Collaborative Research: Network Formation and Bargaining with Exclusionary Commitments

A lot of economic activity involves two-sided markets in which firms on one side of the market form networks with firms on the other side. In many of these markets there are small numbers of firms on each side, and contracts are negotiated bilaterally. The equilibrium network structure and terms of trade are intertwined and emerge through the strategic interactions of buyers and sellers on both sides of the market.

Examples include the market for health insurance in which hospitals negotiate rates with health insurance providers, the market for digital media in which TV stations and other content providers negotiate prices with cable companies and streaming platforms, and manufacturing networks in which downstream firms sign contracts with upstream suppliers. The broad goal of this project is to investigate models of bargaining between multiple buyers and multiple sellers in which each agent may potentially contract with several others on the opposite side of the market.

A narrower goal, and the one we will first investigate, is to understand the role of exclusionary pre-commitments. For instance, a seller facing multiple buyers may find it profitable to create artificial scarcity by committing to trade only with specific subsets of buyers. The research will offer new perspectives on exclusion commitments and how they shape network structure and terms of trade for each link that forms.

Providing a systematic framework for analyzing exclusion commitments and network formation in “thin” markets will expand the toolkit available to applied researchers in health economics and other two-sided markets as well as to policymakers and regulators.

The project will develop a general definition of exclusion commitments compatible with flexible network formation, and will provide powerful characterizations of optimal exclusion commitments for settings without externalities. The research will reveal that flexibly trading with a fixed number of buyers enables sellers to extract higher profits than threatening to exclude particular buyers.

In equilibrium, some buyers are included with certainty and split the marginal surplus equally with the seller. Buyers with lower valuations are excluded with positive probability; bargaining with these buyers is driven by a novel sequential outside option principle. The conclusions will be extended to settings with externalities in which agents on the same side of the market are divided into different categories, and valuations are interdependent within and across categories.

In earlier theoretical work and applications, there has been heavy reliance on the “Nash-in-Nash” bargaining solution and closely related concepts. Preliminary analysis suggests that this reliance might be excessive, and that the Nash-in-Nash framework could lead to conclusions at variance with the predictions generated by plausible and familiar bargaining protocols.

Developing new models of bargaining between multiple buyers and sellers based on natural protocols will contribute to an area that still lacks a settled theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.