Dynamics of extended Schelling models

Abstract

We explore extensions of Schelling's model of social dynamics, in which two types of agents live on a checkerboard lattice and move in order to optimize their own satisfaction, which depends on how many agents among their neighbors are of their same type. For each number $n$ of same-type nearest neighbors we independently assign a binary satisfaction variable $s_k$ which is equal to one only if the agent is satisfied with that condition, and is equal to zero otherwise. This defines 32 different satisfaction rules, which we investigate in detail, focusing on pattern formation and measuring segregation with the help of an "energy" function which is related to the number of neighboring agents of different types and plays no role in the dynamics. We consider the checkerboard lattice to be fully occupied and the dynamics consists of switching the locations of randomly selected unsatisfied agents of opposite types. We show that, starting from a random distribution of agents, only a small number of rules lead to (nearly) fully segregated patterns in the long run, with many rules leading to chaotic steady-state behavior. Nevertheless, other interesting patterns may also be dynamically generated, such as "anti-segregate d" patterns as well as patterns resembling sponges.

References in corpus (12)

• Statistical physics of social dynamics
• Voter Model on Heterogeneous Graphs
• Nonequilibrium phase transition in the coevolution of networks and opinions
• Coarsening and persistence in the voter model
• Ising, Schelling and Self-Organising Segregation
• Competition between collective and individual dynamics
• Phase diagram of a Schelling segregation model
• Schelling segregation in an open city: a kinetically constrained Blume-Emery-Griffiths spin-1 system
• Giant catalytic effect of altruists in Schelling's segregation model
• Socio-economic utility and chemical potential
• Jamming and pattern formation in models of segregation
• A network model of conviction-driven social segregation

Cited by in corpus (2)

• Aging effects in Schelling Segregation model
• Phase transitions in a conservative Game of Life