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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 combined the imitation-driven update rule and the average payoff-driven update rule in the finite populations with positive assortment. • We studied the evolution of cooperative behavior in one-shot and iterated Prisoner 's dilemma game. • The results show that the effectiveness of the average payoff-driven update rule for the promotion of cooperation depends on the reciprocity mechanism. Aspiration-driven or imitation? Which one is most effective for the promotion of cooperation? There is a lot of interest that being brought to this issue. In this paper, we investigate the evolutionary outcomes with a stochastic evolutionary game dynamic that combined the imitation update rule and the average payoff-driven update rule in finite populations, in which both one-shot and iterated Prisoner's dilemma game with positive assortment are implemented. The average abundance of cooperators is obtained through the transition probabilities and the properties of Markov chain. Both numerical and analytical results show that the effectiveness of the average payoff-driven update rule for the promotion of cooperation depends on whether there is a reciprocity mechanism in the system. In detail, average payoff-driven update rule is better than imitation update rule only when our model has one of the following three conditions: (1) small probability of the positive assortment; (2) small probability to the next round; (3) small probability of knowing one's reputation. If the above conditions are not satisfied, then imitation update rule is most effective for the promotion of cooperation. We thus provide a deeper understanding for the effectiveness of these rules regarding the promotion of cooperation. [ABSTRACT FROM AUTHOR]