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A study of the dynamic of influence through differential equations

Author

Listed:
  • Emmanuel Maruani

    () (Nomura International - Nomura International)

  • Michel Grabisch

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)

  • Agnieszka Rusinowska

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université 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.

Suggested Citation

  • 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.
  • Handle: RePEc:hal:cesptp:halshs-00587820
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00587820
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    References listed on IDEAS

    as
    1. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    2. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    3. 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.
    4. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 177-209, August.
    5. 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.
    6. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, Oxford University Press, vol. 118(3), pages 909-968.
    7. repec:hal:journl:halshs-00445126 is not listed on IDEAS
    8. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    differential equations; social network; inclination; decision; influence function; réseau social; fonction d'influence; équation différentielle;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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