In this paper, we provide existence results for matching environments with complementarities, such as markets for patent licenses, differentiated products, or multi-sided platforms. Our results apply to both nontransferable and transferable utility settings, and allow for multilateral agreements and those with externalities. Additionally, we give comparative statics regarding the way primitive characteristics are combined to form the set of available contracts. These show the impact of various contract design decisions, such as the application of antitrust law to disallow patent cross-licenses, on stable outcomes.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.