Probabilistic interconnection between interdependent networks promotes cooperation in the public goods game
Baokui Wang, Xiaojie Chen, Long Wang

TL;DR
This study explores how probabilistic interconnections between two interdependent networks influence cooperation in the public goods game, revealing an optimal interconnection level that maximizes cooperation and promotes agreement between layers.
Contribution
It introduces a model of two interdependent networks with probabilistic links and analyzes how this affects cooperation, highlighting an optimal interconnection probability for maximum cooperation.
Findings
Maximum cooperation occurs at an intermediate interconnection probability.
At optimal interconnection, the fraction of cooperative links between layers is maximized.
Probabilistic interconnection can promote cooperation even when one layer initially lacks cooperators.
Abstract
Most previous works study the evolution of cooperation in a structured population by commonly employing an isolated single network. However, realistic systems are composed of many interdependent networks coupled with each other, rather than the isolated single one. In this paper, we consider a system including two interacting networks with the same size, entangled with each other by the introduction of probabilistic interconnections. We introduce the public goods game into such system, and study how the probabilistic interconnection influences the evolution of cooperation of the whole system and the coupling effect between two layers of interdependent networks. Simulation results show that there exists an intermediate region of interconnection probability leading to the maximum cooperation level in the whole system. Interestingly, we find that at the optimal interconnection probability…
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