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Complex networks are widespread in real-world environments across diverse domains. Real-world networks tend to form spontaneously through interactions between individual agents. Inspired by this, we design an evolutionary game model in which agents participate in a prisoner's dilemma game (PDG) with their neighboring agents. Agents can autonomously modify their connections with neighbors using reinforcement learning to avoid unfavorable environments. Interestingly, our findings reveal some remarkable results. Exploiting reinforcement learning-based adaptive networks improves cooperation when juxtaposed with existing PDGs performed on homogeneous networks. At the same time, the network's topology evolves from homogeneous to heterogeneous states. This change occurs as players gain experience from past games and become more astute in deciding whether to join PDGs with their current neighbors or disconnect from the least profitable neighbors. Instead, they seek out more favorable environments by establishing connections with second-order neighbors with higher rewards. By calculating the degree distribution and modularity of the adaptive network in a steady state, we confirm that the adaptive network follows a power law and has a clear community structure, indicating that the adaptive network is similar to networks in the real world. Our study reports a new phenomenon in evolutionary game theory on networks. It proposes a new perspective to generate scale-free networks, which is generating scale-free networks by the evolution of homogeneous networks rather than typical ways of network growth and preferential connection. Our results provide new aspects to understanding the network structure, the emergence of cooperation, and the behavior of actors in nature and society. [ABSTRACT FROM AUTHOR]

• Aspiration-based exit option in prisoners dilemma game can promote cooperation. • In structured population, the intermediate aspiration level promotes cooperation, because defectors around the cooperative cluster exit the game, which weakens the exploitation of cooperators, and help the cooperators at the edge of the cooperative cluster to expand to inactive nodes or the defectors through network reciprocity. • The combined effect of aspiration level and dilemma strength affects the active state of players. Cooperation is promoted in the structured population when individual has the exit option and it is found that aspiration driven updating rules can also promote cooperation to a certain extent. The right to exit gives individuals the opportunity to get rid of exploitation, and the aspiration is the self-evaluation of individuals. Stimulated by these, we study the effect of aspiration driven exit on cooperation in the spatial prisoner dilemma game. In the game, the aspiration level and payoff of interactive determine the individual's state. When the individual gets more than aspiration level by interacting with other players, the individual will continue to participate in the game as an active player. On the contrary, when the payoff is lower than the aspiration level, individual exits the game as an inactive player. At the same time, inactive player who exits from the game will get random payoff and pay a certain cost. The promotion of cooperative behavior mainly depends on the aspiration level of players. An appropriate level of aspiration will lead to a high cooperation, which is based on the formation of cooperative clusters. These cooperators can get rid of the invasion of defectors, even if there is a great temptation of defection, this is because the inactive defectors who exit have cut off the interaction between the cooperative cluster and the defectors. Our research provides a feasible way to solve the social dilemma and will stimulate further application. [ABSTRACT FROM AUTHOR]

• We consider the repeated pairwise prisoner's dilemma game among two groups of agents. • We found that the mixed strategy-update rule (Q-learning-based update rule and Fermi-function-based update rule) can evaluate cooperation. • If the proportion of AI is moderate, cooperators among the whole population exhibit conditional behavior and moody conditional behavior. Recent studies show that different update rules are invariant regarding the evolutionary outcomes for a well-mixed population or homogeneous network. In this paper, we investigate how the Q-learning algorithm, one of the reinforcement learning methods, affects the evolutionary outcomes in square lattice. Especially, we consider the mixed strategy update rule, among which some agents adopt Q-learning method to update their strategies, the proportion of these agents (these agents are denoted as Artificial Intelligence (AI)) is controlled by a simple parameter ρ. The rest of other agents, the proportion is denoted by 1 − ρ, adopt the Fermi function to update their strategies. Through extensive numerical simulations, we found that the mixed strategy-update rule can facilitate cooperation compared with the pure Fermi- function-based update rule. Besides, if the proportion of AI is moderate, cooperators among the whole population exhibit conditional behavior and moody conditional behavior. However, if the whole population adopts the pure Fermi-function-based strategy update rule or the pure Q-learning-based strategy update rule, then cooperators among the whole population exhibit the hump-shaped conditional behavior. Our results provide a new insight to understand the evolution of cooperation from AI's view. [ABSTRACT FROM AUTHOR]

Information exchange has a significant influence on human behaviour decision-making. To explore the impact of the information exchange mechanism on the evolution of cooperative behaviour on the complex networks, we establish two-layer interdependent networks. Individuals have a certain probability of having information exchange with individuals on another network. In detail, when individuals residing on different networks are connected by links, the update of strategies not only depends on their own payoffs, but also depends on the strategy selections of the corresponding nodes and neighbours on the other network. Numerous simulations reveal that high cooperation level can be achieved for a large coupling probability and intermediate heterogeneity. Counter-intuitively, cooperation is not always promoted by the expansion of information sources. Our study thus enhances the understanding of the evolution of cooperation on interdependent networks. • We explore the effect of information exchange for the evolution of cooperation on interdependent networks. • Information exchange is a double-edged sword for cooperation. • Large coupling density warrants strongest location synchronization effect for cooperation. [ABSTRACT FROM AUTHOR]