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Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination

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  • 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 de Lyon - ENS Lyon, LET - Laboratoire d'économie des transports - CNRS : UMR5593 - Université Lumière - Lyon II - Ecole Nationale des Travaux Publics de l'Etat, 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)

  • 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)

Abstract

In his 1971's Dynamic Models of Segregation paper, the economist Thomas C. Schelling showed that a small preference for one's neighbors to be of the same color could lead to total segregation, even if total segregation does not correspond to individual preferences and to a residential configuration maximizing the collective utility. The present work is aimed at deepening the understanding of the properties of dynamic models of segregation based on Schelling's hypotheses. Its main contributions are (i) to offer a comprehensive and up-to-date review of this family of models ; (ii) to provide an analytical solution to the most general form of this model under rather general assumptions ; to the best of our knowledge, such a solution did not exist so far ; (iii) to analyse the effect of two devices aimed at decreasing segregation in such a model. Chapter one summarizes the ingredients of Schelling's models. We show how the choices of the agent's utility function, of the neighborhood description and of the dynamical rule can impact the outcome of a model. Based on the observation of simulations' results, we find that the neighborhood description does not have a qualitative impact. As regards the dynamical rules, we show that the Logit Behavioral rule introduced in this literature by Young (1998) ; Zhang (2004b) presents several advantages relatively to the Best Response rule. Chapter two presents a general analytical solution to the model. To that aim, Schelling's model is recasted within the framework of evolutionary game theory, as previously done by Young (1998) ; Zhang (2004b). This allows to define sufficient assumptions regarding agents' utility functions that permit predicting the final state of the system starting from any configuration. This analytical resolution is then used to consider the outcomes of Schelling's utility function and of other utility functions previously used in this context. Chapter three examines the effects of introducing coordination in the moving decisions. This coordination is achieved through two different ways. We first impose different levels of taxes proportional to the externality generated by each move of the agents. It is shown that even a low level of tax is sufficient under certain circumstances to significantly reduce segregation. We then investigate the effect of the introduction of a local coordination by vote of co-proprietors, who are defined as the closest neighbors of each agent. It is shown that even a small amount of coordination can break segregation.

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Paper provided by HAL in its series Post-Print with number halshs-00404400.

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Date of creation: 2009
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Handle: RePEc:hal:journl:halshs-00404400

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Keywords: segregation; Schelling; potential function; coordination; tax; vote;

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  1. David Card & Alexandre Mas & Jesse Rothstein, 2007. "Tipping and the Dynamics of Segregation," NBER Working Papers 13052, National Bureau of Economic Research, Inc.
  2. Fagiolo, Giorgio & Valente, Marco & Vriend, Nicolaas J., 2007. "Segregation in networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 316-336.
  3. Carrington, William J & Troske, Kenneth R, 1997. "On Measuring Segregation in Samples with Small Units," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 402-09, October.
  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. 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. William Clark, 1992. "Residential preferences and residential choices in a multiethnic context," Demography, Springer, vol. 29(3), pages 451-466, August.
  7. Jason M Barr & Troy Tassier, 2008. "Segregation and Strategic Neighborhood Interaction," Eastern Economic Journal, Palgrave Macmillan, vol. 34(4), pages 480-503.
  8. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  10. Joshua M. Epstein & Robert L. Axtell, 1996. "Growing Artificial Societies: Social Science from the Bottom Up," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262550253, December.
  11. W. Clark, 1991. "Residential preferences and neighborhood racial segregation: A test of the schelling segregation model," Demography, Springer, vol. 28(1), pages 1-19, February.
  12. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
  13. 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. Sylvain Barde, 2011. "Back to the Future: A Simple Solution to Schelling Segregation," Studies in Economics 1104, Department of Economics, University of Kent.
  2. repec:spo:wpecon:info:hdl:2441/5l6uh8ogmqildh09h5623b6bg is not listed on IDEAS
  3. Sébastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2010. "Dynamic models of residential ségrégation: an analytical solution," Post-Print halshs-00502758, HAL.

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