A Biform Game Model with the Shapley Allocation Functions

A Biform Game Model with the Shapley Allocation Functions

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...

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Bibliographic Details
Main Authors: Chenwei Liu, Shuwen Xiang, Yanlong Yang
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Mathematics
Subjects:
biform games
Shapley allocation function
mixed strategy
Nash equilibrium
properties
Online Access:https://www.mdpi.com/2227-7390/9/16/1872
Description
Summary: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.
ISSN:2227-7390

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