  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 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 familiar,
explicit game interactions shows that the adaptation dynamics exhibits a
diversity of collective behaviors. The simplicity of the assumptions underlying
the macroscopic equations suggests that these behaviors should be expected
broadly in collective adaptation. We also analyze the adaptation dynamics from
an information-theoretic viewpoint and discuss self-organization induced by
information flux between agents, giving a novel view of collective adaptation.
