IDEAS home Printed from https://ideas.repec.org/a/vrs/founma/v9y2017i1p257-272n18.html
   My bibliography  Save this article

Modification of Shapley Value and its Implementation in Decision Making

Author

Listed:
  • Zaremba Leszek

    (Academy of Finance and Business Vistula, Institute of Management, Warszawa, Poland)

  • Zaremba Cezary S.

    (Peaceful Games Cezary Zaremba, Warszawa, Poland)

  • Suchenek Marek

    (California State Univ. Dominquez Hills, Computer Science Department, Carson, Calif. USA)

Abstract

The article presents a solution of a problem that is critical from a practical point of view: how to share a higher than usual discount of $10 million among 5 importers. The discount is a result of forming a coalition by 5 current, formerly competing, importers. The use of Shapley value as a concept for co-operative games yielded a solution that was satisfactory for 4 lesser importers and not satisfactory for the biggest importer. Appropriate modification of Shapley value presented in this article allowed to identify appropriate distribution of the saved purchase amount, which according to each player accurately reflects their actual strength and position on the importer market. A computer program was used in order to make appropriate calculations for 325 permutations of all possible coalitions. In the last chapter of this paper, we recognize the lasting contributions of Lloyd Shapley to the cooperative game theory, commemorating his recent (March 12, 2016) descent from this world.

Suggested Citation

  • Zaremba Leszek & Zaremba Cezary S. & Suchenek Marek, 2017. "Modification of Shapley Value and its Implementation in Decision Making," Foundations of Management, Sciendo, vol. 9(1), pages 257-272, October.
  • Handle: RePEc:vrs:founma:v:9:y:2017:i:1:p:257-272:n:18
    DOI: 10.1515/fman-2017-0020
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/fman-2017-0020
    Download Restriction: no

    File URL: https://libkey.io/10.1515/fman-2017-0020?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
    ---><---

    References listed on IDEAS

    as
    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Roth,Alvin E. (ed.), 2005. "The Shapley Value," Cambridge Books, Cambridge University Press, number 9780521021333, September.
    3. J. W. Milnor & L. S. Shapley, 1978. "Values of Large Games II: Oceanic Games," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 290-307, November.
    4. Casajus, André & Huettner, Frank, 2013. "Null players, solidarity, and the egalitarian Shapley values," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 58-61.
    5. Marcin Malawski, 2013. "“Procedural” values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 305-324, February.
    6. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    7. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
    8. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    9. Carreras, Francesc & Owen, Guillermo, 1988. "Evaluation of the Catalonian Parliament, 1980-1984," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 87-92, February.
    10. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    11. R J Johnston, 1978. "On the Measurement of Power: Some Reactions to Laver," Environment and Planning A, , vol. 10(8), pages 907-914, August.
    12. Bernard Steunenberg & Dieter Schmidtchen & Christian Koboldt, 1999. "Strategic Power in the European Union," Journal of Theoretical Politics, , vol. 11(3), pages 339-366, July.
    13. N. Z. Shapiro & L. S. Shapley, 1978. "Values of Large Games, I: A Limit Theorem," Mathematics of Operations Research, INFORMS, vol. 3(1), pages 1-9, February.
    14. Ursula F. Ott, 2006. "International Joint Ventures," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-62546-4, October.
    15. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    16. Monderer, Dov & Samet, Dov, 2002. "Variations on the shapley value," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 54, pages 2055-2076, Elsevier.
    17. Honorata Sosnowska, 2014. "Banzhaf value for games analyzing voting with rotation," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(4), pages 75-88.
    18. Jacek W. Mercik, 2000. "Index of Power for Cabinet," Homo Oeconomicus, Institute of SocioEconomics, vol. 17, pages 125-136.
    19. Mercik, Jacek W. & Kolodziejczyk, Waldemar, 1986. "Taxonomy approach to a cabinet formation problem," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 159-167, October.
    20. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    21. 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.
    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. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, September.
    2. Sascha Kurz, 2016. "The inverse problem for power distributions in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 65-88, June.
    3. Borkowski, Agnieszka, 2003. "Machtverteilung Im Ministerrat Nach Dem Vertrag Von Nizza Und Den Konventsvorschlagen In Einer Erweiterten Europaischen Union," IAMO Discussion Papers 14887, Institute of Agricultural Development in Transition Economies (IAMO).
    4. Julien Reynaud & Fabien Lange & Łukasz Gątarek & Christian Thimann, 2011. "Proximity in Coalition Building," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 3(3), pages 111-132, September.
    5. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    6. Abraham Neyman & Rann Smorodinsky, 2004. "Asymptotic Values of Vector Measure Games," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 739-775, November.
    7. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "Axiomatization and implementation of a class of solidarity values for TU-games," Theory and Decision, Springer, vol. 83(1), pages 61-94, June.
    8. Barış Çiftçi & Peter Borm & Herbert Hamers, 2010. "Population monotonic path schemes for simple games," Theory and Decision, Springer, vol. 69(2), pages 205-218, August.
    9. Neyman, Abraham, 2010. "Singular games in bv'NA," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 384-387, July.
    10. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
    11. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "A Class of Solidarity Allocation Rules for TU-games," Working Papers 2015-03, CRESE.
    12. Chameni Nembua, C. & Miamo Wendji, C., 2016. "Ordinal equivalence of values, Pigou–Dalton transfers and inequality in TU-games," Games and Economic Behavior, Elsevier, vol. 99(C), pages 117-133.
    13. Koji Yokote & Takumi Kongo & Yukihiko Funaki, 2021. "Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values," Theory and Decision, Springer, vol. 91(1), pages 81-98, July.
    14. Michela Chessa & Vito Fragnelli, 2014. "The bargaining set for sharing the power," Annals of Operations Research, Springer, vol. 215(1), pages 49-61, April.
    15. Ciftci, B.B. & Dimitrov, D.A., 2006. "Stable Coalition Structures in Simple Games with Veto Control," Other publications TiSEM fd2410e3-8e9d-4319-86fb-b, Tilburg University, School of Economics and Management.
    16. Kim, Chulyoung & Kim, Sang-Hyun & Lee, Jinhyuk & Lee, Joosung, 2022. "Strategic alliances in a veto game: An experimental study," European Journal of Political Economy, Elsevier, vol. 75(C).
    17. Stefano Benati & Giuseppe Vittucci Marzetti, 2013. "Probabilistic spatial power indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 391-410, February.
    18. Borkowski, Agnieszka, 2003. "Machtverteilung im Ministerrat: nach dem Vertrag von Nizza und den Konventsvorschlägen in einer erweiterten Europäischen Union," IAMO Discussion Papers 54, Leibniz Institute of Agricultural Development in Transition Economies (IAMO).
    19. Badinger, Harald & Mühlböck, Monika & Nindl, Elisabeth & Reuter, Wolf Heinrich, 2014. "Theoretical vs. empirical power indices: Do preferences matter?," European Journal of Political Economy, Elsevier, vol. 36(C), pages 158-176.
    20. Borkotokey, Surajit & Choudhury, Dhrubajit & Gogoi, Loyimee & Kumar, Rajnish, 2020. "Group contributions in TU-games: A class of k-lateral Shapley values," European Journal of Operational Research, Elsevier, vol. 286(2), pages 637-648.

    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:vrs:founma:v:9:y:2017:i:1:p:257-272:n:18. 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: Peter Golla (email available below). General contact details of provider: https://www.sciendo.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.