We show that a two-sided matching platform can successfully compete by limiting the number of choices it offers to its customers, while charging higher prices than platforms with unrestricted choice. We develop a stylized model of online dating where agents with different outside options match based on how much they like each other. Starting from these microfoundations, we derive the strength and direction of indirect network effects and show that increasing the number of potential matches has a positive effect due to larger choice, but also a negative effect due to competition between agents on the same side. Agents resolve the trade-off between these competing effects differently, depending on their outside options. For agents with high outside options, the choice effect is stronger than the competition effect, leading them to prefer an unrestricted-choice platform. The opposite is the case for agents with low outside options, who then have higher willingness to pay for a platform restricting choice, as it also restricts the choice set of their potential matches. Moreover, since only agents with low outside options self-select into the restricted choice platform, the competition effect is mitigated further. This allows multiple platforms offering different number of choices to coexist without the market tipping.