Giant Catalytic Effect of Altruists in Schelling’s Segregation Model

Abstract

We study the effect of introducing altruistic agents in a Schelling-like model of residential segregation. We find that even an infinitesimal proportion of altruists has dramatic catalytic effects on the collective utility of the system. Altruists provide pathways that move the system away from the suboptimal equilibrium it would reach if the system included only egoist agents, allowing it to reach the optimal steady state.

Modeling cities

“…This utility has to satisfy the general constraints ∂U ∂s > 0 , ∂U ∂z > 0 (20) which means that households in general prefer larger apartment and smaller costs. The budget constraint is given by…”

“…Another important question where statistical physics contributed a lot is the social structure of cities. First discussed by Schelling [15], agents are described by Ising like spins with tolerance level for other kinds and was later naturally rediscussed and improved by physicists [16][17][18][19][20].…”

Critical mass effect in evolutionary games triggered by zealots

“…The payoffs displayed in Eqs. ( 29) and (30), and those in Eqs. ( 31) and ( 32) are equivalent with the identification w = 1/(1 + ε).…”

“…Zealotry can elicit consensus in human/animal behavior [18][19][20], the polarization of opinions in the voter model [21], majority rule [13], naming game [22][23][24], Social Knowledge Structure (SKS) [25], and Cooperative Decision Making Model (CDMM) [26] models. Zealotry can also drive the emergence of cooperation in evolutionary games [27][28][29], and the attainment of the optimal equilibrium in the Schelling's model of social segregation dynamics [30]. Conversely, zealous (i.e., stubborn) dissenters can disrupt flocking in the Vicsek's active matter model [9].…”

“…One question about zealots is whether or not their catalytic role in migrating the system across equilibria requires a critical mass. Specifically, an infinitesimal fraction of zealots is enough to shift the equilibria in the voter [21], CDMM [26], and Schelling's [30] dynamics, whereas finite fractions are needed in both the majority rule [13] and Vicsek [9] dynamics, as well as in the naming game theoretically [22,24] and experimentally [32].…”