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Iterating influence between players in a social network

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  • Michel Grabisch

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

  • Agnieszka Rusinowska

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

Abstract

We generalize a yes-no model of influence in a social network with a single step of mutual influence to a framework with iterated influence. Each agent makes an acceptance- rejection decision and has an inclination to say either ‘yes' or ‘no'. Due to influence by others, an agent's decision may be different from his original inclination. Such a transformation from the inclinations to the decisions is represented by an influence function. We analyze the decision process in which the mutual influence does not stop after one step but iterates. Any classical influence function can be coded by a stochastic matrix, and a generalization leads to stochastic influence functions. We apply Markov chains theory to the analysis of stochastic binary influence functions. We deliver a general analysis of the convergence of an influence function and then study the convergence of particular influence functions. This model is compared with the Asavathiratham model of influence. We also investigate models based on aggregation functions. In this context, we give a complete description of terminal classes, and show that the only terminal states are the consensus states if all players are weakly essential.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2010. "Iterating influence between players in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00543840, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00543840
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00543840
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    References listed on IDEAS

    as
    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Bogaçhan Çelen & Shachar Kariv, 2004. "Distinguishing Informational Cascades from Herd Behavior in the Laboratory," American Economic Review, American Economic Association, vol. 94(3), pages 484-498, June.
    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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    Cited by:

    1. repec:hal:journl:hal-00633859 is not listed on IDEAS
    2. Agnieszka Rusinowska & Rudolf Berghammer & Harrie De Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.

    More about this item

    Keywords

    Markov chains; aggregation functions.; convergence; terminal class; stochastic influence function; aggregation functions; Social network; influence; agrégation.; chaine de Markov; Réseau social;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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