Emergence Of Cooperation And Self-organization In Complex Systems

Collective behaviors of abundant individuals in complex systems, including emer-gence of cooperation and self-organized patterns, have received increasing attention in the area of sociology, biology and physics. This thesis investigates the collective behav-iors among selfish individuals and competing species in the framework of evolutional game and complex network theory. Besides, the transmission of information on com-plex networks, such as opinion spreading and rating systems, is also discussed. There are three parts in this thesis.First of all, self-organized patterns and biodiversity are investigated in a ecological game, consisting of following three point:1. In a ecology system with three competing species playing rock-paper-scissors game, target waves emerge with incorporating a periodic current of the three species in a small area located at the center. The periodic current acts as a pacemaker, which able to nucleate target waves spreading across the whole population even in the random initial conditions. As a result, the target wave arises finally owing to periodic oscilla-tions of three species'density in both local area and the whole system. Three route toward target waves are observed:synchronization between the periodic current and oscillations of the density of the three species, intermittent synchronization, and non-synchronization. We show the mechanisms of emergence of self-organized pattern due to the interplay between local and global dynamics in a ecology system where three competing species playing the rock-paper-scissors game.2. If there are no periodic current, but instead of regular initial conditions with three competing species distributing in ordered, single-armed spiral, multi-armed spi-rals the pair of spirals and anti-spirals are observed. It is found that the single-armed spiral is more stable than the multi-armed spirals, while the multi-armed spirals is more stable than the pair of spiral and anti-spirals with the same number of arms.3. We also study effects of interaction intensity on the biodiversity and self- organized patterns. When individuals move slowly, large and small interaction in-tensities promote biodiversity so that all species coexist. Large interaction intensities in particular ensure this by evoking ordered spiral waves traveling across the spatial grid. Conversely, medium interaction intensities jeopardize biodiversity and indeed prohibit coexistence of the three species. When mobility of individuals is high, on the other hand, only small interaction intensities are able to sustain biodiversity while large interaction intensities fail. By considering heterogeneous initial distributions of the three species, we observe a critical influence of interaction intensity on spiral wave formation. In particular, globally ordered spiral waves can be observed only for inter-action intensities that are below a critical value. Once above, the spiral waves break up and form disordered spatial structures. This work thus indicates that interaction in-tensity is vital for the sustenance of biodiversity and emergence of pattern formation in ecosystems governed by cyclical interactions.Secondly, cooperation among selfish individuals and its self-organized structure are studied in the framework of spatial game, containing the following three aspects:1. We investigate the role of adaptive migration in spatial prisoners'dilemma game and the snowdrift game where selfish individuals apply an alternative migration strategy requiring only local information obtainable through game interactions. It is found that adaptive migration can be effective in promoting cooperation in two ways. First, there exists optimal population density leading to the highest cooperation level. Second, adaptive migration can induce an outbreak of cooperation from an environ-ment dominated by defectors.2. Based on the prisoners'dilemma game, we introduce a regulation strength of payoff to reduce the heterogeneity of the distribution of all such payoffs. There exists an optimal regulation strength, which leads to the cooperation optimally promoted, and the promotive effect disappears if the heterogeneity is regulated to be either too weak or too strong. We find that cooperators on the spatial grid are not isolated but form compact clusters, and the distribution of these clusters is crucial for the promotion of cooperation.3. Working together in groups may be beneficial with respect to isolated efforts. Yet this is true only if all group members contribute to the success. If not, group ef-forts may become detrimental on individual prosperity. Here we study the evolution of cooperation in public goods games on scale-free networks that are subject to dele-tion of links connected to the highest degree individuals, e.g., under attack. We focus on situations where either only a single group is considered for payoff evaluation or all groups with which a given player is affiliated. While in single-group public goods games there exist an optimal number of removed links for which cooperation thrives best, the effect is monotonously negative for multi-group public goods games. The findings are explained via wealth distributions and analytical approximations, confirm-ing that socially diverse states are crucial for the successful evolution of cooperation.Last but not least, opinion dynamics and reputation systems are discussed based on the complex networks theory:1. The influence of the self-affirmation on opinion dynamics is investigated in a directed small-world social network. The system displays a non-equilibrium phase transition from a consensus state to a disordered state with coexistence of opinions. The density of long-range-directed interactions and the strength of self-affirmation strongly affect opinion dynamics. When the long-range-directed interactions are sparse and individual generally does not insist on its opinion, the system will undergo a continuous phase transition, in the opposite case with strong self-affirmation and dense long-range-directed interactions, the system does not display a phase transition. Between those two extreme cases, a discontinuous phase transition emerges in the system.2. How to rank web pages, scientists and online resources has recently received increasing attention ranging from computer scientists to physicists. We study the rank-ing problem of rating systems where objects are voted by users with discrete ratings. An algorithm is proposed that can simultaneously evaluate the user reputation and ob-ject quality in an iterative refinement way. Ranking accuracy is considerably improved by our algorithm in both the artificially generated data and the real data from Movie-Lens and Amazon. We provide a new way to evaluate and compare the performances of different reputation systems.