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

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Author Info
Sebastian Grauwin (University of Lyon, Lyon, F-69003, France; ENS-LYON, Laboratoire de Physique, UMR 5672, Lyon, F-69007, France, Institut rhonalpin des systemes complexes, IXXI, Lyon, F-69007, France)
Florence Goffette-Nagot () (University of Lyon, Lyon, F-69003, France; CNRS, UMR 5824, GATE, Ecully, F-69130, France; ENS LSH, Lyon, F-69007, France)
Pablo Jensen () (University of Lyon, Lyon, F-69003, France; CNRS, LET, UMR 5593, Lyon, F-69363 France, ENS-LYON, Laboratoire de Physique, UMR 5672, Lyon, F-69007, France, Institut rhônalpin des systèmes complexes, IXXI, Lyon, F-69007, France)
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 conï¬guration 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 ï¬nal state of the system starting from any conï¬guration. 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 ï¬rst 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 deï¬ned 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 Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure in its series Working Papers with number 0914.

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Length: 55 pages
Date of creation: 2009
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Handle: RePEc:gat:wpaper:0914

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

Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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 and Races; Non-labor Discrimination

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  1. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
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  3. 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. [Downloadable!]
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  4. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May. [Downloadable!] (restricted)
  5. 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.
  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. [Downloadable!] (restricted)
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  7. Zhang, Junfu, 2004. "Residential segregation in an all-integrationist world," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 533-550, August. [Downloadable!] (restricted)
  8. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
  9. Fagiolo, Giorgio & Valente, Marco & Vriend, Nicolaas J., 2007. "Segregation in networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 316-336. [Downloadable!] (restricted)
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