How the weak and strong links affect the evolution of prisoner's dilemma game

Abstract

The complex interactions between individuals are intertwined with time in multilayer networks. In this paper, we propose a prisoner's dilemma game on a two-layered network, including the weak-link layer and the strong-link layer. Based on the mean-field theory and numerical simulations, we show that if the players update their strategies primarily depending on the information received in the weaklink layer, i.e. the weak relations have the dominate influences on the individuals' strategies choice, the cooperation becomes the most abundant strategy. More comparative analysis of the different structures on the strong-link layer indicates that a higher connectivity heterogeneity of the strong-link layer could be conducive to promote the individuals' cooperation behavior. In the situation while the relation between the players' connections in the strong-link layer and their activity rates in the weaklink layer is negative correlated, i.e. ones' connections increase with the decrease of their activity rates, the propensity for cooperation can be greatly enhanced.hand, most of the previous researches of evolutionary game were concentrated on non-time-varying networks. Whereas the individuals' interactive networks are not only intertwined, but also evolving with time [34][35][36][37][38][39]. In fact, for the time-varying networks, such as social networks, the structure is usually twofold. For one thing, some links are temporally dynamical during network evolution, which can be treated as weak connections between nodes. For another, some links are static and invariant, we treat these as strong connections. For example, we could view the individuals who comment on an event in some online social platform as a link, and when all individuals comment on different news events, different relations are established between the pair of individuals. As the relations may change over time, so we call such varying relations as the weak links. However, an individual's offline relations generally do not change or will not change in a period, such as the kinship or friendship, which we call these constant relations as the strong links [40,41].Weak links and strong links play a very important role in the social structure, and are the effective bridge to transmit information between different social clusters. As a result, the different links of the players would heavily affect the change of their strategies. However, the influence of weak links and strong links on human behavior has remained unclear. In order to uncover how the weak and strong links affect the evolution of players' strategies, we explore the PD game in a two-layered network. We use the activity-driven model to describe the network structure of the weak-link layer [42]. In addition, we analyze and simulate the PD game, mainly focusing on three types of networks of the strong-link layer, which are the lattice network, the ER random network and the BA scare-free network, respectively. If the weak relations have the dominate influences on the individuals' strategy choice, the...

Hidden order behind the cooperation

“…The individuals' interactive networks are not only intertwined, but also evolving with time [58][59][60]. Unlike the static network, the link of nodes in the time-varying network changes with time as shown in fig.…”

Fairness-Aware Predictive Graph Learning in Social Networks

“…Graph predictive learning models will naturally output biased learning results with those unbalanced distribution data. Since numerous studies have illustrated that strong links and weak links are equally important for networks [11][12][13], it is necessary to put forward fairness-aware predictive learning models that can present non-discriminatory prediction results to learn balanced distribution data [14]. In this work, we firstly define two types of biases that widely exist in current methods, i.e., Preference and Favoritism (shown as Figure 1).…”

How the intimate relationship affects the individuals' behaviors in a two-layer network

“…Li et al explored how the weak and strong links affect the evolution of PD game. They claimed that while the relation between the players' connections in the stronglink layer and their activity rates in the weak-link layer is negatively correlated, the propensity for cooperation can be greatly enhanced [29]. Wang et al investigated the interdependent network reciprocity in evolutionary games.…”