Matching, Estimation, and Mutual Selection: Bilateral Interactions in Two-Sided Markets

Overview

Bilateral interactions in two-sided markets and the platform economy are phenomena that figure in many real-world activities such as regional and international trade, e-commerce, the sharing economy, transportation and urban planning, and migrations studied in the social sciences. For instance, in trade and supply-chain analysis, buyers and sellers interact via a two-sided network to meet their business needs; in transportation and migration, travelers and migrants move from one place to another for various purposes via physical and social networks. What is needed for better understanding and design of markets, networks, and platforms is in-depth study of how and why such interactions in two-sided networks occur.

Matching theory, one of the most exciting intellectual endeavors of the collective human mind, promises suitable methodologies and powerful analytical tools for the study of decision-making and interaction among the agents in a network or market, and hence for how to improve the formulation of matching mechanisms for desirable outcomes. This book aims to contribute to the literature on bilateral interactions in two-sided networks by studying generalized matching, estimation, and mutual selection in the context of a new, more powerful intervening opportunities theory that expands the existing matching theory to multi-unit many-to-many matching with quota constraints.

This is a more general—and more realistic—framework for matching that takes place in real-world situations. First, models of two-sided and one-sided matching with newly defined preference relationships and solution concepts are developed to establish the theoretical foundation for analyzing multi-unit and multi-partner matching with quota constraints. New matching mechanisms are then designed to produce stable and favorable matching outcomes. Second, a hybrid model for generalized matching is established to encompass both one-sided and two-sided matching within the generalized framework. Again, the corresponding hybrid matching mechanism with desired properties is proposed and discussed. Next, linking the newly proposed theoretical work to empirical applications, a novel bi-level estimation model is proposed for generalized matching in order to make inferences of agents’ matching behaviors/decisions. We then move on to argue that the existing intervening opportunities theory and the corresponding model fail to incorporate the mutual selection effect in determining bilateral transactions in two-sided networks. A mutual-selection intervening opportunities theory and its mathematical model are proposed and developed for the estimation of bilateral flows. We conclude the book by pointing out the remaining challenges and offering opinions on directions and topics for further research.

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Logic of Matching