Influence functions, followers and command games

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.
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Games and Economic Behavior, Elsevier, 2011, 72 (1), pp.123-138. 〈10.1016/j.geb.2010.06.003〉
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Michel Grabisch, Agnieszka Rusinowska. Influence functions, followers and command games. Games and Economic Behavior, Elsevier, 2011, 72 (1), pp.123-138. 〈10.1016/j.geb.2010.06.003〉. 〈halshs-00583867〉

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