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A piecewise smooth model of evolutionary game for residential mobility and segregation

Laura Gardini () and Davide Radi ()

No 1802, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

Abstract: The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents bene?t from integration. Despite the di?erences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilib- rium while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dy- namic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several di?erent kinds of bifurcations, smooth and border collision, in a complicated interplay. A social planner that aims to maximize integration can use our global analysis of the dynamics of the model to understand the possible achievements of social policies that manipulate people?s preferences for integration. Length: 24 pages

Date: 2018, Revised 2018
New Economics Papers: this item is included in nep-evo, nep-gth and nep-ure
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