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Dynamic models of residential segregation: An analytical solution

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  • Sebastian Grauwin

    ()
    (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - CNRS : UMR5672 - École Normale Supérieure (ENS) - Lyon)

  • Florence Goffette-Nagot

    ()
    (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

  • Pablo Jensen

    ()
    (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - CNRS : UMR5672 - École Normale Supérieure (ENS) - Lyon, LET - Laboratoire d'économie des transports - CNRS : UMR5593 - École Nationale des Travaux Publics de l'État [ENTPE] - Université Lumière - Lyon II)

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.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number hal-00650292.

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Date of creation: 2012
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Publication status: Published, Journal of Public Economics, 2012, 96, 1-2, 124-141
Handle: RePEc:hal:journl:hal-00650292

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00650292
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  1. Sébastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2010. "Dynamic models of residential ségrégation: an analytical solution," Post-Print halshs-00502758, HAL.
  2. David Card & Alexandre Mas & Jesse Rothstein, 2007. "Tipping and the Dynamics of Segregation," NBER Working Papers 13052, National Bureau of Economic Research, Inc.
  3. David Cutler & Edward Glaeser & Jacob Vigdor, 2004. "Is the Melting Pot Still Hot? Explaining the Resurgence of Immigrant Segregation," Working Papers 04-10, Center for Economic Studies, U.S. Census Bureau.
  4. Romans Pancs & Nicolaas J. Vriend, 2003. "Schelling's Spatial Proximity Model of Segregation Revisited," Computing in Economics and Finance 2003 63, Society for Computational Economics.
  5. Junfu Zhang, 2011. "Tipping And Residential Segregation: A Unified Schelling Model," Journal of Regional Science, Wiley Blackwell, vol. 51(1), pages 167-193, 02.
  6. Fagiolo, Giorgio & Valente, Marco & Vriend, Nicolaas J., 2007. "Segregation in networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 316-336.
  7. 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 (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  8. Jason M Barr & Troy Tassier, 2008. "Segregation and Strategic Neighborhood Interaction," Eastern Economic Journal, Palgrave Macmillan, vol. 34(4), pages 480-503.
  9. 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.
  10. John Iceland & Melissa Scopilliti, 2008. "Immigrant residential segregation in U.S. metropolitan areas, 1990–2000," Demography, Springer, vol. 45(1), pages 79-94, February.
  11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  12. 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.
  13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  14. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
  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, vol. 45(3), pages 489-514, August.
  16. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
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Cited by:
  1. 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 (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  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. Jean-Philippe Bouchaud, 2012. "Crises and collective socio-economic phenomena: simple models and challenges," Papers 1209.0453, arXiv.org, revised Dec 2012.
  4. Sato, Yasuhiro & Zenou, Yves, 2014. "How Urbanization Affect Employment and Social Interactions," CEPR Discussion Papers 9805, C.E.P.R. Discussion Papers.

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