Price of Anarchy in Algorithmic Matching of Romantic Partners

TL;DR

This paper analyzes how self-interest in online dating platforms impacts social efficiency, using game theory to quantify the price-of-anarchy and demonstrating that competition can improve overall matching quality.

Contribution

It introduces a theoretical framework to bound the price-of-anarchy in online dating, and empirically shows that competition aligns agents' interests with social welfare.

Findings

Price-of-anarchy is bounded by a constant independent of user base size.

Competition among dating sites improves social welfare.

Selfish matching algorithms can be mitigated through market competition.

Abstract

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.