Stability and Diversity in Collective Adaptation

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual adaptive agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several explicit interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. We also analyze the adaptation dynamics in terms of information theory, giving a novel view for collective adaptation.