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Dynamic models of residential ségrégation: an analytical solution

  • Sébastian Grauwin

    (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - CNRS - Centre National de la Recherche Scientifique - ENS Lyon - École normale supérieure - Lyon, IXXI - Institut Rhône-Alpin des systèmes complexes - CNRS - Centre National de la Recherche Scientifique - Institut de recherche pour le développement [IRD] - INRIA - UJF - Université Joseph Fourier - UCBL - Université Claude Bernard Lyon 1 - INSA - Institut National des Sciences Appliquées - ENS Lyon - École normale supérieure - Lyon - Ecole Normale Supérieure Lettres et Sciences Humaines)

  • Florence Goffette-Nagot

    ()

    (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université Jean Monnet - Saint-Etienne - PRES Université de Lyon - 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, IXXI - Institut Rhône-Alpin des systèmes complexes - CNRS - Centre National de la Recherche Scientifique - Institut de recherche pour le développement [IRD] - INRIA - UJF - Université Joseph Fourier - UCBL - Université Claude Bernard Lyon 1 - INSA - Institut National des Sciences Appliquées - ENS Lyon - École normale supérieure - Lyon - Ecole Normale Supérieure Lettres et Sciences Humaines, 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 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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Publication status: Published in Working Paper GATE 2010-17. 2010
Handle: RePEc:hal:journl:halshs-00502758
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00502758
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  1. David M. Cutler & Edward L. Glaeser & Jacob L. Vigdor, 2005. "Is the Melting Pot Still Hot? Explaining the Resurgence of Immigrant Segregation," Harvard Institute of Economic Research Working Papers 2071, Harvard - Institute of Economic Research.
  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, 2007. "Tipping and the Dynamics of Segregation," NBER Working Papers 13052, National Bureau of Economic Research, Inc.
  4. 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.
  5. 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.
  6. 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.
  7. Romans Pancs & Nicolaas J. Vriend, . "Schelling's Spatial Proximity Model of Segregation Revisited," Modeling, Computing, and Mastering Complexity 2003 15, Society for Computational Economics.
  8. 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.
  9. Jason M Barr & Troy Tassier, 2008. "Segregation and Strategic Neighborhood Interaction," Eastern Economic Journal, Palgrave Macmillan, vol. 34(4), pages 480-503.
  10. Fagiolo, Giorgio & Valente, Marco & Vriend, Nicolaas J., 2007. "Segregation in networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 316-336.
  11. 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.
  12. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  13. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
  14. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
  15. 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.
  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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