A Biform Game Model with the Shapley Allocation Functions

Chenwei Liu, Shuwen Xiang and Yanlong Yang
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Chenwei Liu: School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China
Shuwen Xiang: School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China
Yanlong Yang: School of Mathematics and Statistics, Guizhou University, Huaxidadao, Guiyang 550025, China

Mathematics, 2021, vol. 9, issue 16, 1-14

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.

Keywords: biform games; Shapley allocation function; mixed strategy; Nash equilibrium; properties (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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