On Modeling of Coevolution of Strategies and Structure in Autonomous Overlay Networks
Currently, on one hand, there exist much work about network formation and/or growth models, and on the other hand, cooperative strategy evolutions are extensively investigated in biological, economic, and social systems. Generally, overlay networks are heterogeneous, dynamic, and distributed environments managed by multiple administrative authorities, shared by users with different and competing interests, or even autonomously provided by independent and rational users. Thus, the structure of a whole overlay network and the peers' rational strategies are ever coevolving. However, there are very few approaches that theoretically investigate the coevolution between network structure and individual rational behaviors. The main motivation of our article lies in that: Unlike existing work which empirically illustrates the interaction between rational strategies and network structure (through simulations), based on EGT (Evolutionary Game Theory), we not only infer a condition that could favor the cooperative strategy over defect strategy, but also theoretically characterizes the structural properties of the formed network. Specifically, our contributions are twofold. First, we strictly derive the critical benefit-to-cost ratio (b/c) that would facilitate the evolution of cooperation. The critical ratio depends on the network structure (the number of peers in system and the average degree of each peer), and the evolutionary rule (the strategy and linking mutation probabilities). Then, according to the evolutionary rules, we formally derive the structural properties of the formed network in full cooperative state. Especially, the degree distribution is compatible with the power-law, and the exponent is (4-3 upsilon)/(1-3 upsilon), where v is peer's linking mutation probability. Furthermore, we show that, without being harmful to cooperation evolution, a slight change of the evolutionary rule will evolve the network into a small-world structure (high global efficiency and average clustering coefficient), with the same power-law degree distribution as in the original evolution model.
coevolution structure overlay networks rational strategy