UCLA

Two-sided online matching is a crucial aspect of optimizing social welfare sequentially within economic frameworks, achieved through pairing participants via third-party platforms. These platforms are utilized across various marketplaces such as college admissions, ride-sharing, doctor placement, dating, and job applications. Typically, these markets allocate indivisible ``good'' to multiple agents based on mutual compatibility, with preferences often being unknown due to the large participant volume, making it explicitly challenging. Moreover, matching markets inherently involve scarcity due to limited resources on both sides. This dissertation presents significant advances in statistical sequential modeling for two-sided online matching markets, considering dynamic markets, quota constraints, and participants' incentive compatibility. Situated at the intersection of sequential decision-making algorithm design and economics, this work introduces new algorithms, theories, and insights with applications spanning economics, statistics, and machine learning.

Part I establishes foundational concepts of statistical sequential decision making and relevant economic terminology. Chapter 1 explores bandit algorithms, probability theory, and concentration inequalities, while Chapter 2 elucidates essential concepts of two-sided matching markets from an economic perspective, laying the groundwork for subsequent applications.

Part II presents a theoretical framework for multi-agent competitive two-sided matching markets, crucial for online recommendation systems in job markets. The first project, detailed in Chapter 3, introduces an online statistical ridge estimation method for the dynamic matching problem (DMP) with its application in the LinkedIn text data. The second project, discussed in Chapter 4, presents an online statistical sequential decision-making method for the competing matching under complementary preferences recommendation problem (CMCPR), along with a novel algorithm addressing both complementary preferences and quota constraints simultaneously.