Fame emerges as a result of small memory

A dynamic memory model is proposed in which an agent "learns" a new agent by means of recommendation. The agents can also "remember" and "forget." The memory size is decreased while the population size is kept constant. "Fame" emerged as a few agents become very well known in expense of the majority being completely forgotten. The minimum and the maximum of fame change linearly with the relative memory size. The network properties of the who-knows-who graph, which represents the state of the system, are investigated.