In Web retrieval, there are many cases of competition between authors of Web documents: their incentive is to have their documents highly ranked for queries of interest. As such, the Web is a prominent example of a competitive search setting. Past work on competitive search focused on ranking functions based solely on relevance estimation. We study ranking functions that integrate a results-diversification aspect. We show that the competitive search setting with diversity-based ranking has an equilibrium. Furthermore, we theoretically and empirically show that the phenomenon of authors mimicking content in documents highly ranked in the past, which was demonstrated in previous work, is mitigated when search results diversification is applied.