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Dynamic models of residential segregation: An analytical solution

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  • Grauwin, Sébastian
  • Goffette-Nagot, Florence
  • Jensen, Pablo

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

Article provided by Elsevier in its journal Journal of Public Economics.

Volume (Year): 96 (2012)
Issue (Month): 1 ()
Pages: 124-141

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Handle: RePEc:eee:pubeco:v:96:y:2012:i:1:p:124-141

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Web page: http://www.elsevier.com/locate/inca/505578

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Keywords: Residential segregation; Schelling; Dynamic model; Potential function; Social preferences;

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References

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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. 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.
  3. Sébastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2010. "Dynamic models of residential ségrégation: an analytical solution," Post-Print halshs-00502758, HAL.
  4. 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.
  5. Jason Barr & Troy Tassier, 2007. "Segregation and Strategic Neighborhood Interaction," Working Papers Rutgers University, Newark 2007-001, Department of Economics, Rutgers University, Newark.
  6. 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.
  7. 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.
  8. Giorgio Fagiolo & Marco Valente & Nicolaas J. Vriend, 2005. "Segregation in Networks," LEM Papers Series 2005/22, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  9. 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.
  10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  11. 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.
  12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  13. John Iceland & Melissa Scopilliti, 2008. "Immigrant residential segregation in U.S. metropolitan areas, 1990–2000," Demography, Springer, vol. 45(1), pages 79-94, February.
  14. 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.
  15. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, 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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Citations

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Cited by:
  1. Yasuhiro Sato & Yves Zenou, 2013. "How Urbanization Affect Employment and Social Interactions," Discussion Papers in Economics and Business 13-32, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
  2. Jean-Philippe Bouchaud, 2012. "Crises and collective socio-economic phenomena: simple models and challenges," Papers 1209.0453, arXiv.org, revised Dec 2012.
  3. 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.
  4. Helsley, Robert & Zenou, Yves, 2011. "Social Networks and Interactions in Cities," CEPR Discussion Papers 8260, C.E.P.R. Discussion Papers.

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