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Dynamic models of residential segregation : an analytical solution

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  • Sebastian Grauwin

    () (Université de Lyon, Lyon, F-69007, France, Institut rhônalpin des systèmes complexes, IXXI, Lyon, F-69007, France, ENS-LYON, Laboratoire de Physique, UMR 5672, Lyon, F-69007, France)

  • Florence Goffette-Nagot

    () (Université de Lyon, Lyon, F-69007, France, CNRS, GATE Lyon-St Etienne, UMR 5824, Ecully, F-69130)

  • Pablo Jensen

    () (Université de Lyon, Lyon, F-69007, France, Institut rhônalpin des systèmes complexes, IXXI, Lyon, F-69007, France, ENS-LYON, Laboratoire de Physique, UMR 5672, Lyon, F-69007, France, CNRS, Laboratoire d'Economie des Transports (LET), UMR 5593, Lyon, F-69363, France)

Abstract

We propose an analytical resolution of Schelling segregation model for a general class of utility functions. Using evolutionary game theory, we provide conditions under which a potential function, which characterizes the global configuration of the city and is maximized in the stationary state, exists. 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. Schelling original utility function is shown to drive segregation at the expense of collective utility. If agents have a strict preference for mixed neighborhoods but still prefer being in the majority versus in the minority, the model converges to perfectly segregated configurations, which clearly diverge from the social optimum. Departing from earlier literature, these conclusions are based on analytical results. These results pave the way to the analysis of many structures of preferences, for instance those based on empirical findings concerning racial preferences. As a by-product, our analysis builds a bridge between Schelling model and the Duncan and Duncan segregation index.

Suggested Citation

  • Sebastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2010. "Dynamic models of residential segregation : an analytical solution," Working Papers 1017, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
  • Handle: RePEc:gat:wpaper:1017
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    References listed on IDEAS

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    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. 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.
    4. 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.
    5. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
    6. 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.
    7. 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.
    8. Fagiolo, Giorgio & Valente, Marco & Vriend, Nicolaas J., 2007. "Segregation in networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 316-336.
    9. 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.
    10. Sebastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2009. "Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination," Working Papers 0914, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    11. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    12. 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.
    13. Junfu Zhang, 2011. "Tipping And Residential Segregation: A Unified Schelling Model," Journal of Regional Science, Wiley Blackwell, vol. 51(1), pages 167-193, February.
    14. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
    15. 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.
    16. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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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. Pierre Picard & Yves Zenou, 2014. "Urban Spatial Structure, Employement and Social Ties," CREA Discussion Paper Series 14-31, Center for Research in Economic Analysis, University of Luxembourg.
    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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