Self-organized Segregation on the Grid

We consider an agent-based model in which two types of agents interact locally over a graph and have a common intolerance threshold $\tau$ for changing their types with exponentially distributed waiting times. The model is equivalent to an unperturbed Schelling model of self-organized segregation, an Asynchronous Cellular Automata (ACA) with extended Moore neighborhoods, or a zero-temperature Ising model with Glauber dynamics, and has applications in the analysis of social and biological networks, and spin glasses systems. Some rigorous results were recently obtained in the theoretical computer science literature, and this work provides several extensions. We enlarge the intolerance interval leading to the formation of large segregated regions of agents of a single type from the known size $\epsilon>0$ to size $\approx 0.134$. Namely, we show that for $0.433 < \tau < 1/2$ (and by symmetry $1/2<\tau<0.567$), the expected size of the largest segregated region containing an arbitrary agent is exponential in the size of the neighborhood. We further extend the interval leading to large segregated regions to size $\approx 0.312$ considering "almost segregated" regions, namely regions where the ratio of the number of agents of one type and the number of agents of the other type vanishes quickly as the size of the neighborhood grows. In this case, we show that for $0.344 < \tau \leq 0.433$ (and by symmetry for $0.567 \leq \tau<0.656$) the expected size of the largest almost segregated region containing an arbitrary agent is exponential in the size of the neighborhood. The exponential bounds that we provide also imply that complete segregation, where agents of a single type cover the whole grid, does not occur with high probability for $p=1/2$ and the range of tolerance considered

Statistical physics of the Schelling model of segregation

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics methods shed light on the rich phenomenology of this simple model, exhibiting static phase transitions typical of kinetic constrained models, nontrivial coarsening like in driven-particle systems and percolation-related phenomena.Comment: 4 pages, 3 figure

Sequential vs. Simultaneous Schelling Models: Experimental Evidence

This paper shows the results of experiments where subjects play the Schelling's spatial proximity model (1969, 1971a). Two types of experiments are conducted; one in which choices are made sequentially, and a variation of the first where the decision-making is simultaneous. The results of the sequential experiments are identical to Schelling's prediction: subjects finish in a segregated equilibrium. Likewise, in the variant of the simultaneous decision experiment the same result is reached: segregation. Subjects’ heterogeneity generates a series of focal points in the first round. In order to locate themselves, subjects use these focal points immediately, and as a result, the segregation takes place again. Furthermore, simultaneous experiments with commuting costs allow us to conclude that introducing positive moving costs does not affect segregation.Schelling models, economic experiments, segregation

Urban skylines from Schelling model

We propose a metapopulation version of the Schelling model where two kinds of agents relocate themselves, with unconstrained destination, if their local fitness is lower than a tolerance threshold. We show that, for small values of the latter, the population redistributes highly heterogeneously among the available places. The system thus stabilizes on these heterogeneous skylines after a long quasi-stationary transient period, during which the population remains in a well mixed phase. Varying the tolerance passing from large to small values, we identify three possible global regimes: microscopic clusters with local coexistence of both kinds of agents, macroscopic clusters with local coexistence (soft segregation), macroscopic clusters with local segregation but homogeneous densities (hard segregation). The model is studied numerically and complemented with an analytical study in the limit of extremely large node capacity.Comment: 16 pages, 10 figure