IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1872-d609680.html
   My bibliography  Save this article

A Biform Game Model with the Shapley Allocation Functions

Author

Listed:
  • Chenwei Liu

    (School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China
    These authors contributed equally to this work.)

  • Shuwen Xiang

    (School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China
    These authors contributed equally to this work.)

  • Yanlong Yang

    (School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China)

Abstract

We define the mixed strategy form of the characteristic function of the biform games and build the Shapley allocation function (SAF) on each mixed strategy profile in the second stage of the biform games. SAF provides a more detailed and accurate picture of the fairness of the strategic contribution and reflects the degree of the players’ further choices of strategies. SAF can guarantee the existence of Nash equilibrium in the first stage of the non-cooperative games. The existence and uniqueness of SAF on each mixed strategy profile overcome the defect that the core may be an empty set and provide a fair allocation method when the core element is not unique. Moreover, SAF can be used as an important reference or substitute for the core with the confidence index.

Suggested Citation

  • Chenwei Liu & Shuwen Xiang & Yanlong Yang, 2021. "A Biform Game Model with the Shapley Allocation Functions," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1872-:d:609680
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1872/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1872/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hart, Oliver & Moore, John, 1990. "Property Rights and the Nature of the Firm," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1119-1158, December.
    2. Erica L. Plambeck & Terry A. Taylor, 2005. "Sell the Plant? The Impact of Contract Manufacturing on Innovation, Capacity, and Profitability," Management Science, INFORMS, vol. 51(1), pages 133-150, January.
    3. Grossman, Sanford J & Hart, Oliver D, 1986. "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 691-719, August.
    4. Feess, Eberhard & Thun, Jörn-Henrik, 2014. "Surplus division and investment incentives in supply chains: A biform-game analysis," European Journal of Operational Research, Elsevier, vol. 234(3), pages 763-773.
    5. Summerfield, Nichalin S. & Dror, Moshe, 2013. "Biform game: Reflection as a stochastic programming problem," International Journal of Production Economics, Elsevier, vol. 142(1), pages 124-129.
    6. Fuentes González, Fabián & van der Weijde, Adriaan Hendrik & Sauma, Enzo, 2020. "The promotion of community energy projects in Chile and Scotland: An economic approach using biform games," Energy Economics, Elsevier, vol. 86(C).
    7. Harborne W. Stuart, Jr., 2005. "Biform Analysis of Inventory Competition," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 347-359, July.
    8. Günter Fandel & Jan Trockel, 2016. "Investment and lot size planning in a supply chain: coordinating a just-in-time-delivery with a Harris- or a Wagner/Whitin-solution," Journal of Business Economics, Springer, vol. 86(1), pages 173-195, January.
    9. Petr Fiala, 2016. "Profit allocation games in supply chains," 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. 24(2), pages 267-281, June.
    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. Fuentes González, Fabián & van der Weijde, Adriaan Hendrik & Sauma, Enzo, 2020. "The promotion of community energy projects in Chile and Scotland: An economic approach using biform games," Energy Economics, Elsevier, vol. 86(C).
    2. Zheng, Xiao-Xue & Li, Deng-Feng, 2023. "A new biform game-based investment incentive mechanism for eco-efficient innovation in supply chain," International Journal of Production Economics, Elsevier, vol. 258(C).
    3. Zheng, Xiao-Xue & Zhang, Shiyuan & Jia, Fu & Lin, Xiao, 2024. "A new biform game-based coordination mechanism for a carbon complementary supply chain under hybrid carbon regulations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 187(C).
    4. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2021. "Cooperation and Competition in Linear Production and Sequencing Processes," Discussion Paper 2021-011, Tilburg University, Center for Economic Research.
    5. Kabiraj, Tarun & Sinha, Uday Bhanu, 2016. "Strategic outsourcing with technology transfer under price competition," International Review of Economics & Finance, Elsevier, vol. 44(C), pages 281-290.
    6. Jia, Fu & Zhang, Shiyuan & Zheng, Xiao-Xue & Choi, Tsan-Ming, 2023. "A novel coordination mechanism to coordinate the multi-agent reverse supply chain with fairness concerns," International Journal of Production Economics, Elsevier, vol. 265(C).
    7. S. Katie Moon & Gordon M. Phillips, 2021. "Outsourcing Through Purchase Contracts and Firm Capital Structure," Management Science, INFORMS, vol. 67(1), pages 363-387, January.
    8. Günter Fandel & Jan Trockel, 2016. "Investment and lot size planning in a supply chain: coordinating a just-in-time-delivery with a Harris- or a Wagner/Whitin-solution," Journal of Business Economics, Springer, vol. 86(1), pages 173-195, January.
    9. Heather Berry & Aseem Kaul, 2015. "Global Sourcing and Foreign Knowledge Seeking," Management Science, INFORMS, vol. 61(5), pages 1052-1071, May.
    10. S. Katie Moon & Gordon M. Phillips, 2014. "Outside Purchase Contracts, Human Capital and Firm Capital Structure," NBER Working Papers 20579, National Bureau of Economic Research, Inc.
    11. Fuentes González, Fabián & Sauma, Enzo & van der Weijde, Adriaan Hendrik, 2022. "Community energy projects in the context of generation and transmission expansion planning," Energy Economics, Elsevier, vol. 108(C).
    12. Guillaume Roels & Christopher S. Tang, 2017. "Win-Win Capacity Allocation Contracts in Coproduction and Codistribution Alliances," Management Science, INFORMS, vol. 63(3), pages 861-881, March.
    13. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2023. "Competition and cooperation in linear production and sequencing processes," Games and Economic Behavior, Elsevier, vol. 139(C), pages 117-132.
    14. Schwarz Mordechai E., 2012. "Subgame Perfect Plea Bargaining in Biform Judicial Contests," Review of Law & Economics, De Gruyter, vol. 8(1), pages 297-330, September.
    15. Kaplow, Louis & Shapiro, Carl, 2007. "Antitrust," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 2, chapter 15, pages 1073-1225, Elsevier.
    16. Cécile Cézanne, 2012. "Berle and Means," Chapters, in: Michael Dietrich & Jackie Krafft (ed.), Handbook on the Economics and Theory of the Firm, chapter 7, Edward Elgar Publishing.
    17. Scott Gehlbach & Konstantin Sonin & Ekaterina Zhuravskaya, 2010. "Businessman Candidates," American Journal of Political Science, John Wiley & Sons, vol. 54(3), pages 718-736, July.
    18. Peter G. Klein & Michael E. Sykuta, 2010. "Editors’ Introduction," Chapters, in: Peter G. Klein & Michael E. Sykuta (ed.), The Elgar Companion to Transaction Cost Economics, chapter 1, Edward Elgar Publishing.
    19. Schmid, Andreas, 2007. "Incentive Compatibility and Efficiency in the contractual Insurer-Provider Relationship: Economic Theory and practical Implications: The Case of North Carolina," MPRA Paper 23311, University Library of Munich, Germany, revised 2008.
    20. Surajeet Chakravarty & W. Bentley MacLeod, 2006. "Construction Contracts (or “How to Get the Right Building at the Right Price?”)," CESifo Working Paper Series 1714, CESifo.

    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:gam:jmathe:v:9:y:2021:i:16:p:1872-:d:609680. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.