Coevolutionary Games On Complex Networks

Complex networks effectively characterize the connections among individuals in natural and social complex systems. Evolutionary game theory as a branch of science studying the strategies and decisions, has perfectly captured the essence in strategy choice and evolution in interactions among sel?sh individuals. Combination of complex networks and evolutionary game theory has provided a powerful theoretical framework to depict and address issues concerning relations and interactions among individuals in complex systems. And it has attracted wide attentions in the ?elds of physics, biology,sociology, psychology, and engineering. As a natural extension of evolutionary game theory, coevolutionary game considers the coevolution of game strategies and external environment or other mechanisms. Inspired by the international research interests, this dissertation focuses on the evolution and coevolution of cooperation strategy in prisoner’s dilemma game and public goods game played on complex networks, concerning aspects of network structure, coevolutionary mechanisms, and time scale in covolutionary games. Contributions of this dissertation are as follows:1. We investigate the robustness of cooperation on highly clustered scale free networks. Previous researches have shown that scale free networks and clustering coeffcient favor cooperation. We introduce the strategy mutation into evolution to check the robustness of cooperation when error occurs in strategy propagation. It is found that cooperation is more sensitive and vulnerable to strategy mutation in more highly clustered networks. Only if the mutation rate is relatively low can clustering coeffcient promote cooperation. When mutation rate is high, cooperation level is signi?cantly reduced. By inspecting the fraction of cooperators in nodes of different degrees, it is found when mutation is high enough to affect the hub node in the network, clustering coeffcient promotes the spreading of defection.2. A reputation based migration model is proposed to study the effect on cooperation. Mobility of individual has been considered as an important coevolutionary mechanism promoting cooperation. Mobility patterns in previous works are either random-like, or driven by payoff-related properties or aspirations. Inspired by the significant in?uences of reputation on strategy choice in real world interactions, we propose a reputation-based model to explore the effect of migration on cooperation in the contest of the prisoner’s dilemma game. In this model, individuals earn their reputation scores through previous cooperative behaviors. An individual tends to migrate to a new place if he has a neighborhood of low reputation. We show that cooperation is promoted for relatively large population density and not very large temptation to defect. A higher mobility sensitivity to reputation is always better for cooperation. A longer reputation memory favors cooperation, provided that the corresponding mobility sensitivity to reputation is strong enough. By inspecting the snapshot of time evolution, we provide a microscopic explanation for the observed results.3. We explore the effects of time scales in the coevolution of networks and strategies.Most previous studies concerning spatial games have assumed strategy updating occurs with a ?xed ratio relative to interactions. We here set up a coevolutionary model to investigate how different ratio affects the evolution of cooperation on adaptive networks.In each round, an individual plays game with the opponent, and severs the link to the opponent with a probability dependent on opponent’s strategy and rewires the link to others. After a tunable number of rounds, strategy updating occurs synchronously for all individuals. Results show that slower natural selection enhances cooperation. Meanwhile, slower selection induces larger network heterogeneity. Strong selection contracts the parameter area where cooperation thrives. Slow and weak selection provides enough chances for individuals to adapt to the environment, and thus cooperation is enhanced.In?uences of different initial networks and the cost of rewiring have also been checked.4. We study the in?uence of institutional punishment and reward on cooperation.Punishment and reward are important mechanisms promoting cooperation. Previous studies either check the effects of them in separate or regard them as different individuals or institutions and make the comparison. We have proposed a model to investigate how institutional punishment and reward affect the evolution of cooperation in PGG played in a well-mixed ?nite population. Institution splits the funds it acquires into two parts that are used to both punishing free-riding players and rewarding its members. We mainly focus on the effect of different splitting ratios. Results show that it is essential for the institution to utilize punishment to suppress defective members and on the other hand, to reward its cooperative members to support cooperation. There exists an optimal ratio leading to maximum cooperation.