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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.

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Paper provided by HAL in its series Post-Print with number halshs-00502758.

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Date of creation: 2010
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Handle: RePEc:hal:journl:halshs-00502758

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Related research

Keywords: Residential segregation ; Schelling ; dynamic model ; potential function ; social preferences;

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Find related papers by 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, and Immigrants; Non-labor Discrimination

This paper has been announced in the following NEP Reports:

• NEP-ALL-2010-07-24 (All new papers)
• NEP-UPT-2010-07-24 (Utility Models & Prospect Theory)
• NEP-URE-2010-07-24 (Urban & Real Estate Economics)

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1. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.

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