We take a differential game approach to study the dynamic market interaction between two Internet Service Providers (ISP) offering services characterized by different quality levels. Web congestion is accounted for, consisting in the fact that for a given network capacity, i.e. for given amount of resources to be shared, the quality of services decreases with the number of customers. ISP firms, by accumulating capital, may invest in order to increase their own network capacity. In contrast with the acquired wisdom, we prove that there exists an admissible intertemporal parameters subset wherein the low quality firm performs better than the high quality firm in terms of equilibrium profits. Furthermore, we establish conditions under which the low quality firm becomes a natural monopolist. Finally, we prove that consumers may be better off under cooperative rather than under non cooperative play.