We investigate the effects of memory on the stability of evolutionary selection dynamics based on a multinomial logit model in a simple asset pricing model with heterogeneous beliefs. Whether memory is stabilizing or destabilizing depends in general on three key factors: (1) whether or not the weights on past observations are normalized; (2) the ecology or composition of forecasting rules, in particular the average trend extrapolation factor and the spread or diversity in biased forecasts; and (3) whether or not costs for information gathering of economic fundamentals have to be incurred.
