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Binary choices in small and large groups: A unified model

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  • Bischi, Gian-Italo
  • Merlone, Ugo

Abstract

Two different ways to model the diffusion of alternative choices within a population of individuals in the presence of social externalities are known in the literature. While Galam’s model of rumors spreading considers a majority rule for interactions in several groups, Schelling considers individuals interacting in one large group, with payoff functions that describe how collective choices influence individual preferences. We incorporate these two approaches into a unified general discrete-time dynamic model for studying individual interactions in variously sized groups. We first illustrate how the two original models can be obtained as particular cases of the more general model we propose, then we show how several other situations can be analyzed. The model we propose goes beyond a theoretical exercise as it allows modeling situations which are relevant in economic and social systems. We consider also other aspects such as the propensity to switch choices and the behavioral momentum, and show how they may affect the dynamics of the whole population.

Suggested Citation

  • Bischi, Gian-Italo & Merlone, Ugo, 2010. "Binary choices in small and large groups: A unified model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 843-853.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:4:p:843-853
    DOI: 10.1016/j.physa.2009.10.010
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    References listed on IDEAS

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    1. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    2. Zhao, Jijun & Szilagyi, Miklos N. & Szidarovszky, Ferenc, 2008. "An n-person battle of sexes game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3669-3677.
    3. Galam, Serge, 2003. "Modelling rumors: the no plane Pentagon French hoax case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 571-580.
    4. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    5. Zhao, Jijun & Szilagyi, Miklos N. & Szidarovszky, Ferenc, 2008. "n-person Battle of sexes games—a simulation study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3678-3688.
    6. Gerardine DeSanctis & R. Brent Gallupe, 1987. "A Foundation for the Study of Group Decision Support Systems," Management Science, INFORMS, vol. 33(5), pages 589-609, May.
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    Cited by:

    1. Gardini, Laura & Merlone, Ugo & Tramontana, Fabio, 2011. "Inertia in binary choices: Continuity breaking and big-bang bifurcation points," Journal of Economic Behavior & Organization, Elsevier, vol. 80(1), pages 153-167.
    2. Bischi, Gian Italo & Merlone, Ugo & Pruscini, Eros, 2018. "Evolutionary dynamics in club goods binary games," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 104-119.
    3. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2016. "A family of models for Schelling binary choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 276-296.
    4. Dal Forno, Arianna & Merlone, Ugo, 2013. "Border-collision bifurcations in a model of Braess paradox," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 1-18.
    5. Gian Italo Bischi & Ugo Merlone, 2017. "Evolutionary minority games with memory," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 859-875, November.
    6. Qian, Shen & Liu, Yijun & Galam, Serge, 2015. "Activeness as a key to counter democratic balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 187-196.
    7. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.

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