Income redistribution is the transfer of income from some individuals to others directly or indirectly by means of social mechanisms, such as taxation, public services and so on. Employing a spatial public goods game, we study the influence of income redistribution on the evolution of cooperation. Two kinds of evolutionary models are constructed, which describe local and global redistribution of income respectively. In the local model, players have to pay part of their income after each PGG and the accumulated income is redistributed to the members. While in the global model, all the players pay part of their income after engaging in all the local PGGs, which are centred on himself and his nearest neighbours, and the accumulated income is redistributed to the whole population. We show that the cooperation prospers significantly with increasing income expenditure proportion in the local redistribution of income, while in the global model the situation is opposite. Furthermore, the cooperation drops dramatically from the maximum curvature point of income expenditure proportion. In particular, the intermediate critical points are closely related to the renormalized enhancement factors.

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Along with the rapid development of network-based information technology, such as cloud computing, big data, the IoT, and so on, human society has stepped into a new era of complex networks. People’s life and production activities depend more and more on various complex networks to ensure security and reliability. The complex interrelationships between human and nature establish a link to explain the cooperation of individual behaviour, especially for individual diversity. However, existing researches mostly ignore the influence of individual diversity on networks involved in individual behaviour to strategy selection. Therefore, it needs further research on how to consider both individual diversity and independent networks in the evolution of cooperative behaviour. To address this issue, we extend a simple game model into the interdependent networks through the mixed coupling (i.e., utility and probability) in this work. Also, we divide the kinds of strategic behaviour of a player in one layer concerning individual diversity. Moreover, there exists an optimal region of mixed coupling between networks such that cooperation can be promoted. Finally, experimental results can open the path to understanding the emergence and maintenance of cooperation within various interconnected and interrelated real-world systems newly.

The social networks as a complex set of networks fully reflect internal relations of individual interactions between them. Individual as an integral part of networks can show different functions under different levels. In the vast majority of current research realm of spatial evolutionary game, individuals who are often treated as identical peers interact with the local neighbours on a single, isolated same network, even the independent networks extended the content of spatial reciprocity. However, the individual diversity, including gender, wealth and social status and so on, usually is presented within the population. Individual heterogeneity impacts on the evolution of cooperation amongst selfish individuals. With this motivation, here we consider that two forms including Prisoner's Dilemma (PD) and Snowdrift Game (SG) take place on interdependent weighted networks via the mixed-coupling in which individuals participate in different networks of interactions, cooperative behaviour can be maintained. Remarkably, the numerical analysis shows that, as the network interdependence considering individual diversity increases, cooperation thrives on one network joining in PD, the other engaging in SG may be plagued by defectors. Meanwhile, there exists an optimal region of mixed-coupling between networks to persist in cooperation of one network. Furthermore, individual diversity may be a link between non-trivial systems across the network connection, thus probing in how to schedule heterogeneous competitive tasks and services in complex manufacturing systems.