On the correspondence of contracts to salaries in (many-to-many) matching

Kominers, Scott Duke

doi:10.1016/j.geb.2011.12.002

Cited by 31 publications

(21 citation statements)

References 14 publications

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“…We first re-state the familiar Laws of Aggregate Demand and Supply (LAD/LAS) Milgrom, 2005, Hatfield andKominers, 2012). LAD (LAS) states that when a firm has more upstream (downstream) contracts available (holding the same downstream (upstream) contracts), the number of downstream (upstream) contracts the firms chooses does not increase more than the number of upstream (downstream) contracts the firm chooses.…”

Section: Laws Of Aggregate Demand and Supplymentioning

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: Laws Of Aggregate Demand and Supplymentioning

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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“…Moreover, the gross substitutability condition that is the key assumption of the analysis of Kelso and Crawford (1982) is satisfied in the market with salaries. This result can be extended to many-to-many models of matching with contracts (Kominers, 2012).…”

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confidence: 78%

“…There exists a "marginal" preference ranking of the contracts x and x with worker w that is independent of the contracts that f signs with other workers (Hatfield and Kojima, 2010). This condition, which we call separability (the previous literature uses the term "Pareto separability"), is important for the embedding results of Echenique (2012) and Kominers (2012).…”

Section: Matching With Contractsmentioning

confidence: 99%

“…Separability in many-to-one markets with contracts is implied by substitutability but not by unilateral substitutability (Hatfield and Kojima, 2010). Thus, under unilateral substitutability we cannot use the embedding construction of Echenique (2012) and Kominers (2012). The underlying observation behind our embedding is that firm preferences can be modified such that they become essentially separable while the essential properties of the market (in particular, the set of efficient and individually rational allocations and preferences over those allocations) remain unchanged.…”

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confidence: 99%

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Contracts versus salaries in matching: A general result

Schlegel

2015

Journal of Economic Theory

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“…While these failures of substitutability place airline seat upgrade allocation outside the reach of the prior literature, our results show that upgrade allocation can indeed be conducted through matching with contracts in a manner that is fair, conflict of interest among agents in the context of stable assignment. 7 Thus, in particular, our model falls outside of the domain which Echenique (2012) has shown can be handled with only the Kelso and Crawford (1982) matching with salaries framework (see also Kominers (2012)). …”

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confidence: 99%

Designing for diversity in matching

Kominers

Sönmez

2013

Proceedings of the Fourteenth ACM Conference on Electronic Commerce

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To encourage diversity, schools often "reserve" some slots for students of specific types. Students only care about their school assignments and contractual terms like tuition, and hence are indifferent among slots within a school. Because these indifferences can be resolved in multiple ways, they present an opportunity for novel market design.We introduce a two-sided, many-to-one matching with contracts model in which agents with unit demand match to branches, which may have multiple slots available to accept contracts. Each slot has its own linear priority order over contracts; a branch chooses contracts by filling its slots sequentially. We demonstrate that in these matching markets with slot-specific priorities, branches' choice functions may not satisfy the substitutability conditions typically crucial for matching with contracts. Despite this complication, we are able to show that stable outcomes exist in this framework and can be found by a cumulative offer mechanism that is strategy-proof and respects unambiguous improvements in priority. Our results provide insight into the design of transparent affirmative action matching mechanisms. Additionally, they enable us to introduce a new market design application-allocation of airline seat upgrades-and show the value of a seemingly ad hoc administrative decision in the United States Military Academy's branch-of-choice program.JEL classification: C78, D63, D78.

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On the correspondence of contracts to salaries in (many-to-many) matching

Cited by 31 publications

References 14 publications

Trading networks with bilateral contracts

Trading networks with bilateral contracts

Contracts versus salaries in matching: A general result

Designing for diversity in matching

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