Xiaojie Chen

Feedback between game strategies and environmental states is common in human--natural systems. Existing studies have reported several interesting dynamical behaviors by studying the impact of environmental state on strategy selection. In this paper we construct a characterization of environmental states, assuming that environmental states are determined by local and global environmental states. Based on this we construct a spatial multiagent coevolutionary model to describe the strategy evolution of populations and analyze the model's dynamics by means of Monte Carlo simulations and mean-field approximation. We find that spatial structure can enhance the system stability, preventing the emergence of complex dynamical behaviors such as chaos. Furthermore, we incorporate a diffusion mechanism into the model. Results show that resource diffusion accelerates strategy switching by weakening differences in local environmental states. Numerical results further indicate that spatial structure significantly affects the system stability: the system self-organizes into stable spatial structures analogous to Turing patterns, thus enhancing the system stability. This study investigates the mechanisms by which environmental states and spatial structures influence system stability, offering new insights into understanding the coevolutionary dynamics in real-world systems.

In recent years, the coevolutionary dynamics between game strategies and environmental states have attracted considerable attention. Most existing relevant studies focus on well-mixed populations or regular lattices and have yet to systematically investigate strategy-environment coevolutionary dynamics on complex spatial structures. In this work, we construct spatially embedded networks with three typical degree distributions (delta, Poisson, and power-law distributions), based on which we establish a multi-agent coevolutionary model with local and global environmental feedbacks. Using Monte Carlo simulations, we investigate the impacts of degree heterogeneity, average degree, and random connectivity on system dynamics. Simulation results show that the degree distribution significantly alters the system’s dynamical behaviors. Among the three network topologies, homogeneous-degree networks are most conducive to dynamical stability. Moreover, average degree exerts a universal effect across all networks: cooperation level follows a unimodal trend, increasing first and then decreasing as average degree increases, with the maximum achieved at an intermediate average degree. This study explores how spatially embedded networks shape coevolutionary game dynamics and offers insights into the evolution of cooperation in complex adaptive systems.

The reporting phenomenon is ubiquitous in human society. However, how reporting-triggered institutional incentives influence public cooperation remains theoretically unresolved. Here, we construct a public goods game where individuals adopt one of three strategies: report, cooperate, and defect. In this game, cooperators and reporters contribute a cost to the common pool, whereas defectors make no contribution. Furthermore, each reporter pays a monitoring cost to detect defection and subsequently report it to the institution. Upon receiving a report, the institution will punish defectors and reward reporters with a response probability, irrespective of the number of reporters. We introduce the proposed game into a structured population and analytically derive the average fractions of cooperators, defectors, and reporters in the weak-selection limit by using the coalescing random walk method. We demonstrate that increasing the institutional response probability, reward intensity, or punishment intensity elevates the average fraction of reporters and reduces that of defectors, while keeping the average fraction of cooperators invariant. We further determine the conditions under which reporters are favored by natural selection, reporters are favored over cooperators, and contributors, including cooperators and reporters, prevail, respectively. We find that only when institutional incentives adequately offset the costs of contribution and monitoring can reporters gain an evolutionary advantage and contributors become dominant in the population. Notably, our main results remain robust under a group-dependent implementation rule, where the probability of implementing institutional incentives depends on the number of reporters in the group. Finally, these theoretical predictions are validated by numerical simulations.

The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic properties in structured populations, derive theoretical conditions for cooperation, and identify the optimal game distribution for promoting cooperation. To address these issues, we propose the variable game framework in a structured population, where the game interactions between different individuals change over time. By means of the Markov chain and the pair approximation method, we derive theoretical conditions under which cooperation is favored by natural selection and when it is favored over defection under weak selection. Furthermore, we, respectively, formulate and solve two optimization problems to determine the optimal game distribution that most effectively fosters the evolution of cooperation by maximizing the gradient of cooperation selection and minimizing the fitness difference between defectors and cooperators. The theoretical predictions regarding both the conditions for cooperation and optimal game distribution are further validated by numerical calculations and extensive Monte Carlo simulations. Our findings offer novel insights into the mechanisms driving cooperative behavior in complex systems and provide theoretical guidance for designing optimal game environments that facilitate the evolution of cooperation.

In this article, we study the quasi-synchronization problems in multiplex networks under deception attacks. First, we propose a new model of multiplex networks with interlayer couplings under deception attacks. We assume that the attackers inject false data into the communication channels. Since interlayer couplings are taken into account, we consider not only the case where attacks occur in the intralayer channels, but also the case where attacks occur in the interlayer communication channels. Furthermore, we set two binary variables obeying a random Bernoulli distribution to characterize whether the attacks occur or not. We then design an impulsive controller to enable the nodal states to achieve the desired states. By means of the Lyapunov function method and the average impulsive interval method, we obtain the sufficient conditions under which the nodal states can achieve interlayer quasi-synchronization and intralayer quasi-synchronization, respectively. Naturally, we obtain the sufficient conditions under which the nodal states can achieve complete quasi-synchronization. Furthermore, we introduce a leader and design a different impulsive controller. Using the same theoretical approach, we derive the sufficient conditions under which the nodal states can achieve complete quasi-synchronization. Finally, we provide three numerical examples to confirm the theoretical results.

Institutional punishment is widely used to promote cooperation, yet most existing studies assume that institutions can perfectly identify individual strategies. Under this idealized assumption, cooperators are typically trusted and exempt from monitoring, while sanctions are imposed exclusively on known defectors, thereby neglecting the informational imperfections inherent in real-world governance. To address these limitations, we adopt the zero-trust principle of “never trust, always verify” and develop a zero-trust institutional framework, in which all individuals are subject to uniform monitoring, and sanctions are applied only upon the actual detection of defection. Given that institutional enforcement intensity in practice is rarely static, we further introduce enforcement intensity as an endogenous variable into the Prisoner’s Dilemma game and construct a coevolutionary model in which the enforcement intensity and population state are mutually coupled through a closed feedback loop; that is, higher cooperation levels drive the growth of enforcement, while prevalence of defection leads to institutional relaxation. Under fixed and adaptive enforcement intensities, our theoretical and numerical results reveal distinct evolutionary outcomes characterized by different stable equilibria. Finally, by devising the institutional cost functions, we demonstrate that under fixed enforcement, zero-trust punishment outperforms non-zero-trust one in terms of long-run cost-efficiency at intermediate levels of enforcement. Under adaptive zero-trust enforcement, increasing enforcement responsiveness to population state reduces long-run costs when enforcement itself is relatively inexpensive, albeit with diminishing marginal returns, whereas excessive responsiveness increases overall governance costs when enforcement is expensive.