IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v176y2019icp75-78.html
   My bibliography  Save this article

Relaxations of symmetry and the weighted Shapley values

Author

Listed:
  • Casajus, André

Abstract

We revisit Kalai and Samet’s (1987) first characterization of the class of weighted Shapley values. While keeping efficiency, additivity, and the null player property from the original characterization of the symmetric Shapley value, they replace symmetry with positivity and partnership consistency. The latter two properties, however, are neither implied by nor related to symmetry. We suggest relaxations of symmetry that together with efficiency, additivity, and the null player property characterize classes of weighted Shapley values. For example, weak sign symmetry requires the payoffs of mutually dependent players to have the same sign. Mutually dependent players are symmetric players whose marginal contributions to coalitions containing neither of them are zero.

Suggested Citation

  • Casajus, André, 2019. "Relaxations of symmetry and the weighted Shapley values," Economics Letters, Elsevier, vol. 176(C), pages 75-78.
    • Handle: RePEc:eee:ecolet:v:176:y:2019:i:c:p:75-78
    DOI: 10.1016/j.econlet.2018.12.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016517651830524X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2018.12.031?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. Casajus, André, 2018. "Sign symmetry vs symmetry: Young’s characterization of the Shapley value revisited," Economics Letters, Elsevier, vol. 169(C), pages 59-62.
    2. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    4. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    5. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 1-9.
    6. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    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. Besner, Manfred, 2019. "Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set," MPRA Paper 92771, University Library of Munich, Germany.
    2. Casajus, André, 2021. "Weakly balanced contributions and the weighted Shapley values," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    3. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Post-Print hal-03252179, HAL.
    4. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    5. Sokolov, Denis, 2022. "Shapley value for TU-games with multiple memberships and externalities," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 76-90.
    6. Kongo, Takumi, 2019. "Players’ nullification and the weighted (surplus) division values," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    7. Sylvain Béal & Sylvain Ferrières & Adriana Navarro‐Ramos & Philippe Solal, 2023. "Axiomatic characterizations of the family of Weighted priority values," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 787-816, December.
    8. Li, Wenzhong & Xu, Genjiu & van den Brink, René, 2024. "Sign properties and axiomatizations of the weighted division values," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    9. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.

    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. Li, Wenzhong & Xu, Genjiu & van den Brink, René, 2024. "Sign properties and axiomatizations of the weighted division values," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    2. Casajus, André, 2021. "Weakly balanced contributions and the weighted Shapley values," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    3. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    4. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    5. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    6. Manfred Besner, 2020. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 851-873, September.
    7. Sylvain Béal & Sylvain Ferrières & Adriana Navarro‐Ramos & Philippe Solal, 2023. "Axiomatic characterizations of the family of Weighted priority values," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 787-816, December.
    8. Takaaki Abe & Satoshi Nakada, 2019. "The weighted-egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 197-213, February.
    9. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, University Library of Munich, Germany.
    10. Estela Sánchez-Rodríguez & Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Iago Núñez Lugilde, 2024. "Coalition-weighted Shapley values," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 547-577, June.
    11. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    12. Koji Yokote, 2015. "Weak addition invariance and axiomatization of the weighted Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 275-293, May.
    13. Yokote, Koji & Kongo, Takumi & Funaki, Yukihiko, 2018. "The balanced contributions property for equal contributors," Games and Economic Behavior, Elsevier, vol. 108(C), pages 113-124.
    14. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    15. Kranich, Laurence, 1997. "Cooperative Games with Hedonic Coalitions," Games and Economic Behavior, Elsevier, vol. 18(1), pages 83-97, January.
    16. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    17. Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.
    18. Takaaki Abe & Satoshi Nakada, 2023. "Core stability of the Shapley value for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 523-543, May.
    19. Besner, Manfred, 2017. "Axiomatizations of the proportional Shapley value," MPRA Paper 82990, University Library of Munich, Germany.
    20. Federico Valenciano & Annick Laruelle, 2003. "Potential, Value And Probability," Working Papers. Serie AD 2003-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

    More about this item

    Keywords

    TU game; Weighted Shapley values; Sign symmetry; Mutual dependence; Weak sign symmetry; Superweak sign symmetry;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

    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:eee:ecolet:v:176:y:2019:i:c:p:75-78. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.