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Dynamic models of residential segregation: An analytical solution

  • Sebastian Grauwin


    (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - CNRS - Centre National de la Recherche Scientifique - ENS Lyon - École normale supérieure - Lyon)

  • Florence Goffette-Nagot


    (GATE - Groupe d'analyse et de théorie économique - UL2 - Université Lumière - Lyon 2 - Ecole Normale Supérieure Lettres et Sciences Humaines - CNRS - Centre National de la Recherche Scientifique)

  • Pablo Jensen


    (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - CNRS - Centre National de la Recherche Scientifique - ENS Lyon - École normale supérieure - Lyon, LET - Laboratoire d'économie des transports - UL2 - Université Lumière - Lyon 2 - École Nationale des Travaux Publics de l'État [ENTPE] - CNRS - Centre National de la Recherche Scientifique)

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

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Date of creation: 2012
Date of revision:
Publication status: Published in Journal of Public Economics, Elsevier, 2012, 96 (1-2), pp.124-141. <10.1016/j.jpubeco.2011.08.011>
Handle: RePEc:hal:journl:hal-00650292
DOI: 10.1016/j.jpubeco.2011.08.011
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  1. 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.
  2. Junfu Zhang, 2011. "Tipping And Residential Segregation: A Unified Schelling Model," Journal of Regional Science, Wiley Blackwell, vol. 51(1), pages 167-193, 02.
  3. 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.
  4. Florence Goffette-Nagot & Pablo Jensen & Sébastian Grauwin, 2009. "Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination," Post-Print halshs-00404400, HAL.
  5. 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.
  6. 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.
  7. Giorgio Fagiolo & Marco Valente & Nicolaas J. Vriend, 2005. "Segregation in Networks," Working Papers of BETA 2005-14, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  8. 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.
  9. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
  10. Giorgio Fagiolo & Marco Valente & Nicolaas J. Vriend, 2007. "Dynamic Models of Segregation in Small-World Networks," LEM Papers Series 2007/09, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  11. 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.
  12. Sebastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2012. "Dynamic models of residential segregation: An analytical solution," Post-Print hal-00650292, HAL.
  13. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
  14. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  15. 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.
  16. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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