Heterogeneous information lags and evolutionary stability

We investigate the effect of information lags in discrete time evolutionary game dynamics on symmetric games. At the end of each period, some players obtain information about the distribution of strategies among the entire population. They update their strategies according to this information. In contrast to the previous literature (e.g., Tao and Wang (1997)) where large delays lead to instability, we show that the relationship between information lags and the stability of equilibria is not "monotonic." In anti-coordination games under smoothed best-response dynamics, a small probability of delay can stabilize the equilibrium, while a large probability can destabilize it.