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The Internet search engine market has seen a proliferation of entrants over the last few years. While Yahoo! was the early market leader, there has been entry by both lower quality engines and higher quality ones. Prior work on quality differentiation requires that low quality products have low prices, in order to survive in a market with high quality products. However, the price charged to users of search engines is typically zero. Therefore, consumers do not face a trade-off between quality and price. We develop a vertical differentiation model to show that even lower quality engines can survive in this market. A key property of the model is that, due to low costs users who try out one engine may also sample a lower quality engine in the same session. This "residual demand" allows lower products to survive in equilibrium. We consider a two-period dynamic game between an incumbent and an entrant who enters in the second period. The incumbent has the first mover advantage due to early entry and brand loyalty, while the entrant may have a cost advantage, based on superior technology. The interaction of these two effects determines which product has higher quality in equilibrium, We also consider the issue of strategic investments inequality and show that incumbent may under invest or over-invest in its quality depending on entrant's cost structure.