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 sametype 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 consist 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 steadystate behavior. Nevertheless, other interesting patterns may also be dynamically generated, such as ‘antisegregated’ patterns as well as patterns resembling sponges.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 January 2020
 DOI:
 10.1088/17425468/ab5b8d
 arXiv:
 arXiv:2001.08284
 Bibcode:
 2020JSMTE..01.3212V
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Computer Science  Multiagent Systems;
 Nonlinear Sciences  Cellular Automata and Lattice Gases
 EPrint:
 Journal of Statistical Mechanics: Theory and Experiment (2020) 013212