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.

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.

Crowdsourcing, which decomposes tasks or projects through the internet platform and outsources them to a large number of people, has gained significant academic and industry interest due to its efficiency. Although prior theoretical studies have employed evolutionary game theory to study crowdsourcing systems, existing studies have predominantly focused on the game interactions between crowdsourcing worker and requester, often neglecting the platform as a stakeholder. Here we propose an evolutionary game model for tripartite crowdsourcing, accounting for bounded rationality and potential collusion between platform and crowdsourcing worker, with incentives designed to counteract free-riding and deceptive feedback. Our theoretical results indicate that the system can achieve a desired state where worker is certain to choose to provide high-quality work, platform is certain to implement diligent monitoring, and requester is certain to adopt an integrity strategy. Moreover, when the platform consistently adopts the monitoring strategy, the system exhibits oscillatory dynamics, with the probabilities of the worker providing high-quality work and the requester adopting an integrity strategy fluctuating within a bounded interval. Finally, we present numerical examples to validate our theoretical results.

Agents usually adjust their strategic behaviors based on their own payoff and aspiration in gaming environments. Hence, aspiration-based learning rules play an important role in the evolutionary dynamics in a population of competing agents. However, there exist different options for how to use the aspiration information for specifying the microscopic learning rules. It is also interesting to investigate under what conditions the aspiration-based learning rules can favor the emergence of cooperative behavior in population games. A new learning rule, called as "Satisfied-Cooperate, Unsatisfied-Defect," is proposed here, which is based on aspiration. Under this learning rule, agents prefer to cooperate when their income is satisfied; otherwise, they prefer the strategy of defection. We introduce this learning rule to a population of agents playing a generalized two-person game. We, respectively, obtain the mathematical conditions in which cooperation is more abundant in finite well-mixed, infinite well-mixed, and structured populations under weak selection. Interestingly, we find that these conditions are identical, no matter whether the aspiration levels for cooperators and defectors are the same or not. Furthermore, we consider the prisoner's dilemma game (PDG) as an example and perform numerical calculations and computer simulations. Our numerical and simulation results agree well and both support our theoretical predictions in the three different types of populations. We further find that our aspiration-based learning rule can promote cooperation more effectively than alternative aspiration-based learning rules in the PDG.

Promoting cooperation among conflicting entities in human society and intelligent systems is a formidable task. One potential solution could involve the formulation of incentives designed to decrease the benefits of noncooperators and/or increase the rewards for cooperators. We put forth a novel incentive approach, specifically, a guidance strategy where certain cooperators willingly bear a cost to alter the actions of agents who intend to defect prior to the actual commencement of a game. We introduce an innovative game-theoretical framework that sheds light on the dynamics of guidance strategies, encompassing both peer guidance and pool guidance. Under the peer guidance scheme, each guider independently incurs the cost to influence agents intending to defect, whereas in the pool guidance scheme, guiders organically establish an institution to influence agents prone to free riding. Regardless of whether a peer or pool guidance scheme is utilized, the implementation of a guidance strategy has proven to be remarkably effective in reducing the instances of pure cooperation, also known as second-order free riding. Intriguingly, our result suggests that the pool guidance strategy demonstrates a more potent deterrent effect on second-order free-riding behavior than the peer guidance strategy, particularly when the cost of guidance is exceptionally high. These findings underscore the significance of preguidance in fostering cooperation in human and multiagent AI systems and could offer valuable insights for the development of a regulatory mechanism for preemptive guidance and subsequent punishment.

Recently, reputation-based indirect reciprocity has been widely applied to the study on fairness behavior. Previous works mainly investigate indirect reciprocity by considering compulsory participation. While in reality, individuals may choose voluntary participation according to the opponent's reputation. It is still unclear how such reputation-based voluntary participation influences the evolution of fairness. To address this question, we introduce indirect reciprocity with voluntary participation into the dictator game (DG). We respectively consider good dictators or recipients can voluntarily participate in games when the opponents are assessed as bad. We theoretically calculate the fairness level under all social norms of third-order information. Our findings reveal that several social norms induce the high fairness level in both scenarios. However, more social norms lead to a high fairness level for voluntary participation of recipients, compared with the one of good dictators. The results also hold when the probability of voluntary participation is not low. Our results demonstrate that recipients’ voluntary participation is more effective in promoting the emergence of fairness behavior.

Utilizing common resources is always a dilemma for community members. While cooperator players restrain themselves and consider the proper state of resources, defectors demand more than their supposed share for a higher payoff. To avoid the tragedy of the common state, punishing the latter group seems to be an adequate reaction. This conclusion, however, is less straightforward when we acknowledge the fact that resources are finite and even a renewable resource has limited growing capacity. To clarify the possible consequences, we consider a coevolutionary model where beside the payoff-driven competition of cooperator and defector players the level of a renewable resource depends sensitively on the fraction of cooperators and the total consumption of all players. The applied feedback-evolving game reveals that beside a delicately adjusted punishment it is also fundamental that cooperators should pay special attention to the growing capacity of renewable resources. Otherwise, even the usage of tough punishment cannot save the community from an undesired end.