Measuring influence in command games

Michel Grabisch and Agnieszka Rusinowska

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Abstract: In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. For some influence functions we define the command games such that the influence functions are compatible with these games. We show that not for all influence functions such command games exist. Moreover, we propose a more general definition of the influence index and show that some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. We show exact relations between an influence function and a follower function, between a command game and commandable players, and between influence functions and command games. An example of the Confucian model of society is broadly examined.

Keywords: Banzhaf index; Coleman indices; command game; follower of a coalition; influence function; influence indices; Shapley-Shubik index (search for similar items in EconPapers)
Date: 2008
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00269084v1
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Published in 2008

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Related works:
Journal Article: Measuring influence in command games (2009)
Working Paper: Measuring influence in command games (2009)
Working Paper: Measuring influence in command games (2009)
Working Paper: Measuring influence in command games (2008)
Working Paper: Measuring influence in command games (2008)
Working Paper: Measuring influence in command games (2008)
Working Paper: Measuring influence in command games (2008)
Working Paper: Measuring influence in command games (2008)
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