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Influence functions, followers and command games

  • Grabisch, Michel
  • Rusinowska, Agnieszka

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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 72 (2011)
Issue (Month): 1 (May)
Pages: 123-138

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Handle: RePEc:eee:gamebe:v:72:y:2011:i:1:p:123-138
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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