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Dynamic models of residential segregation: An analytical solution

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  • Grauwin, Sébastian
  • Goffette-Nagot, Florence
  • Jensen, Pablo

Abstract

We propose an analytical solution to a Schelling segregation model for a relatively broad range of utility functions. Using evolutionary game theory, we provide existence conditions for a potential function, which characterizes the global configuration of the city and is maximized in the stationary state. We use this potential function to analyze the outcome of the model for three utility functions corresponding to different degrees of preference for mixed neighborhoods: (i) we show that linear utility functions is the only case where the potential function is proportional to collective utility, the latter being therefore maximized in stationary configurations; (ii) Schelling's original utility function is shown to drive segregation at the expense of collective utility; (iii) if agents have a strict preference for mixed neighborhoods but also prefer to be in the majority versus the minority, the model converges to perfectly segregated configurations, which clearly diverge from the social optimum. Departing from the existing literature, these conclusions are based on analytical results which open the way to analysis of many preference structures. Since our model is based on bounded rather than continuous neighborhoods as in Schelling's original model, we discuss the differences generated by the bounded- and continuous-neighborhood definitions and show that, in the case of the continuous neighborhood, a potential function exists if and only if the utility functions are linear. A side result is that our analysis builds a bridge between Schelling's model and the Duncan and Duncan segregation index.

Suggested Citation

  • Grauwin, Sébastian & Goffette-Nagot, Florence & Jensen, Pablo, 2012. "Dynamic models of residential segregation: An analytical solution," Journal of Public Economics, Elsevier, vol. 96(1), pages 124-141.
  • Handle: RePEc:eee:pubeco:v:96:y:2012:i:1:p:124-141
    DOI: 10.1016/j.jpubeco.2011.08.011
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    References listed on IDEAS

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    1. Jason M Barr & Troy Tassier, 2008. "Segregation and Strategic Neighborhood Interaction," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 34(4), pages 480-503.
    2. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
    3. David M. Cutler & Edward L. Glaeser & Jacob L. Vigdor, 2008. "Is the Melting Pot Still Hot? Explaining the Resurgence of Immigrant Segregation," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 478-497, August.
    4. Grauwin, Sébastian & Goffette-Nagot, Florence & Jensen, Pablo, 2012. "Dynamic models of residential segregation: An analytical solution," Journal of Public Economics, Elsevier, vol. 96(1), pages 124-141.
    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. John Iceland & Melissa Scopilliti, 2008. "Immigrant residential segregation in U.S. metropolitan areas, 1990–2000," Demography, Springer;Population Association of America (PAA), vol. 45(1), pages 79-94, February.
    7. 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.
    8. Junfu Zhang, 2011. "Tipping And Residential Segregation: A Unified Schelling Model," Journal of Regional Science, Wiley Blackwell, vol. 51(1), pages 167-193, February.
    9. David Card & Alexandre Mas & Jesse Rothstein, 2008. "Tipping and the Dynamics of Segregation," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 177-218.
    10. Florence Goffette-Nagot & Pablo Jensen & Sebastian Grauwin, 2009. "Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination," Post-Print halshs-00404400, HAL.
    11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    12. 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.
    13. O'Sullivan, Arthur, 2009. "Schelling's model revisited: Residential sorting with competitive bidding for land," Regional Science and Urban Economics, Elsevier, vol. 39(4), pages 397-408, July.
    14. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    15. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
    16. Sean Reardon & Stephen Matthews & David O’Sullivan & Barrett Lee & Glenn Firebaugh & Chad Farrell & Kendra Bischoff, 2008. "The geographic scale of Metropolitan racial segregation," Demography, Springer;Population Association of America (PAA), vol. 45(3), pages 489-514, August.
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    Citations

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    Cited by:

    1. Ioannides, Yannis M., 2015. "Neighborhoods to nations via social interactions," Economic Modelling, Elsevier, vol. 48(C), pages 5-15.
    2. Helsley, Robert W. & Zenou, Yves, 2014. "Social networks and interactions in cities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 426-466.
    3. repec:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-015-0526-2 is not listed on IDEAS
    4. Picard, Pierre M. & Zenou, Yves, 2018. "Urban spatial structure, employment and social ties," Journal of Urban Economics, Elsevier, vol. 104(C), pages 77-93.
    5. Sylvain Barde, 2015. "Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 337-358, February.
    6. Sato, Yasuhiro & Zenou, Yves, 2015. "How urbanization affect employment and social interactions," European Economic Review, Elsevier, vol. 75(C), pages 131-155.
    7. Florent Dubois & Christophe Muller, 2017. "Segregation and the Perception of the Minority," AMSE Working Papers 1718, Aix-Marseille School of Economics, Marseille, France.
    8. Roger Waldeck, 2016. "Modeling criminality: the impact of emotions, norms and interaction structures," Computational and Mathematical Organization Theory, Springer, vol. 22(2), pages 135-160, June.
    9. Jean-Philippe Bouchaud, 2012. "Crises and collective socio-economic phenomena: simple models and challenges," Papers 1209.0453, arXiv.org, revised Dec 2012.
    10. Rémi Lemoy & Charles Raux & Pablo Jensen, 2016. "Exploring the polycentric city with multi-worker households: an agent-based microeconomic model," Post-Print hal-00602087, HAL.
    11. Grauwin, Sébastian & Goffette-Nagot, Florence & Jensen, Pablo, 2012. "Dynamic models of residential segregation: An analytical solution," Journal of Public Economics, Elsevier, vol. 96(1), pages 124-141.
    12. Picard, Pierre M. & Zenou, Yves, 2015. "Urban Spatial Structure, Employment and Social Ties: European versus American Cities," IZA Discussion Papers 9166, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    Residential segregation; Schelling; Dynamic model; Potential function; Social preferences;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • J15 - Labor and Demographic Economics - - Demographic Economics - - - Economics of Minorities, Races, Indigenous Peoples, and Immigrants; Non-labor Discrimination

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