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Influence functions, followers and command games

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  • Grabisch, Michel
  • Rusinowska, Agnieszka

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Influence function Follower function Lower and upper inverses Kernel Command game Command function Minimal sets generating a command game;

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References

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  1. DeMarzo, Peter M., 1992. "Coalitions, leadership, and social norms: The power of suggestion in games," Games and Economic Behavior, Elsevier, vol. 4(1), pages 72-100, January.
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  7. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer, vol. 33(2), pages 177-209, August.
  9. Matthew O. Jackson, 2001. "Strongly Stable Networks," University of Oregon Economics Department Working Papers 2001-3, University of Oregon Economics Department, revised 15 Nov 2002.
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  13. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
  14. Hojman, Daniel A. & Szeidl, Adam, 2006. "Endogenous networks, social games, and evolution," Games and Economic Behavior, Elsevier, vol. 55(1), pages 112-130, April.
  15. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
  16. 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.
  17. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
  18. 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.
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Citations

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Cited by:
  1. Manuel Foerster & Michel Grabisch & Agnieszka Rusinowska, 2013. "Anonymous social influence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00913235, HAL.
  2. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, Open Access Journal, vol. 2(1), pages 45-77, March.
  3. Michel Grabisch & Agnieszka Rusinowska, 2013. "A Model of Influence Based on Aggregation Function," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00906367, HAL.
  4. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
  5. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2011. "A study of the dynamic of influence through differential equations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00587820, HAL.
  6. Tomas Rodriguez Barraquer, 2013. "From sets of equilibria to structures of interaction underlying binary games of strategic complements," Discussion Paper Series dp655, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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