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Influence functions, followers and command games

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  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Agnieszka Rusinowska

    ()
    (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

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

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00355632.

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Date of creation: 2008
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Handle: RePEc:hal:cesptp:halshs-00355632

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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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References

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  1. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer, Springer, vol. 33(2), pages 177-209, August.
  2. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, Elsevier, vol. 51(1), pages 128-154, April.
  3. Jackson, Matthew O. & van den Nouweland, Anne, 2002. "Strongly Stable Networks," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1147, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. Dunia López-Pintado, 2004. "Diffusion In Complex Social Networks," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2004-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. DeMarzo, Peter M., 1992. "Coalitions, leadership, and social norms: The power of suggestion in games," Games and Economic Behavior, Elsevier, Elsevier, vol. 4(1), pages 72-100, January.
  6. Edward M. Bolger, 2000. "A consistent value for games with n players and r alternatives," International Journal of Game Theory, Springer, Springer, vol. 29(1), pages 93-99.
  7. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, Elsevier, vol. 66(1), pages 39-56, May.
  8. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(1), pages 181-221, October.
  9. Dan S. Felsenthal & Moshé Machover, 2002. "Models and Reality: the Curios Case of the Absent Abstention," Homo Oeconomicus, Institute of SocioEconomics, Institute of SocioEconomics, vol. 19, pages 297-310.
  10. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Hojman, Daniel A. & Szeidl, Adam, 2006. "Endogenous networks, social games, and evolution," Games and Economic Behavior, Elsevier, Elsevier, vol. 55(1), pages 112-130, April.
  12. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, Econometric Society, vol. 68(5), pages 1181-1230, September.
  13. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(1), pages 153-170, October.
  14. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00344457, HAL.
  15. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, Springer, vol. 26(3), pages 335-351.
  16. Laruelle, Annick & Valenciano, Federico, 2009. "Cooperative bargaining foundations of the Shapley-Shubik index," Games and Economic Behavior, Elsevier, Elsevier, vol. 65(1), pages 242-255, January.
  17. Bolger, Edward M, 1993. "A Value for Games with n Players and r Alternatives," International Journal of Game Theory, Springer, Springer, vol. 22(4), pages 319-34.
  18. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, Springer, vol. 15(3), pages 175-86.
  19. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, Elsevier, vol. 5(2), pages 240-256, April.
  20. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(1), pages 132-152, October.
  21. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer, Springer, vol. 28(4), pages 547-565.
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Citations

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Cited by:
  1. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, Open Access Journal, MDPI, Open Access Journal, vol. 2(1), pages 45-77, March.
  2. Tomas Rodriguez Barraquer, 2013. "From sets of equilibria to structures of interaction underlying binary games of strategic complements," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp655, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. 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), HAL halshs-00587820, HAL.
  4. Manuel Förster & Michel Grabisch & Agnieszka Rusinowsk, 2013. "Anonymous Social Influence," Working Papers, Fondazione Eni Enrico Mattei 2013.51, Fondazione Eni Enrico Mattei.
  5. Michel Grabisch & Agnieszka Rusinowska, 2011. "A model of influence based on aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00639677, HAL.
  6. Büchel, Berno & Hellmann, Tim & Klößner, Stefan, 2013. "Opinion Dynamics and Wisdom under Conformity," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order, Verein für Socialpolitik / German Economic Association 79770, Verein für Socialpolitik / German Economic Association.
  7. Agnieszka Rusinowska & Michel Grabisch, 2010. "A model of influence with an ordered set of possible actions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL hal-00519413, HAL.

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