Game theory has long been applied in multidisciplinary fields such as economics, the military, and the evolution of species, etc. Evolutionary game theory generalizes natural selection into game theory to understand cooperative behaviors and the evolution of populations. Current research reveals that the competition between egoistic and altruistic behaviors seems contradictory but actually shares the same internal motivation. Complex networks, as a rising topic that help to study the stochastic interaction patterns of individuals, provide an excellent framework for the research on social behaviors with stochasticity. The network structure formed by relations between individuals is found to have a crucial impact on the emergence of cooperation. Overall, evolutionary game theory and stochastic modeling on complex networks have been widely developed and acted as powerful tools to analyze structural species evolution, economic competition, and many other problems involving complex systems with stochasticity in reality.In this Research Topic, we aim to address the emergence, evolution, and phase transition of social behaviors and the stochastic modeling of complex networks. Our method primarily focuses on stochastic network modeling and the spatial evolutionary game theory to model and explain the emergence and maintenance of social behaviors with stochasticity, where complex networks characterize the structure of the system and games describe the interaction properties between individuals. In addition, the evolutionary games and stochastic modeling on complex networks have recently yielded many fruitful results. For example, Hauert and Doebeli extended the analysis of cooperation in social dilemmas from well-mixed populations to structured populations and found that spatial structure has important and diverse impacts on evolutionary diversification in continuous prisoner's dilemmas and snowdrift games. Wang and Perc performed a mean field analysis of the public goods games with bilateral costly expulsion, revealing a fascinating new path to public cooperation and showing that the costs of well-intended actions need not be low to be effective. Tajeuna et al. proposed a novel model to simulate the evolution of the community structure and utilized survival analysis techniques to predict the future changes the community may undergo. Oldham et al. derived a new formalism that more accurately captured the competing pressures of wiring cost minimization and topological complexity, and the findings indicated that stochastic models offered an incomplete account of connectome organization.This Research Topic publishes research in the field of complex networks and evolutionary games, which covers subjects including stochastic network modeling, strategy dynamics, social behavior, and fixation probability. This Research Topic focuses on the influence of network topology and evolution rules on population strategies, and the co-evolution of network structure and social behaviors. The primary interest of this Research Topic includes novel mathematical modeling and analysis of complex networks or evolutionary games, along with detailed simulation and discussion. Contributions with real-world data sets and applications are encouraged. Specifically, potential topics of interest to this Research Topic include but are not limited to the following:• Evolutionary game theory on complex networks• Stochastic modeling on complex networks• Topological properties of complex networks• Evolution mechanism of complex networks• Applications of complex networks and evolutionary games• How cooperation emerges and maintains on complex networks• Strategy and structure co-evolution on complex networks• How evolution mechanism affects individual behaviors on complex networks
Game theory has long been applied in multidisciplinary fields such as economics, the military, and the evolution of species, etc. Evolutionary game theory generalizes natural selection into game theory to understand cooperative behaviors and the evolution of populations. Current research reveals that the competition between egoistic and altruistic behaviors seems contradictory but actually shares the same internal motivation. Complex networks, as a rising topic that help to study the stochastic interaction patterns of individuals, provide an excellent framework for the research on social behaviors with stochasticity. The network structure formed by relations between individuals is found to have a crucial impact on the emergence of cooperation. Overall, evolutionary game theory and stochastic modeling on complex networks have been widely developed and acted as powerful tools to analyze structural species evolution, economic competition, and many other problems involving complex systems with stochasticity in reality.In this Research Topic, we aim to address the emergence, evolution, and phase transition of social behaviors and the stochastic modeling of complex networks. Our method primarily focuses on stochastic network modeling and the spatial evolutionary game theory to model and explain the emergence and maintenance of social behaviors with stochasticity, where complex networks characterize the structure of the system and games describe the interaction properties between individuals. In addition, the evolutionary games and stochastic modeling on complex networks have recently yielded many fruitful results. For example, Hauert and Doebeli extended the analysis of cooperation in social dilemmas from well-mixed populations to structured populations and found that spatial structure has important and diverse impacts on evolutionary diversification in continuous prisoner's dilemmas and snowdrift games. Wang and Perc performed a mean field analysis of the public goods games with bilateral costly expulsion, revealing a fascinating new path to public cooperation and showing that the costs of well-intended actions need not be low to be effective. Tajeuna et al. proposed a novel model to simulate the evolution of the community structure and utilized survival analysis techniques to predict the future changes the community may undergo. Oldham et al. derived a new formalism that more accurately captured the competing pressures of wiring cost minimization and topological complexity, and the findings indicated that stochastic models offered an incomplete account of connectome organization.This Research Topic publishes research in the field of complex networks and evolutionary games, which covers subjects including stochastic network modeling, strategy dynamics, social behavior, and fixation probability. This Research Topic focuses on the influence of network topology and evolution rules on population strategies, and the co-evolution of network structure and social behaviors. The primary interest of this Research Topic includes novel mathematical modeling and analysis of complex networks or evolutionary games, along with detailed simulation and discussion. Contributions with real-world data sets and applications are encouraged. Specifically, potential topics of interest to this Research Topic include but are not limited to the following:• Evolutionary game theory on complex networks• Stochastic modeling on complex networks• Topological properties of complex networks• Evolution mechanism of complex networks• Applications of complex networks and evolutionary games• How cooperation emerges and maintains on complex networks• Strategy and structure co-evolution on complex networks• How evolution mechanism affects individual behaviors on complex networks