Escalation of Memory Length in Finite Populations

The escalation of complexity is a commonly cited benefit of coevolutionary systems, but computational simulations generally fail to demonstrate this capacity to a satisfactory degree. We draw on a macroevolutionary theory of escalation to develop a set of criteria for coevolutionary systems to exhibit escalation of strategic complexity. By expanding on a previously developed model of the evolution of memory length for cooperative strategies by Kristian Lindgren, we resolve previously observed limitations to the escalation of memory length. We present long-term coevolutionary simulations showing that larger population sizes tend to support greater escalation of complexity than smaller population sizes. Additionally, escalation is sensitive to perturbation during transitions of complexity. In whole, a long-standing counter-argument to the ubiquitous nature of coevolution is resolved, suggesting that the escalation of coevolutionary arms races can be harnessed by computational simulations.