  We present a simple game model where agents with different memory lengths
compete for finite resources. We show by simulation and analytically that an
instability exists at a critical memory length, and as a result, different
memory lengths can compete and co-exist in a dynamical equilibrium. Our
analytical formulation makes a connection to statistical urn models, and we
show that temperature is mirrored by the agent's memory. Our analysis is easily
generalisable to many other game models with implications that we briefly
discuss.
