higher scoring agent and the total score of the pair shared equally between the original and its copy. In this way the total payoff in the population remains at zero. In Figure \[popDyn\] we show the evolution of the fractions of short and long memory agents in such a simulation, along with the probability weight for paper, as a signifier for the presence of oscillations. Initially we have a single long memory agent, whose descendants reproduce rapidly due to their enhanced ability to determine the optimal strategy to play. However, once these long memory agents are in sufficient concentration, they create a limit cycle. The presence of this cycle gives short memory agents an advantage, because although their samples have a higher noise, they contain more recent data. In circumstances of rapid change, older data becomes irrelevant, and skews the sample of the long memory agents, leading them to make poorer choices. In consequence the effectiveness of the two memory lengths comes into balance. The population sizes undergo noisy oscillations about the bifurcation point once their collective strategies begin to oscillate. This indicates that the bifurcation point is itself a self organized state, driven by population dynamics.

The fact that 