Giant Catalytic Effect of Altruists in Schelling's Segregation Model

Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling models

How robust are socioeconomic agent-based models with respect to the details of the agents' decision rule? We tackle this question by considering an occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of utility functions and decision rules, we pinpoint the nonequilibrium nature of the agent dynamics, while recovering an equilibrium-like phase separation phenomenology. Within the mean-field approximation we show how the model can be mapped, to some extent, onto an active matter field description. Finally, we consider nonreciprocal interactions between two populations and show how they can lead to nonsteady macroscopic behavior. We believe our approach provides a unifying framework to further study geography-dependent agent-based models, notably paving the way for joint consideration of population and price dynamics within a field theoretic approach.

Aging effects in Schelling segregation model

The Schelling model has become a paradigm in social sciences to explain the emergence of residential spatial segregation, even in the presence of high tolerance to mixed neighborhoods by the side of citizens. In particular, we consider a noisy constrained version of the Schelling model, in which agents maximize its satisfaction, related to the composition of the local neighborhood, by infinite-range movements towards satisfying vacancies. We add to it an aging effect by making the probability of agents to move inversely proportional to the time they have been satisfied in their present location. This mechanism simulates the development of an emotional attachment to a location where an agent has been satisfied for a while. The introduction of aging has several major impacts on the model statics and dynamics: the phase transition between a segregated and a mixed phase of the original model disappears, and we observe segregated states with a high level of agent satisfaction even for high values of tolerance. In addition, the new segregated phase is dynamically characterized by a slow power-law coarsening process similar to a glassy-like dynamics.

Homophily Based on Few Attributes Can Impede Structural Balance

Homophily between agents and structural balance in connected triads of agents are complementary mechanisms thought to shape social groups leading to, for instance, consensus or polarization. To capture both processes in a unified manner, we propose a model of pair and triadic interactions. We consider N fully connected agents, where each agent has G underlying attributes, and the similarity between agents in attribute space (i.e., homophily) is used to determine the link weight between them. For structural balance we use a triad-updating rule where only one attribute of one agent is changed intentionally in each update, but this also leads to accidental changes in link weights and even link polarities. The link weight dynamics in the limit of large G is described by a Fokker-Planck equation from which the conditions for a phase transition to a fully balanced state with all links positive can be obtained. This "paradise state" of global cooperation is, however, difficult to achieve requiring G>O(N^{2}) and p>0.5, where the parameter p captures a willingness for consensus. Allowing edge weights to be a consequence of attributes naturally captures homophily and reveals that many real-world social systems would have a subcritical number of attributes necessary to achieve structural balance.

Intriguing effects of underlying star topology in Schelling's model with blocks

We explore the intriguing effects of the underlying star topological structure in the framework of Schelling's segregation model with blocks. The significant consequences exerted by the star topology are both theoretically analyzed and numerically simulated with and without introducing a fraction of altruistic agents, respectively. The collective utility of the model with egoists alone can be optimized and the optimum stationary state is achieved with the underlying star topology of blocks. More surprisingly, once a proportion of altruists is introduced, the average utility gradually decreases as the fraction of altruists increases. This presents a sharp contrast to the results in Schelling's model with a lattice topology of blocks. Furthermore, an adding-link mechanism is introduced to bridge the gap between the lattice and the star topologies and extend our analysis to more general scenarios. A scaling law of the average utility function is found for the star topology of blocks.