Evolutionary Dynamics in Complex Networks of Adaptive and Competing Agents

We use minority game model to investigate evolutionary dynamics in complex networks of adaptive agents competing for limited resources. We show that the dynamics and the phase structures critically depend on the underlying network organizations, and evolution is a key mechanism for the emergence of high-order coordination among the networked agents. A non-growing random directed network admits a clear phrase transition from a stable or “critical” state to a “chaotic” state. In contrast, no such phrase transition has been detected in a growing directed network; Instead, it permits stable or “critical” dynamics for all the connectivity. The dynamics of a scalefree directed network is found sensitive to its connectivity if a small fraction of link reversal is allowed in the network: The evolutionary dynamics exhibits a gradual phase transition from the stable (or “critical”) state to the “chaotic” regime with increase of the connectivity number K; this suggesting that the scale-free directed network is vulnerable to a small fraction of “errors” in its network organization. The underlying sources for the emergence of these dynamics are the organizations of the networks and can be understood with a descendant clusters theory. Evolution dramatically enhances the performance of a system in a stable or “critical” regime, but has no effect on a system in “chaotic” state; such attribute can be empowered to typify the dynamics of a complex network. The impact of evolution on system efficiency lies in its ability in reducing “crowdedness” of agents’ strategies and can be explained by a crowd-anticrowd theory.