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A study of the dynamic of influence through differential equations

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  • Emmanuel Maruani

    () (Nomura International - Nomura International)

  • Michel Grabisch

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

  • Agnieszka Rusinowska

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

Abstract

The paper concerns a model of influence in which agents make their decisions on a certain issue. It is assumed that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. The use of continuous variable permits the application of differential equations systems to the analysis of the convergence of agents' decisions in long-time. In particular, by applying the approach based on differential equations of the influence model, we recover the results of the discrete model on classical influence functions and the results on the boss and approval sets for the command games equivalent to some influence functions.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00587820.

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Date of creation: Apr 2011
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Handle: RePEc:hal:cesptp:halshs-00587820

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Keywords: Social network; inclination; decision; influence function; differential equations.;

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  1. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer, vol. 33(2), pages 177-209, August.
  2. 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.
  3. 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.
  4. 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.
  5. DeMarzo, Peter M. & Vayanos, Dimitri & Zwiebel, Jeffrey, 2003. "Persuasion bias, social influence, and uni-dimensional opinions," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
  6. Michel Grabisch & Agnieszka Rusinowska, 2010. "Different Approaches to Influence Based on Social Networks and Simple Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00514850, HAL.
  7. Lorenz, Jan, 2005. "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 217-223.
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