The phenomenon of electronic commerce has led to a proliferation of web sites competing for the attention and resources of millions of consumers. As has been recently shown, the resulting dynamics is such that a few sites command most of the traffic in the web, a signature of a winner-take-all market[1].In order to explore the effects of competition among web sites and to determine how they affect the nature of markets, we present a dynamical model of web site growth and competition, which takes into account both the evolution of the probabilities that a person visits sites as well as the existence of links between sites.We show that under general conditions, as the competition between sites increases, the model exhibits a sudden transition from a regime in which many sites thrive simultaneously, to a "winner take all market" in which a few sites grab almost all the users, while most other sites go nearly extinct. This transition is similar to what in ecology is called the Principle of Competitive Exclusion.Furthermore, we study the effect of site linkage on the number of visitors to both competitive and cooperative sites, as well as the implications of our results for linking strategies as practiced on the web. Common link structures found on the web, such as web rings, are also analyzed.Finally, we show web usage data that motivates our work and places the different behaviors in context.