A Fixed-Point Approach to Stable Matchings and Some Applications

Fleiner, Tamás

doi:10.1287/moor.28.1.103.14256

Cited by 245 publications

(216 citation statements)

References 26 publications

(62 reference statements)

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“…We say that choice functions of f ∈ F satisfy the irrelevance of rejected contracts (IRC) condition if for any Y ⊆ X and (Blair, 1988, Alkan, 2002, Fleiner, 2003, Echenique, 2007, Aygün and Sönmez, 2013.…”

Section: Ingredientsmentioning

confidence: 99%

Trading networks with bilateral contracts

Fleiner

Jankó

Tamura

et al. 2015

Proceedings of the the Third Conference on Auctions, Market Mechanisms and Their Applications

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We consider general networks of bilateral contracts that include supply chains. We define a new stability concept, called trail stability, and show that any network of bilateral contracts has a trailstable outcome whenever agents' choice functions satisfy full substitutability. Trail stability is a natural extension of chain stability, but is a stronger solution concept in general contract networks. Trail-stable outcomes are not immune to deviations of arbitrary sets of firms. In fact, we show that outcomes satisfying an even more demanding stability property -full trail stability -always exist. For fully trailstable outcomes, we prove results on the lattice structure, the rural hospitals theorem, strategy-proofness and comparative statics of firm entry and exit. We pin down a condition under which trail-stable and fully trail-stable outcomes coincide. We then completely describe the relationships between various other concepts. When contracts specify trades and prices, we also show that competitive equilibrium exists in networked markets even in the absence of fully transferrable utility. The competitive equilibrium outcome is (fully) trail-stable.Keywords: trail stability, chain stability, set stability, matching markets, supply chains, networks, contracts, competitive equilibrium.JEL Classification: C78, L14 * We would like to thank Samson Alva, Scott Kominers and Michael Ostrovsky for their valuable comments on the recent versions of the paper. Vincent Crawford, Umut Dur, Jens Gudmundsson, Claudia Herrestahl, Paul Klemperer, Collin Raymond, and Zaifu Yang also gave great comments on much earlier drafts. We had enlightening conversations with Alex Nichifor, Alex Westkamp and M. Bumin Yenmez about the project. Moreover, we are also grateful to seminar participants at the Southern

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Section: Ingredientsmentioning

confidence: 99%

Trading networks with bilateral contracts

Fleiner

Jankó

Tamura

et al. 2015

Proceedings of the the Third Conference on Auctions, Market Mechanisms and Their Applications

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“…The algorithm is based on characterizing the stable matchings as the fixed points of a certain mapping. This characterization is a standard technique in the literature of matching problems (See Adachi [1], Fleiner [22], Echenique and Oviedo [17,18], Hatfield and Milgrom [28], Ostrovsky [47]). …”

Section: T 2 -Algorithmmentioning

confidence: 99%

Two-Sided Matching With Externalities: A Survey

Bando

Kawasaki

Muto

2016

JORSJ

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The literature on two-sided matching markets with externalities has grown over the past several years, as it is now one of the primary topics of research in two-sided matching theory. A matching market with externalities is different from the classical matching market in that agents not only care about who they are matched with, but also care about whom other agents are matched to. In this survey, we start with two-sided matching markets with externalities for the one-to-one case and then focus on the many-to-one case. For many-to-one matching problems, these externalities often are present in two ways. First, the agents on the "many" side may care about who their colleagues are, that is, who else is matched to the same "one." Second, the "one" side may care about how the others are matched.

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“…For various applications of fixed point theorems on posets the reader can browse [18,26,29,32,36,37,49,62,63,66].…”

Section: Remark 26mentioning

confidence: 99%