IDEAS home Printed from https://ideas.repec.org/p/has/discpr/1224.html

The Shapley value for shortest path games

Author

Listed:
  • Miklos Pinter

    (Department of Mathematics, Corvinus University of Budapest)

  • Anna Radvanyi

    (Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Department of Mathematics, Corvinus University of Budapest)

Abstract

In this paper shortest path games are considered. The transportation of a good in a network has costs and benefit too. The problem is to divide the profit of the transportation among the players. Fragnelli et al (2000) introduce the class of shortest path games, which coincides with the class of monotone games. They also give a characterization of the Shapley value on this class of games. In this paper we consider further four characterizations of the Shapley value (Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s axiomatizations), and conclude that all the mentioned axiomatizations are valid for shortest path games. Fragnelli et al (2000)'s axioms are based on the graph behind the problem, in this paper we do not consider graph specific axioms, we take TU axioms only, that is, we consider all shortest path problems and we take the view of an abstract decision maker who focuses rather on the abstract problem than on the concrete situations.

Suggested Citation

  • Miklos Pinter & Anna Radvanyi, 2012. "The Shapley value for shortest path games," KRTK-KTI WORKING PAPERS 1224, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1224
    as

    Download full text from publisher

    File URL: http://econ.core.hu/file/download/mtdp/MTDP1224.pdf
    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. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    3. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
    4. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, January.
    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. Youngsub Chun & Boram Park, 2012. "Population solidarity, population fair-ranking, and the egalitarian value," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 255-270, May.
    2. Miklós Pintér & Anna Radványi, 2013. "The Shapley value for shortest path games: a non-graph-based approach," 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. 21(4), pages 769-781, December.
    3. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    4. 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.
    5. René Brink & Youngsub Chun, 2012. "Balanced consistency and balanced cost reduction for sequencing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 519-529, March.
    6. Daniel Li & Erfang Shan, 2025. "Solidarity Value for Graph Games," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-13, August.
    7. Parishmita Boruah & Niharika Kakoty & Surajit Borkotokey, 2025. "The k-Egalitarian Myerson Values: Characterizations and Implementation," SN Operations Research Forum, Springer, vol. 6(1), pages 1-25, March.
    8. Dinko Dimitrov & Ching-jen Sun, 2025. "Blend-in fairness and equal split," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-21, December.
    9. J. C. Gonc{c}alves-Dosantos & R. Mart'inez & J. S'anchez-Soriano, 2026. "Null player neutrality in TU-games: Egalitarian and Shapley solutions," Papers 2605.20113, arXiv.org.
    10. Florian Navarro, 2025. "Cooperative games with types, outside options, and the egalitarian value," Post-Print hal-04324424, HAL.
    11. Koji Yokote & Takumi Kongo & Yukihiko Funaki, 2021. "Correction to: Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values," Theory and Decision, Springer, vol. 91(1), pages 99-99, July.
    12. Moulin, Herve, 2001. "Normative Microeconomics and the Social Contract," Working Papers 2001-04, Rice University, Department of Economics.
    13. Li, Daniel Li & Shan, Erfang, 2023. "Tree solutions and standardness for cycle-free graph games," Economics Letters, Elsevier, vol. 222(C).
    14. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    15. Tongseok Lim, 2022. "Cooperative networks and Hodge-Shapley value," Papers 2203.06860, arXiv.org, revised Aug 2024.
    16. Béal, Sylvain & Moyouwou, Issofa & Rémila, Eric & Solal, Philippe, 2020. "Cooperative games on intersection closed systems and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 15-22.
    17. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Fairness and fairness for neighbors: The difference between the Myerson value and component-wise egalitarian solutions," Economics Letters, Elsevier, vol. 117(1), pages 263-267.
    18. Navarro, Florian, 2025. "Cooperative games with types, outside options, and the egalitarian value," Mathematical Social Sciences, Elsevier, vol. 134(C), pages 42-49.
    19. Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
    20. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.

    More about this item

    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:has:discpr:1224. 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: Nora Horvath The email address of this maintainer does not seem to be valid anymore. Please ask Nora Horvath to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/iehashu.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.