Percolation threshold determines the optimal population density for public cooperation

Abstract

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.

4 two-column pages, 5 figures; accepted for publication in Physical Review E

References in corpus (6)

• Evolutionary games on graphs
• Dynamical Organization of Cooperation in Complex Topologies
• Punish, but not too hard: How costly punishment spreads in the spatial public goods game
• Does mobility decrease cooperation?
• Random mobility and spatial structure often enhance cooperation
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Cited by in corpus (7)

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• Evolutionary games on multilayer networks: A colloquium
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• Risk-driven migration and the collective-risk social dilemma
• Effectiveness of conditional punishment for the evolution of public cooperation
• Percolation and cooperation with mobile agents: Geometric and strategy clusters
• Mobility, fitness collection, and the breakdown of cooperation