Deterrence through punishment can resolve collective risk dilemmas in carbon emission games

Recent achievements in nonlinear dynamics, synchronization, and networks

This Focus Issue covers recent developments in the broad areas of nonlinear dynamics, synchronization, and emergent behavior in dynamical networks. It targets current progress on issues such as time series analysis and data-driven modeling from real data such as climate, brain, and social dynamics. Predicting and detecting early warning signals of extreme climate conditions, epileptic seizures, or other catastrophic conditions are the primary tasks from real or experimental data. Exploring machine-based learning from real data for the purpose of modeling and prediction is an emerging area. Application of the evolutionary game theory in biological systems (eco-evolutionary game theory) is a developing direction for future research for the purpose of understanding the interactions between species. Recent progress of research on bifurcations, time series analysis, control, and time-delay systems is also discussed.

Heterogeneous decision-making dynamics of threshold-switching agents on complex networks

In the classical two-player decision-making scenario, individuals may have different tendencies to take a certain action, given that there exists a sufficient number of neighbors adopting a particular option. This is ubiquitous in many real-life contexts including traffic congestion, crowd evacuation, and minimal vertex cover problem. Under best-response dynamics, we investigate the decision-making behaviors of heterogeneous agents on complex networks. Results of the networked games are twofold: for networks of uniform degree distribution (e.g., the lattice) and fraction of the strategy is of a linear function of the threshold setting. Moreover, the equilibrium analysis is provided and the relationship between the equilibrium dynamics and the change of the threshold value is given quantitatively. Next, if the games are played on networks with non-uniform degree distribution (e.g., random regular and scale-free networks), influence of the threshold-switching will be weakened. Robust experiments indicate that it is not the value of the average degree, but the degree distribution that influences how the strategy evolves affected by the threshold settings. Our result shows that the decision-making behaviors can be effectively manipulated by tuning the parameters in the utility function (i.e., thresholds) of some agents for more regular network structures.

The evolution of cooperation in the unidirectional division of labour on a tree network

Division of labour on complex networks is rarely investigated using evolutionary game theory. We investigate a division of labour where divided roles are assigned to groups on the nodes of a general unidirectional finite tree graph network. From the network's original node, a task flows and is divided along the branches. A player is randomly selected in each group of cooperators and defectors, who receives a benefit from a cooperator in the upstream group and a part of the task. A cooperator completes their part by paying a cost and then passing it downstream until the entire task is completed. Defectors do not do anything and the division of labour stops, causing all groups to suffer losses due to the incomplete task. We develop a novel method to analyse the local stability in this general tree. We discover that not the benefits but the costs of the cooperation influence the evolution of cooperation, and defections in groups that are directly related to that group's task cause damage to players in that group. We introduce two sanction systems, one of which induces the evolution of cooperation more than the system without sanctions, and promote the coexistence of cooperator and defector groups.

Evolutionary dynamics of N-player sender-receiver game in networks with community structure

Network typology largely affects the evolutionary dynamics of collective behaviors in many real-world complex systems. As a conventional transmission model, the sender-receiver game paves the way to explore the evolution of honest signals between senders and receivers. In practice, the utilities of an agent often depend not only on pairwise interactions, but also on the group influence of players around them, and thus there is an urgent need for deeper theoretical modeling and investigations on individuals' non-pairwise interactions. Considering the underlying evolutionary game dynamics and multiple community network structures, we explore the evolution of honest behaviors by extending the sender-receiver game to multiple communities. With the new dynamical model of the multi-community system, we perform a stability analysis of the system equilibrium state. Our results reveal the condition to promote the evolution of honest behaviors and provide an effective method for enhancing collaboration behaviors in distributed complex systems. Current results help us to deeply understand how collective decision-making behaviors evolve, influenced by the spread of true information and misinformation in large dynamic systems.

Evolution of conditional cooperation in collective-risk social dilemma with repeated group interactions

The evolution and long-term sustenance of cooperation has consistently piqued scholarly interest across the disciplines of evolutionary biology and social sciences. Previous theoretical and experimental studies on collective risk social dilemma games have revealed that the risk of collective failure will affect the evolution of cooperation. In the real world, individuals usually adjust their decisions based on environmental factors such as risk intensity and cooperation level. However, it is still not well understood how such conditional behaviours affect the evolution of cooperation in repeated group interactions scenario from a theoretical perspective. Here, we construct an evolutionary game model with repeated interactions, in which defectors decide whether to cooperate in subsequent rounds of the game based on whether the risk exceeds their tolerance threshold and whether the number of cooperators exceeds the collective goal in the early rounds of the game. We find that the introduction of conditional cooperation strategy can effectively promote the emergence of cooperation, especially when the risk is low. In addition, the risk threshold significantly affects the evolutionary outcomes, with a high risk promoting the emergence of cooperation. Importantly, when the risk of failure to reach collective goals exceeds a certain threshold, the timely transition from a defective strategy to a cooperative strategy by conditional cooperators is beneficial for maintaining high-level cooperation.