Classification-based prediction of network connectivity robustness.

Today, there is an increasing concern about malicious attacks on various networks in society and industry, against which the network robustness is critical. Network connectivity robustness, in particular, is of fundamental importance, which is generally measured by a sequence of calculated values that indicate the connectedness of the remaining network after a sequence of attacks by means of node- or edge-removal. It is computationally time-consuming, however, to measure and evaluate the network connectivity robustness using the conventional attack simulations, especially for large-scale networked systems. In the present paper, an efficient robustness predictor based on multiple convolutional neural networks (mCNN-RP) is proposed for predicting the network connectivity robustness, which is an natural extension of the single CNN-based predictor. In mCNN-RP, one CNN works as the classifier, while each of the rest CNNs works as an estimator for predicting the connectivity robustness of every classified network category. The network categories are classified according to the available prior knowledge. A data-based filter is installed for predictive data refinement. Extensive experimental studies on both synthetic and real-world networks, including directed and undirected as well as weighted and unweighted topologies, verify the effectiveness of mCNN-RP. The results demonstrate that the average prediction error is lower than the standard deviation of the tested data, which outperforms the single CNN-based framework. The runtime in assessing network connectivity robustness is significantly reduced by using the CNN-based technique. The proposed mCNN-RP not only can accurately predict the connectivity robustness of various complex networks, but also provides an excellent indicator for the connectivity robustness, better than other existing prediction measures.

Cooperative Mining in Blockchain Networks With Zero-Determinant Strategies.

In proof-of-work (PoW)-based blockchain networks, the miners contribute their distributed computation in solving a crypto-puzzle competition to win the reward. To secure stable profits, some miners organize mining pools and share the rewards from the pool in proportion to each miner's contribution. However, some miners may exhibit malicious behaviors which cause a waste of distributed computation resource, even posing a threat on the efficiency of blockchain networks. In this paper, we propose a new game-theoretic framework to incentivize miners mining honestly and help to bring about a higher total welfare of blockchain networks. We first formulate the mining process as a noncooperative iterated game. We then propose a mechanism in terms of zero-determinant strategies (ZD strategies) to encourage the cooperative mining and improve the efficiency of mining in PoW-based blockchain networks. In addition, we theoretically analyze the maximum system welfare of the target pool through the method of optimization. Numerical illustrations are also presented to support our theoretical results.

Asymmetric Game: A Silver Bullet to Weighted Vertex Cover of Networks.

Weighted vertex cover (WVC), a generalized type of vertex cover, is one of the most important combinatorial optimization problems. In this paper, we provide a novel solution to the WVC problem from the view of network engineering. We model the WVC problem as an asymmetric game on weighted networks, where each vertex is treated as an intelligent rational agent rather than an inanimate one. Under the framework of asymmetric game, we find that strict Nash equilibriums of the asymmetric game are the intermediate states between the WVC states and the minimum WVC (MWVC) states. Besides, we propose best response algorithms with memory and feedback to solve the WVC problem, and find that a better approximate solution to the MWVC can be obtained under the feedback-based best response algorithm. Numerical illustrations verify the performance of the proposed game solution on weighted networks. Our findings pave a new way to solve the WVC problem from the perspective of asymmetric game, which opens a bottom-up avenue to address the combinatorial optimization problems.

When Reputation Enforces Evolutionary Cooperation in Unreliable MANETs.

In self-organized mobile ad hoc networks (MANETs), network functions rely on cooperation of self-interested nodes, where a challenge is to enforce their mutual cooperation. In this paper, we study cooperative packet forwarding in a one-hop unreliable channel which results from loss of packets and noisy observation of transmissions. We propose an indirect reciprocity framework based on evolutionary game theory, and enforce cooperation of packet forwarding strategies in both structured and unstructured MANETs. Furthermore, we analyze the evolutionary dynamics of cooperative strategies and derive the threshold of benefit-to-cost ratio to guarantee the convergence of cooperation. The numerical simulations verify that the proposed evolutionary game theoretic solution enforces cooperation when the benefit-to-cost ratio of the altruistic exceeds the critical condition. In addition, the network throughput performance of our proposed strategy in structured MANETs is measured, which is in close agreement with that of the full cooperative strategy.

Evolutionary origin of asymptotically stable consensus.

Consensus is widely observed in nature as well as in society. Up to now, many works have focused on what kind of (and how) isolated single structures lead to consensus, while the dynamics of consensus in interdependent populations remains unclear, although interactive structures are everywhere. For such consensus in interdependent populations, we refer that the fraction of population adopting a specified strategy is the same across different interactive structures. A two-strategy game as a conflict is adopted to explore how natural selection affects the consensus in such interdependent populations. It is shown that when selection is absent, all the consensus states are stable, but none are evolutionarily stable. In other words, the final consensus state can go back and forth from one to another. When selection is present, there is only a small number of stable consensus state which are evolutionarily stable. Our study highlights the importance of evolution on stabilizing consensus in interdependent populations.

Moderate intra-group bias maximizes cooperation on interdependent populations.

Evolutionary game theory on spatial structures has received increasing attention during the past decades. However, the majority of these achievements focuses on single and static population structures, which is not fully consistent with the fact that real structures are composed of many interactive groups. These groups are interdependent on each other and present dynamical features, in which individuals mimic the strategy of neighbors and switch their partnerships continually. It is however unclear how the dynamical and interdependent interactions among groups affect the evolution of collective behaviors. In this work, we employ the prisoner's dilemma game to investigate how the dynamics of structure influences cooperation on interdependent populations, where populations are represented by group structures. It is found that the more robust the links between cooperators (or the more fragile the links between cooperators and defectors), the more prevalent of cooperation. Furthermore, theoretical analysis shows that the intra-group bias can favor cooperation, which is only possible when individuals are likely to attach neighbors within the same group. Yet, interestingly, cooperation can be even inhibited for large intra-group bias, allowing the moderate intra-group bias maximizes the cooperation level.

The σ law of evolutionary dynamics in community-structured population.

Evolutionary game dynamics in finite populations provide a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call σ law, describes how to determine the selection between two competing strategies: in most evolutionary processes with two strategies, A and B, strategy A is favored over B in weak selection if and only if σR+S>T+σP. This relationship holds for a wide variety of structured populations with mutation rate and weak selection under certain assumptions. In this paper, we propose a model of games based on a community-structured population and revisit this law under the Moran process. By calculating the average payoffs of A and B individuals with the method of effective sojourn time, we find that σ features not only the structured population characteristics, but also the reaction rate between individuals. That is to say, an interaction between two individuals are not uniform, and we can take σ as a reaction rate between any two individuals with the same strategy. We verify this viewpoint by the modified replicator equation with non-uniform interaction rates in a simplified version of the prisoner's dilemma game (PDG).