Influence functions, followers and command games

Michel Grabisch and Agnieszka Rusinowska

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We study and compare two frameworks : a model of influence, and command games. In the influence model, in which players are to make a certain acceptance/rejection decision, due to influence of other players, the decision of a player may be different from his inclination. We study a relation between two central concepts of this model : influence function, and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function, and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered.

Keywords: Influence function; follower function; lower and upper inverses; kernel; command game; command function; minimal sets generating a command game.; minimal sets generating a command game; Fonction d'influence; fonction disciple; noyau; jeu de commande; fonction de commande. (search for similar items in EconPapers)
Date: 2008-11
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00344823v1
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Citations: View citations in EconPapers (2)

Published in 2008

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Related works:
Journal Article: Influence functions, followers and command games (2011)
Working Paper: Influence functions, followers and command games (2011)
Working Paper: Influence functions, followers and command games (2011)
Working Paper: Influence functions, followers and command games (2008)
Working Paper: Influence functions, followers and command games (2008)
Working Paper: Influence functions, followers and command games (2008)
Working Paper: Influence functions, followers and command games (2008)
Working Paper: Influence functions, followers and command games (2008)
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