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

Florence Goffette-Nagot, Pablo Jensen () and Sebastian Grauwin ()
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Pablo Jensen: Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS de Lyon - École normale supérieure de Lyon - Université de 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 - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UJF - Université Joseph Fourier - Grenoble 1 - UJML - Université Jean Moulin - Lyon 3 - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique
Sebastian Grauwin: Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - CNRS - Centre National de la Recherche Scientifique, IXXI - Institut Rhône-Alpin des systèmes complexes - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UJF - Université Joseph Fourier - Grenoble 1 - UJML - Université Jean Moulin - Lyon 3 - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: segregation; Schelling; potential function; coordination; tax; vote (search for similar items in EconPapers)
Date: 2009
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00404400v1
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Citations: View citations in EconPapers (8)

Published in 2009

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Working Paper: Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination (2009)
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