Matching With Complementary Contracts

Abstract

In this paper, we show that stable outcomes exist in matching environments with complementarities, such as social media platforms or markets for patent licenses. Our results apply to both nontransferable and transferable utility settings, and allow for multilateral agreements and those with externalities. In particular, we show that stable outcomes in these settings are characterized by the largest fixed point of a monotone operator, and so can be found using an algorithm; in the nontransferable utility case, this is a one‐sided deferred acceptance algorithm, rather than a Gale–Shapley algorithm. We also give a monotone comparative statics result as well as a comparative static on the effect of bundling contracts together. These illustrate the impact of design decisions, such as increased privacy protections on social media, or the use of antitrust law to disallow patent pools, on stable outcomes.

Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson*

“…Theoretically, market‐clearing prices might exist in the absence of substitutability although only in fairly restricted preference domains – see, for example, Bikhchandani and Mamer (1997), Danilov et al . (2001), Sun and Yang (2006), Baldwin and Klemperer (2019), and Rostek and Yoder (2020) – but even then, there is no guarantee that an ascending auction, such as the SMRA, would find equilibrium prices even if they exist.…”