Significance: The evolution of cooperation has a formative role in human societies—civilized life on Earth would be impossible without cooperation. However, it is unclear why cooperation would evolve in the first place because Darwinian selection favors selfish individuals. After struggling with this problem for >150 y, recent scientific breakthroughs have uncovered multiple cooperation-promoting mechanisms. We build on these breakthroughs by examining whether two widely known cooperation-promoting mechanisms—network reciprocity and costly punishment—create synergies in a social dilemma experiment. While network reciprocity fulfilled its expected role, costly punishment proved to be surprisingly ineffective in promoting cooperation. This ineffectiveness suggests that the rational response to punishment assumed in theoretical studies is overly stylized and needs reexamining.

Mining communities or clusters in networks is valuable in analyzing, designing, and optimizing many natural and engineering complex systems, e.g., protein networks, power grid, and transportation systems. Most of the existing techniques view the community mining problem as an optimization problem based on a given quality function(e.g., modularity), however none of them are grounded with a systematic theory to identify the central nodes in the network. Moreover, how to reconcile the mining efficiency and the community quality still remains an open problem. In this paper, we attempt to address the above challenges by introducing a novel algorithm. First, a kernel function with a tunable influence factor is proposed to measure the leadership of each node, those nodes with highest local leadership can be viewed as the candidate central nodes. Then, we use a discrete-time dynamical system to describe the dynamical assignment of community membership; and formulate the serval conditions to guarantee the convergence of each node's dynamic trajectory, by which the hierarchical community structure of the network can be revealed. The proposed dynamical system is independent of the quality function used, so could also be applied in other community mining models. Our algorithm is highly efficient: the computational complexity analysis shows that the execution time is nearly linearly dependent on the number of nodes in sparse networks. We finally give demonstrative applications of the algorithm to a set of synthetic benchmark networks and also real-world networks to verify the algorithmic performance.

In many electronic commerce systems, detecting significant clusters is of great value to the analysis, design, and optimization of the commerce behaviors. In this article, we propose a new dynamical approach to detect the cluster configuration fast and accurately which can be applied to electronic commerce systems. First, we analyze the two-stage game in which the leader group members make contributions prior to the follower group, and propose an exact index, i.e., the leadership, to characterize the key leaders. Then an efficient dynamical system is used to guarantee the cluster configuration converges to an optimal state, which assigns each node to the corresponding cluster based on quality optimization, repeatedly. Our method is of high efficiency-the exponential term in the proposed dynamical system makes the convergence to be very fast with a nearly linear time. Extensive experiments on multiple types of datesets demonstrate the state-of-the-art performance of proposed method.

With the explosion of social media networks, many modern applications are concerning about people's connections, which leads to the so-called social computing. An elusive question is to study how opinion communities form and evolve in real-world networks with great individual diversity and complex human connections. In this paper, we attempt to model a realistic social media network as a discrete-time dynamical system, where the opinion matrix and the community structure could mutually affect each other. The community detection in social media networks is naturally formulated as a multi-objective optimization problem, i.e., finding a set of densely connected components with similar opinion vectors. We propose a novel and powerful graph K-means framework, which is composed of three coupled phases in each discrete-time period. Specifically, the first phase uses a fast heuristic approach to identify those opinion leaders who have relatively high local reputation; the second phase adopts a novel dynamic game model to find the locally Pareto-optimal community structure; the final phase employs a robust opinion dynamics model to simulate the evolution of the opinion matrix. We conduct a series of comprehensive experiments on real-world benchmark networks to validate the performance of GK-means through comparisons with the state-of-the-art graph clustering technologies.