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Dynamic models of residential ségrégation: an analytical solution

  • Sébastian Grauwin

    (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - CNRS : UMR5672 - École normale supérieure de Lyon - ENS Lyon, IXXI - Institut Rhône-Alpin des systèmes complexes - INRIA - École normale supérieure de Lyon - ENS Lyon - Institut National des Sciences Appliquées de Lyon - Université Claude Bernard - Lyon I - Ecole Normale Supérieure Lettres et Sciences Humaines - Université Joseph Fourier - Grenoble I - CNRS - IRD)

  • Florence Goffette-Nagot

    ()

    (GATE Lyon Saint-Etienne - 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 de Lyon - ENS Lyon, IXXI - Institut Rhône-Alpin des systèmes complexes - INRIA - École normale supérieure de Lyon - ENS Lyon - Institut National des Sciences Appliquées de Lyon - Université Claude Bernard - Lyon I - Ecole Normale Supérieure Lettres et Sciences Humaines - Université Joseph Fourier - Grenoble I - CNRS - IRD, LET - Laboratoire d'économie des transports - CNRS : UMR5593 - Université Lumière - Lyon II - Ecole Nationale des Travaux Publics de l'Etat)

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.

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Paper provided by HAL in its series Post-Print with number halshs-00502758.

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Date of creation: 2010
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Handle: RePEc:hal:journl:halshs-00502758
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  1. Junfu Zhang, 2011. "Tipping And Residential Segregation: A Unified Schelling Model," Journal of Regional Science, Wiley Blackwell, vol. 51(1), pages 167-193, 02.
  2. Sebastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2012. "Dynamic models of residential segregation: An analytical solution," Post-Print hal-00650292, HAL.
  3. 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.
  4. David Card & Alexandre Mas & Jesse Rothstein, 2008. "Tipping and the Dynamics of Segregation," The Quarterly Journal of Economics, MIT Press, vol. 123(1), pages 177-218, 02.
  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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  7. John Iceland & Melissa Scopilliti, 2008. "Immigrant residential segregation in U.S. metropolitan areas, 1990–2000," Demography, Springer, vol. 45(1), pages 79-94, February.
  8. 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.
  9. Romans Pancs & Nicolaas J. Vriend, . "Schelling's Spatial Proximity Model of Segregation Revisited," Modeling, Computing, and Mastering Complexity 2003 15, Society for Computational Economics.
  10. 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.
  11. David M. Cutler & Edward L. Glaeser & Jacob L. Vigdor, 2005. "Is the Melting Pot Still Hot? Explaining the Resurgence of Immigrant Segregation," NBER Working Papers 11295, National Bureau of Economic Research, Inc.
  12. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
  13. 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.
  14. 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.
  15. Jason Barr & Troy Tassier, 2007. "Segregation and Strategic Neighborhood Interaction," Working Papers Rutgers University, Newark 2007-001, Department of Economics, Rutgers University, Newark.
  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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