Matching with Multilateral Contracts

Matching with Complementary Contracts

“…In contrast to our setting with complementarities, externalities, like multilateral contracts, are much more challenging to accommodate in their two-sided setting with substitutes. Our results inRostek and Yoder (2018) suggest that this is because stability in these settings relies on each side of the market having well-behaved aggregate demand, but externalities or multilateral contracts can cause the weak axiom to fail under aggregation.…”

“…Note that unlike in goods markets or with transferable utility (Section 6), no excess demand and no excess supply are not equivalent here.10 While Lemma 2 requires complementarities, a similar market-clearing characterization of stability holds more generally; seeRostek and Yoder (2018).…”

“…However, complementarity characterizes many settings without such restrictions, such as the markets for patent licenses, differentiated products, and multisided platforms that we discuss throughout the paper.5 Relative to most of the matching literature, allowing for multilateral contracts is an innovation in its own right: Multilateral contracts have so far been investigated byHatfield and Kominers (2015), who consider divisible agreements, and Teytelboym (2012), who utilizesPycia's (2012) pairwise alignment condition in the contracts context. (We consider multilateral contracts in the substitutes context inRostek and Yoder (2018).) On the other hand, several papers consider externalities in two-sided matching environments; the most general of these isPycia and Yenmez (2017).…”

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). …”