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