Econometrica: Sep 2020, Volume 88, Issue 5

Matching with Complementary Contracts
p. 1793-1827

Marzena Rostek, Nathan Yoder

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.

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Supplemental Material

Supplement to "Matching with Complementary Contracts"

This supplement to “Matching with Complementary Contracts”gives supporting material for Example 3 in the main text, including an alternative numerical example where firms produce complementary products; shows that bundling preserves complementarity in both TU and NTU environments; and provides a lemma supporting the proof of Proposition 5 in the main text.

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