Probabilistic interconnection between interdependent networks promotes cooperation in the public goods game

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 the fraction of internal links between cooperators in two layers is maximal. Also, even if initially there are no cooperators in one layer of interdependent networks, cooperation can still be promoted by probabilistic interconnection, and the cooperation levels in both layers can more easily reach an agreement at the intermediate interconnection probability. Our results may be helpful in understanding the cooperative behavior in some realistic interdependent networks and thus highlight the importance of probabilistic interconnection on the evolution of cooperation.