Source-linked AI summary
Percolation threshold determines the optimal population density for public cooperation
Zhen Wang, Attila Szolnoki, Matjaz Perc
TL;DR
The paper investigates how population density affects public cooperation in structured populations. Its simulations find that cooperation is optimized near the interaction graph’s percolation threshold, where spatial reciprocity is strongest.
Problem
How population density affects public cooperation in structured populations is the research question, given the public goods game’s social dilemma.
Source: p. 1Method
The authors use Monte Carlo simulations of a spatial public goods game on a randomly diluted square lattice, with players initially assigned as cooperators or defectors.
Source: pp. 1–2Results
The percolation threshold of an interaction graph constitutes the optimal population density for public cooperation across the square-lattice settings and triangular lattice examined.
Source: pp. 3–4Takeaways & Limitations
Near the percolation threshold, connected cooperators can form a giant domain, while vacancy below and defectors above that vicinity weaken spatial reciprocity.
Source: pp. 3–4
Abstract
from arXiv · showhide
While worldwide census data provide statistical evidence that firmly link the population density with several indicators of social welfare, the precise mechanisms underlying these observations are largely unknown. Here we study the impact of population density on the evolution of public cooperation in structured populations and find that the optimal density is uniquely related to the percolation threshold of the host graph irrespective of its topological details. We explain our observations by showing that spatial reciprocity peaks in the vicinity of the percolation threshold, when the emergence of a giant cooperative cluster is hindered neither by vacancy nor by invading defectors, thus discovering an intuitive yet universal law that links the population density with social prosperity.