 2000. "Directed Communication Networks," Discussion Paper 2000-84, Tilburg University, Center for Economic Research.
    3. Tobias Hiller, 2021. "Hierarchy and the size of a firm," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 68(3), pages 389-404, September.
    4. Slikker, M. & Gilles, R.P. & Norde, H.W. & Tijs, S.H., 2000. "Directed Communication Networks," Other publications TiSEM 00f2df6e-3a8e-4ed3-84cf-2, Tilburg University, School of Economics and Management.
    5. René Brink, 2010. "Axiomatizations of Banzhaf permission values for games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 445-466, July.
    6. 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.
    7. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    8. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2020. "Allocating extra revenues from broadcasting sports leagues," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 65-73.
    9. Pulido, Manuel A. & Sanchez-Soriano, Joaquin, 2006. "Characterization of the core in games with restricted cooperation," European Journal of Operational Research, Elsevier, vol. 175(2), pages 860-869, December.
    10. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    11. Subhadip Chakrabarti & Amandine Ghintran & Rajnish Kumar, 2019. "Assignment of heterogeneous agents in trees under the permission value," Review of Economic Design, Springer;Society for Economic Design, vol. 23(3), pages 155-188, December.
    12. Funaki, Yukihiko & Núñez, Marina, 2024. "Some advances in cooperative game theory: Indivisibilities, externalities and axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    13. Palestini, Arsen & Pignataro, Giuseppe, 2016. "A graph-based approach to inequality assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 65-78.
    14. Algaba, A. & Bilbao, J.M. & van den Brink, J.R. & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Other publications TiSEM 907b4b44-90f9-4faa-9473-8, Tilburg University, School of Economics and Management.
    15. van den Brink, René & Chun, Youngsub & Funaki, Yukihiko & Zou, Zhengxing, 2023. "Balanced externalities and the proportional allocation of nonseparable contributions," European Journal of Operational Research, Elsevier, vol. 307(2), pages 975-983.
    16. Takashi Ui & Hiroyuki Kojima & Atsushi Kajii, 2011. "The Myerson value for complete coalition structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 427-443, December.
    17. Algaba, A. & Bilbao, J.M. & van den Brink, J.R. & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Discussion Paper 2000-124, Tilburg University, Center for Economic Research.
    18. Robert P. Gilles & Lina Mallozzi, 2022. "Gately Values of Cooperative Games," Papers 2208.10189, arXiv.org, revised Jul 2023.
    19. Wu, Hao & van den Brink, René & Estévez-Fernández, Arantza, 2024. "Highway toll allocation," Transportation Research Part B: Methodological, Elsevier, vol. 180(C).
    20. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.

    More about this item

    Keywords

    Game theory; Cooperative game; Sharing value; Gately point; Core;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    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:spr:joecth:v:79:y:2025:i:3:d:10.1007_s00199-024-01612-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.