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A Biform Game Model with the Shapley Allocation Functions

Author

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  • 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
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