Matching with Complementary Contracts

Abstract

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.

Trading Networks With Frictions

“…Second, can externalities (as analyzed by Pycia and Yenmez (2017) and Rostek and Yoder (2018)) be incorporated into our analysis? First, to what extent can the condition that firms have bounded willingness to pay for trades be relaxed while still ensuring that trail-stable outcomes lift to competitive equilibria?…”

“…First, to what extent can the condition that firms have bounded willingness to pay for trades be relaxed while still ensuring that trail-stable outcomes lift to competitive equilibria? Second, can externalities (as analyzed by Pycia and Yenmez (2017) and Rostek and Yoder (2018)) be incorporated into our analysis?…”

Matching With Complementary Contracts

“…All that matters is that externalities are complementary with other agents' contracts; that is, when other agents sign more contracts, an agent chooses a (weakly) larger set of primitive contracts from the same set of available contracts (in the NTU setting) or at the same price vector (in the TU setting). This is illustrated in a later example (Example ), where each primitive contract has negative externalities, and in Example A.1 in the Supplemental Material (Rostek and Yoder ()), where some primitive contracts have positive externalities and others have negative externalities; in both examples, primitive contracts are gross complements.…”

Full substitutability

“… Note that the concept of substitutability has also been extended to settings with externalities (see, e.g., Pycia and Yenmez 2017 and Rostek and Yoder 2018, ); we do not address such settings in this paper. Likewise, we do not address various strengthenings or weakenings of the substitutability condition (see, e.g., Klaus and Walzl 2009, Hatfield and Kojima 2010, Hatfield and Kominers 2019, Hatfield, Kominers, and Westkamp 2019), or settings in which utility is not transferrable. …”

“… To overcome the modeling difficulties associated with allowing for complementarities, authors have made various assumptions on functional forms of production (Pycia 2012, Dur and Ikizler 2016, Rostek and Yoder 2018, ), or worked in either large‐market limit environments (Kojima et al 2013, Azevedo and Hatfield 2018, Che et al 2019, Jagadeesan 2019) or in settings in which goods are perfectly divisible (Hatfield and Kominers 2015, Bando et al 2019). …”