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 coexist 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 simple model of memory may be incorporated into other game models with implications that we briefly discuss.

• Received 11 May 2015
• Revised 26 August 2015

DOI:https://doi.org/10.1103/PhysRevE.92.032119