Cooperative behavior in evolutionary snowdrift games with the unconditional imitation rule on regular lattices

Cooperation in Social Dilemmas: A Group Game Model with Double-Layer Networks

The combination of complex networks and game theory is one of the most suitable ways to describe the evolutionary laws of various complex systems. In order to explore the evolution of group cooperation in multiple social dilemmas, a model of a group game with a double-layer network is proposed here. Firstly, to simulate a multiplayer game under multiple identities, we combine a double-layer network and public goods game. Secondly, in order to make an individual’s strategy selection process more in line with a practical context, a new strategy learning method that incorporates individual attributes is designed here, referred to as a “public goods game with selection preferences” (PGG-SP), which makes strategic choices that are more humane and diversified. Finally, a co-evolution mechanism for strategies and topologies is introduced based on the double-layer network, which effectively explains the dynamic game process in real life. To verify the role of multiple double-layer networks with a PGG-SP, four types of double-layer networks are applied in this paper. In addition, the corresponding game results are compared between single-layer, double-layer, static, and dynamic networks. Accordingly, the results show that double-layer networks can facilitate cooperation in group games.

Analytical description for the critical fixations of evolutionary coordination games on finite complex structured populations

Evolutionary game theory is crucial to capturing the characteristic interaction patterns among selfish individuals. In a population of coordination games of two strategies, one of the central problems is to determine the fixation probability that the system reaches a state of networkwide of only one strategy, and the corresponding expectation times. The deterministic replicator equations predict the critical value of initial density of one strategy, which separates the two absorbing states of the system. However, numerical estimations of this separatrix show large deviations from the theory in finite populations. Here we provide a stochastic treatment of this dynamic process on complex networks of finite sizes as Markov processes, showing the evolutionary time explicitly. We describe analytically the effects of network structures on the intermediate fixations as observed in numerical simulations. Our theoretical predictions are validated by various simulations on both random and scale free networks. Therefore, our stochastic framework can be helpful in dealing with other networked game dynamics.