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A family of models for Schelling binary choices

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  • Cavalli, Fausto
  • Naimzada, Ahmad
  • Pireddu, Marina

Abstract

We introduce and study a family of discrete-time dynamical systems to model binary choices based on the framework proposed by Schelling in 1973. The model we propose uses a gradient-like adjustment mechanism by means of a family of smooth maps and allows understanding and analytically studying the phenomena qualitatively described by Schelling. In particular, we investigate existence of steady states and their relation to the equilibria of the static model studied by Schelling, and we analyze local stability, linking several examples and considerations provided by Schelling with bifurcation theory. We provide examples to confirm the theoretical results and to numerically investigate the possible destabilizations, as well as the emergence of coexisting attractors. We show the existence of chaos for a particular example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:276-296
    DOI: 10.1016/j.physa.2015.10.038
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    1. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    2. 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.
    3. Norman Braun, 1995. "Individual Thresholds and Social Diffusion," Rationality and Society, , vol. 7(2), pages 167-182, April.
    4. Runge, Carlisle Ford, 1986. "Common property and collective action in economic development," World Development, Elsevier, vol. 14(5), pages 623-635, May.
    5. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August.
    6. Ostasiewicz, K. & Tyc, M.H. & Radosz, A. & Magnuszewski, P. & Goliczewski, P. & Hetman, P. & Sendzimir, J., 2008. "Multistability of impact, utility and threshold concepts of binary choice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(25), pages 6337-6352.
    7. Andvig, Jens Chr. & Moene, Karl Ove, 1990. "How corruption may corrupt," Journal of Economic Behavior & Organization, Elsevier, vol. 13(1), pages 63-76, January.
    8. 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.
    9. Duncan J. Watts & Peter Sheridan Dodds, 2007. "Influentials, Networks, and Public Opinion Formation," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 34(4), pages 441-458, May.
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    Cited by:

    1. Arianna Dal Forno & Ugo Merlone, 2019. "Heterogeneous Society in Binary Choices with Externalities," Dynamic Games and Applications, Springer, vol. 9(2), pages 433-457, June.

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