IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2308.03489.html
   My bibliography  Save this paper

The Expected Shapley value on a class of probabilistic games

Author

Listed:
  • Surajit Borkotokey
  • Sujata Gowala
  • Rajnish Kumar

Abstract

We study a class of probabilistic cooperative games which can be treated as an extension of the classical cooperative games with transferable utilities. The coalitions have an exogenous probability of being realized. This probability distribution is known beforehand and the distribution of the expected worth needs to be done before the realization of the state. We obtain a value for this class of games and present three characterizations of this value using natural extensions of the axioms used in the seminal axiomatization of the Shapley value. The value, which we call the Expected Shapley value, allocates the players their expected worth with respect to a probability distribution.

Suggested Citation

  • Surajit Borkotokey & Sujata Gowala & Rajnish Kumar, 2023. "The Expected Shapley value on a class of probabilistic games," Papers 2308.03489, arXiv.org.
    • Handle: RePEc:arx:papers:2308.03489
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2308.03489
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. Borkotokey, Surajit & Chakrabarti, Subhadip & Gilles, Robert P. & Gogoi, Loyimee & Kumar, Rajnish, 2021. "Probabilistic network values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 169-180.
    5. Annick Laruelle & Federico Valenciano, 2008. "Potential, value, and coalition formation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 73-89, July.
    6. Gómez, D. & González-Arangüena, E. & Manuel, C. & Owen, G., 2008. "A value for generalized probabilistic communication situations," European Journal of Operational Research, Elsevier, vol. 190(2), pages 539-556, October.
    7. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    8. Kamionko, V. & Marakulin, V., 2020. "Shapley's value and its axiomatization in games with prior probabilities of coalition formation," Journal of the New Economic Association, New Economic Association, vol. 46(2), pages 12-29.
    9. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    11. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    12. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    13. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, 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. Borkotokey, Surajit & Chakrabarti, Subhadip & Gilles, Robert P. & Gogoi, Loyimee & Kumar, Rajnish, 2021. "Probabilistic network values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 169-180.
    2. Subhadip Chakrabarti & Loyimee Gogoi & Robert P. Gilles & Surajit Borkotokey & Rajnish Kumar, 2024. "Expected values for variable network games," Annals of Operations Research, Springer, vol. 336(3), pages 2061-2089, May.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    4. González–Arangüena, E. & Manuel, C. & Owen, G. & del Pozo, M., 2017. "The within groups and the between groups Myerson values," European Journal of Operational Research, Elsevier, vol. 257(2), pages 586-600.
    5. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    6. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    7. 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.
    8. Jilei Shi & Erfang Shan, 2021. "The Banzhaf value for generalized probabilistic communication situations," Annals of Operations Research, Springer, vol. 301(1), pages 225-244, June.
    9. Jilei Shi & Lei Cai & Erfang Shan & Wenrong Lyu, 2022. "A value for cooperative games with coalition and probabilistic graph structures," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 646-671, 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. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    12. C. Manuel & E. González-Arangüena & R. Brink, 2013. "Players indifferent to cooperate and characterizations of the Shapley value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 1-14, February.
    13. 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.
    14. 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.
    15. Subhadip Chakrabarti & Robert Gilles, 2007. "Network potentials," Review of Economic Design, Springer;Society for Economic Design, vol. 11(1), pages 13-52, June.
    16. Calvo, Emilio & Santos, Juan Carlos, 1997. "Potentials in cooperative TU-games," Mathematical Social Sciences, Elsevier, vol. 34(2), pages 175-190, October.
    17. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, January.
    18. Julia Belau, 2018. "The class of ASN-position values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 65-99, January.
    19. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2024. "Weighted Myerson value for Network games," Papers 2402.11464, arXiv.org.
    20. Zijun Li & Fanyong Meng, 2023. "The α-Egalitarian Myerson value of games with communication structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 311-338, June.

    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:2308.03489. 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.