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A piecewise smooth model of evolutionary game for residential mobility and segregation


  • Laura Gardini

    () (Department of Economics, Society & Politics, Universit? di Urbino "Carlo Bo")

  • Davide Radi

    () (Department of Economics and Management, University of Pisa)


The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents bene?t from integration. Despite the di?erences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilib- rium while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dy- namic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several di?erent kinds of bifurcations, smooth and border collision, in a complicated interplay. A social planner that aims to maximize integration can use our global analysis of the dynamics of the model to understand the possible achievements of social policies that manipulate people?s preferences for integration. Length: 24 pages

Suggested Citation

  • Laura Gardini & Davide Radi, 2018. "A piecewise smooth model of evolutionary game for residential mobility and segregation," Working Papers 1802, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2018.
  • Handle: RePEc:urb:wpaper:18_02

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    References listed on IDEAS

    1. Pancs, Romans & Vriend, Nicolaas J., 2007. "Schelling's spatial proximity model of segregation revisited," Journal of Public Economics, Elsevier, vol. 91(1-2), pages 1-24, February.
    2. Giorgio Fagiolo & Marco Valente & Nicolaas J. Vriend, 2007. "Dynamic Models of Segregation in Small-World Networks," Working Papers 589, Queen Mary University of London, School of Economics and Finance.
    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. Radi, Davide & Gardini, Laura & Avrutin, Viktor, 2014. "The role of constraints in a segregation model: The symmetric case," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 103-119.
    5. Fagiolo, Giorgio & Valente, Marco & Vriend, Nicolaas J., 2007. "Segregation in networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 316-336.
    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. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
    8. John Logan & Brian Stults & Reynolds Farley, 2004. "Segregation of minorities in the metropolis: two decades of change," Demography, Springer;Population Association of America (PAA), vol. 41(1), pages 1-22, February.
    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, September.
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    Cited by:

    1. 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).
    2. Brianzoni, Serena & Coppier, Raffaella & Michetti, Elisabetta, 2019. "Evolutionary effects of non-compliant behavior in public procurement," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 106-118.

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