In this paper we analyze the structure of contest equilibria with a variable number of agents. First we analyze a situation where the total prize depends on the number of agents and where every single agent faces opportunity costs of investing in the contest. Second we analyze a situation where the agents face a trade-off between productive and appropriative investments. Here, the number of agents may also influence the productivity of productive investments. It turns out that both tyes of contests may lead to opposing results concerning the optimal numnber of contestants depending on the strength of size effects. Whereas in the former case individual utility is J-shaped when the number of agents increases, the opposite holds true for the latter case. We discuss the implications of our findings for the case of competition on markets and for the case fo unstable property rights.