Multilateral Matching

John William Hatfield; Scott Duke Kominers

Article | Journal of Economic Theory

Multilateral Matching

by John William Hatfield and Scott Duke Kominers

Abstract

We introduce a matching model in which agents engage in joint ventures via multilateral contracts. This approach allows us to consider production complementarities previously outside the scope of matching theory. We show analogues of the first and second welfare theorems and, when agents' utilities are concave in venture participation, show that competitive equilibria exist, correspond to stable outcomes, and yield core outcomes. Competitive equilibria exist in our setting even when externalities are present.

Keywords: matching; networks; joint ventures; stability; Competitive equilibrium; Core; Networks; Competition; Joint Ventures; Balance and Stability; Groups and Teams; Entrepreneurship;

Format: Print

Find at Harvard Purchase

Citation:

Hatfield, John William, and Scott Duke Kominers. "Multilateral Matching." Journal of Economic Theory 156 (March 2015): 175–206.

The U.S. residential real estate agency market presents a puzzle for economic theory: commissions on real estate transactions have remained constant and high for decades even though agent entry is frequent and agents’ costs of providing service are low. We model the real estate agency market, and other brokered markets, via repeated extensive form games; in our game, brokers first post prices for customers and then choose which agents on the other side of the market to work with. We show that prices appreciably higher than the competitive prices can be sustained (for a fixed discount factor) regardless of the number of brokers; this is done through strategies that condition willingness to transact with each broker on that broker’s initial posted prices. Our results can thus rationalize why brokered markets exhibit pricing high above marginal cost despite fierce competition for customers; moreover, our model can help explain why agents and platforms who have tried to reduce commissions have had trouble entering the market.

We introduce a new model of school choice with reserves in which a social planner is constrained by a limited supply of reserve seats and tries to find an optimal matching according to a social welfare function. We construct the optimal distribution of reserves via a quartic-time dynamic programming algorithm. Due to the modular nature of the dynamic program, the mechanism is strategy-proof for reserve-eligible students.

This case is set in mid-2019, when Qualcomm was struggling with unwanted takeover battles, fights with Apple and the Chinese government, and internal dissension on the board of directors. Ten years earlier Qualcomm was hailed as a monopoly on CDMA technologies and its derivatives—it appeared to be positioned to become the next dominant technology company in the tradition of Microsoft and Intel. But as the industry changed, Qualcomm’s competitive position seriously weakened. The purpose of the case is to explore central questions in strategy formulation: 1. how to build a long-term sustainable position based on technology, 2. how to design an IP strategy to lock in customers for the long run, 3. how to build a global standard and appropriate returns on that standard, and 4. how to respond when your historical business model starts to crumble.

Faculty & Research

Multilateral Matching

Abstract

Citation:

About the Author

More from the Author