Memory Size

It is a fact that there are many web pages for one to know all. Similarly there are many songs than we can keep in our mp3 players. It is not very difficult to increase examples of "too many itemstoo little memory" cases. We try to model the case where the memory is too small to keep all the items. We consider agents with a limited memory of size m. We let them interact by means of recommending web pages among the ones that they know. The giver agent "remembers" an item that is stored in its memory. The giver recommends the item to the taker agent. Since the taker does not have empty space in its memory, it "forgets" something and uses the emptied slot for the item recommended. We surprisingly observed that this process leads to many items become completely forgotten by the society while a few of them become extremely well known as the ratio of the memory size to the number of items decreases. We interpret this result as the emergence of fame. This may explain why there are so many web pages but only a small percentage is widely known. We also observed that some metrics such as the percentage of completely forgotten items, maximum fame, minimum fame changes linearly with the memory ratio.