Disconnected-connected network transitions and phase separation driven by co-evolving dynamics

Abstract

A general model that involves agents competing in an evolutionary game and an adaptive networking environment is proposed and studied. Using the snowdrift game as an example, an agent may switch character or rewire the connection when the actual payoff is less than what the agent expected of its character. Depending on the value of a payoff parameter and the initial fraction of cooperators, the system shows two distinct phases: A frozen phase, in which all non-cooperative agents are expelled as isolated agents from clusters of cooperators, and a phase in which agents of different characters form a connected network that continues to evolve. The connectivity of agents of different characters differs significantly in both phases. A theory that treats the two characters separately is constructed. The theory captures the co-evolving dynamics driven disconnected-connected network transition, the phase separation, the phase diagram, and how the system evolves in time.