  This paper attempts to find out numerically the distribution of the
queue-length ratio in the context of a model of preferential attachment. Here
we consider two restaurants only and a large number of customers (agents) who
come to these restaurants. Each day the same number of agents sequentially
arrives and decides which restaurant to enter. If all the agents literally
follow the crowd then there is no difference between this model and the famous
`P\'olya's Urn' model. But as agents alter their strategies different kind of
dynamics of the model is seen. It is seen from numerical results that the
existence of a distribution of the fixed points is quite robust and it is also
seen that in some cases the variations in the ratio of the queue-lengths follow
a power-law.

Computer Science and Game Theory;Trading and Market Microstructure