Complementarity in Matching, Games, and Exchange Economies

Rostek, Marzena; Yoder, Nathan

doi:10.2139/ssrn.3567616

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…As we show in Rostek and Yoder (), part (i) of this result, for NTU matching environments, is the matching‐theoretic counterpart of Milgrom and Shannon's () comparative static for Nash equilibria of games with strategic complementarities.…”

Section: Comparative Staticsmentioning

confidence: 68%

“… The matching settings we consider are not transformable into a market for goods when primitive contracts have externalities. Without externalities, a TU matching environment can be transformed into a goods market in a way that preserves gross complementarity and competitive equilibria, but our result does not follow from or imply Baldwin and Klemperer's () unimodularity theorem in this environment—see Examples 1 and 2 in Rostek and Yoder (). …”

mentioning

confidence: 73%

“…Finally, we note that there is a formal connection between our results for matching environments with complementary contracts and results from the literature on normal‐form games with strategic complementarities (e.g., Milgrom and Shannon ()). We explore this connection in Rostek and Yoder ().…”

Section: Resultsmentioning

confidence: 99%

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Matching With Complementary Contracts

Rostek

Yoder

2020

ECTA

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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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