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Influence functions, followers and command games

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Author Info
Michel Grabisch () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
Agnieszka Rusinowska () (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

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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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00344823_v1.

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Date of creation: Nov 2008
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Handle: RePEc:hal:cesptp:halshs-00344823_v1

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Related research
Keywords: Influence function; follower function; lower and upper inverses; kernel; command game; command function; minimal sets generating a command game.;

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  1. Edward M. Bolger, 2000. "A consistent value for games with n players and r alternatives," International Journal of Game Theory, Springer, vol. 29(1), pages 93-99. [Downloadable!] (restricted)
  2. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
  3. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
  4. Bolger, Edward M, 1993. "A Value for Games with n Players and r Alternatives," International Journal of Game Theory, Springer, vol. 22(4), pages 319-34.
  5. Dan S. Felsenthal & Moshé Machover, 2002. "Models and Reality: the Curios Case of the Absent Abstention," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 297-310.
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