Dynamic models of residential ségrégation: an analytical solution

Sebastian Grauwin (), Florence Goffette-Nagot and Pablo Jensen ()
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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
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, 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, 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

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Abstract: We propose an analytical resolution of Schelling segregation model for a general class of utility functions. Using evolutionary game theory, we provide conditions under which a potential function, which characterizes the global configuration of the city and is maximized in the stationary state, exists. 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. Schelling original utility function is shown to drive segregation at the expense of collective utility. If agents have a strict preference for mixed neighborhoods but still prefer being in the majority versus in the minority, the model converges to perfectly segregated configurations, which clearly diverge from the social optimum. Departing from earlier literature, these conclusions are based on analytical results. These results pave the way to the analysis of many structures of preferences, for instance those based on empirical findings concerning racial preferences. As a by-product, our analysis builds a bridge between Schelling model and the Duncan and Duncan segregation index.

Keywords: Residential segregation; Schelling; dynamic model; potential function; social preferences (search for similar items in EconPapers)
Date: 2010
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00502758v1
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Citations: View citations in EconPapers (1)

Published in 2010

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Related works:
Journal Article: Dynamic models of residential segregation: An analytical solution (2012)
Working Paper: Dynamic models of residential segregation: An analytical solution (2012)
Working Paper: Dynamic models of residential segregation: an analytical solution (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00502758

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