Algorithmic-matching sites offer users access to an unprecedented number of potential mates. However, they also pose a principal-agent problem with a potential moral hazard. The agent's interest is to maximize usage of the Web site, while the principal's interest is to find the best possible romantic partners. This creates a conflict of interest: optimally matching users would lead to stable couples and fewer singles using the site, which is detrimental for the online dating industry. Here, we borrow the notion of Price-of-Anarchy from game theory to quantify the decrease in social efficiency of online dating sites caused by the agent's self-interest. We derive theoretical bounds on the price-of-anarchy, showing it can be bounded by a constant that does not depend on the number of users of the dating site. This suggests that as online dating sites grow, their potential benefits scale up without sacrificing social efficiency. Further, we performed experiments involving human subjects in a matching market, and compared the social welfare achieved by an optimal matching service against a self-interest matching algorithm. We show that by introducing competition among dating sites, the selfish behavior of agents aligns with its users, and social efficiency increases.