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.Download Info
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.Bibliographic Info
Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00583867.Length:
Date of creation: May 2011
Date of revision:
Publication status: Published, Games and Economic Behavior, 2011, 72, 1, 123-138
Handle: RePEc:hal:cesptp:halshs-00583867
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00583867
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Related research
Keywords: influence function; follower function; lower and upper inverses; kernel; command game; command function; minimal sets generating a command game;Other versions of this item:
- Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344823, HAL.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00355632, HAL.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Documents de travail du Centre d'Economie de la Sorbonne b08080, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Working Papers 0831, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D7 - Microeconomics - - Analysis of Collective Decision-Making
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-04-16 (All new papers)
- NEP-GTH-2011-04-16 (Game Theory)
- NEP-NET-2011-04-16 (Network Economics)
References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Michel Grabisch & Agnieszka Rusinowska, 2009.
"Measuring influence in command games,"
Social Choice and Welfare,
Springer, vol. 33(2), pages 177-209, August.
- Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445126, HAL.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence in command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00269084, HAL.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence in command games," Documents de travail du Centre d'Economie de la Sorbonne b08078, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence in command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344805, HAL.
- 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.
- Michel Grabisch & Agnieszka Rusinowska, 2008.
"A model of influence in a social network,"
Documents de travail du Centre d'Economie de la Sorbonne
b08066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
- Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308741, HAL.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344457, HAL.
- 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.
- Bloch, Francis & Dutta, Bhaskar, 2005.
"Communication Networks with Endogenous Link Strength,"
The Warwick Economics Research Paper Series (TWERPS)
723, University of Warwick, Department of Economics.
- Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
- Francis Bloch & Bhaskar Dutta, 2008. "Communication networks with endogeneous link strength," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 08-15, Indian Statistical Institute, New Delhi, India.
- 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.
- Matthew O. Jackson, 2003.
"Allocation Rules for Network Games,"
Working Papers
2003.51, Fondazione Eni Enrico Mattei.
- Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
- Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Working Papers 1160, California Institute of Technology, Division of the Humanities and Social Sciences.
- Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Game Theory and Information 0303010, EconWPA.
- Jackson, Matthew O. & van den Nouweland, Anne, 2002.
"Strongly Stable Networks,"
Working Papers
1147, California Institute of Technology, Division of the Humanities and Social Sciences.
- Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
- Matthew O. Jackson & Anne van den Nouweland, 2002. "Strongly Stable Networks," Microeconomics 0211006, EconWPA.
- 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.
- Jackson, Matthew O. & Wolinsky, Asher, 1996.
"A Strategic Model of Social and Economic Networks,"
Journal of Economic Theory,
Elsevier, vol. 71(1), pages 44-74, October.
- 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.
- Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
- Marc Roubens & Michel Grabisch, 1999.
"An axiomatic approach to the concept of interaction among players in cooperative games,"
International Journal of Game Theory,
Springer, vol. 28(4), pages 547-565.
- Grabisch, M. & Roubens, M., 1998. "An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games," Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie 9818, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie.
- Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
- Dunia López-Pintado, 2004.
"Diffusion In Complex Social Networks,"
Working Papers. Serie AD
2004-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
- Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
- Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
- 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.
- Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
- Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
- Hojman, Daniel A. & Szeidl, Adam, 2006. "Endogenous networks, social games, and evolution," Games and Economic Behavior, Elsevier, vol. 55(1), pages 112-130, April.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- 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.
- 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-00519413, HAL.
- Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2011.
"A study of the dynamic of influence through differential equations,"
Documents de travail du Centre d'Economie de la Sorbonne
11022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- 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.
- Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2012. "A study of the dynamic of influence through differential equations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00699012, HAL.
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00583867For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.

