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The Role of Constraints in a Segregation Model: The Asymmetric Case

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  • Davide Radi
  • Laura Gardini
  • Viktor Avrutin

Abstract

We extend the analysis on the effects of the entry constraints on the dynamics of an adaptive segregation model of Shelling’s type when the two populations involved differ in numerosity, level of tolerance toward members of the other population, and speed of reaction. The model is described by a two-dimensional piecewise smooth dynamical system in discrete time, where the entry constraints represent possible exogenous controls imposed by an authority in order to regulate the maximum number of members of the two populations allowed to enter the system, usually the district in which they live in. In this paper, we investigate the nature of some particular border collision bifurcations and discuss the policy implications of the entry constraints in terms of segregation. The investigation reveals that asymmetries in the level of tolerance of the two populations involved may lead to phenomena of overreaction or overshooting in the adjustment process. In order to avoid the risk of segregation, suitable entry limitations must be imposed at least on the more tolerant population.

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  • Davide Radi & Laura Gardini & Viktor Avrutin, 2014. "The Role of Constraints in a Segregation Model: The Asymmetric Case," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-17, August.
    • Handle: RePEc:hin:jnddns:569296
    DOI: 10.1155/2014/569296
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    1. Sushko, Iryna & Agliari, Anna & Gardini, Laura, 2006. "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 756-770.
    2. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2010. "On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 187-205, June.
    3. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
    4. 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.
    5. Fabio Tramontana & Laura Gardini & Frank Westerhoff, 2011. "Heterogeneous Speculators and Asset Price Dynamics: Further Results from a One-Dimensional Discontinuous Piecewise-Linear Map," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 329-347, October.
    6. W. Clark, 1991. "Residential preferences and neighborhood racial segregation: A test of the schelling segregation model," Demography, Springer;Population Association of America (PAA), vol. 28(1), pages 1-19, February.
    7. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2014. "Superstable credit cycles and U-sequence," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 13-27.
    8. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
    9. Joshua M. Epstein & Robert L. Axtell, 1996. "Growing Artificial Societies: Social Science from the Bottom Up," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262550253, April.
    10. Cars Hommes & Helena Nusse, 1991. "“Period three to period two” bifurcation for piecewise linear models," Journal of Economics, Springer, vol. 54(2), pages 157-169, June.
    11. Futter, Ben & Avrutin, Viktor & Schanz, Michael, 2012. "The discontinuous flat top tent map and the nested period incrementing bifurcation structure," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 465-482.
    12. Brianzoni, Serena & Michetti, Elisabetta & Sushko, Iryna, 2010. "Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 52-61.
    13. Dal Forno, Arianna & Gardini, Laura & Merlone, Ugo, 2012. "Ternary choices in repeated games and border collision bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 294-305.
    14. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
    15. Gian Italo Bischi & Laura Gardini & Ugo Merlone, 2009. "Impulsivity in Binary Choices and the Emergence of Periodicity," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-22, August.
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    6. Gardini, Laura & Tikjha, Wirot, 2020. "Dynamics in the transition case invertible/non-invertible in a 2D Piecewise Linear Map," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. Radi, Davide & Gardini, Laura, 2015. "Entry limitations and heterogeneous tolerances in a Schelling-like segregation model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 130-144.
    8. Sameh Askar, 2021. "Complex Investigations of a Piecewise-Smooth Remanufacturing Bertrand Duopoly Game," Mathematics, MDPI, vol. 9(20), pages 1-13, October.

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