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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 - 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 - ENS Lyon - École normale supérieure - Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - CNRS - Centre National de la Recherche Scientifique, LET - Laboratoire d'économie des transports - UL2 - Université Lumière - Lyon 2 - ENTPE - École Nationale des Travaux Publics de l'État - CNRS - Centre National de la Recherche Scientifique, IXXI - Institut Rhône-Alpin des systèmes complexes - UJML - Université Jean Moulin - Lyon III - UL2 - Université Lumière - Lyon 2 - CNRS - Centre National de la Recherche Scientifique - Inria - Institut National de Recherche en Informatique et en Automatique - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJF - Université Joseph Fourier - Grenoble 1 - ENS Lyon - École normale supérieure - Lyon)

  • Sebastian Grauwin

    () (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS Lyon - École normale supérieure - Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - CNRS - Centre National de la Recherche Scientifique, IXXI - Institut Rhône-Alpin des systèmes complexes - UJML - Université Jean Moulin - Lyon III - UL2 - Université Lumière - Lyon 2 - CNRS - Centre National de la Recherche Scientifique - Inria - Institut National de Recherche en Informatique et en Automatique - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJF - Université Joseph Fourier - Grenoble 1 - ENS Lyon - École normale supérieure - Lyon)

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.

Suggested Citation

  • Florence Goffette-Nagot & Pablo Jensen & Sebastian Grauwin, 2009. "Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination," Post-Print halshs-00404400, HAL.
  • Handle: RePEc:hal:journl:halshs-00404400
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00404400
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. David M. Cutler & Edward L. Glaeser & Jacob L. Vigdor, 2008. "Is the Melting Pot Still Hot? Explaining the Resurgence of Immigrant Segregation," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 478-497, August.
    4. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August.
    5. 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.
    6. Fagiolo, Giorgio & Valente, Marco & Vriend, Nicolaas J., 2007. "Segregation in networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 316-336.
    7. William Clark, 1992. "Residential preferences and residential choices in a multiethnic context," Demography, Springer;Population Association of America (PAA), vol. 29(3), pages 451-466, August.
    8. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416-416.
    9. W. Clark, 1991. "Residential preferences and neighborhood racial segregation: A test of the schelling segregation model," Demography, Springer;Population Association of America (PAA), vol. 28(1), pages 1-19, February.
    10. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
    11. 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 402-409, October.
    12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    13. 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, January.
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    Cited by:

    1. Sylvain Barde, 2011. "Back to the future: a simple solution to schelling segregation," Sciences Po publications 2011-05, Sciences Po.
    2. repec:spo:wpecon:info:hdl:2441/5l6uh8ogmqildh09h5623b6bg is not listed on IDEAS
    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.

    More about this item

    Keywords

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

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • J15 - Labor and Demographic Economics - - Demographic Economics - - - Economics of Minorities, Races, Indigenous Peoples, and Immigrants; Non-labor Discrimination

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