Cadet-Branch Matching in a Quasi-Linear Labor Market

Jagadeesan, Ravi

doi:10.1145/2940716.2940783

Cited by 3 publications

(11 citation statements)

References 4 publications

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“…3. Utility function in the Kelso-Crawford economy satisfy stronger regularity conditions in Jagadeesan (2016). In Echenique (2012), monotonicity of utility functions can only be achieved for salaries corresponding to "un-dominated" contracts (see the discussion in Schlegel, 2015), whereas in Jagadeesan (2016) monotonicity can be achieved for all salaries.…”

Section: An Embedding Resultsmentioning

confidence: 99%

“…than the one of Echenique (2012). In the following, when we talk of a "embedding result" we mean embedding in the sense of Jagadeesan (2016). Formally, an isomorphism in the sense of Jagadeesan, 2016(see Definition C.2 in his paper) between a matching market with contracts (Ch, ) and a Kelso-Crawford-economy (Σ, u) is a bijection (f, w, σ) : C ×S ×T → F × W × Σ such that and by the prior assumption that the only allocations ranked between Y ′ and…”

Section: An Embedding Resultsmentioning

confidence: 99%

“…Without monotonicity, DA-equivalence requires that choices coincide on all sets of contracts which contain at most one contract per student. (see Theorem 1 of Jagadeesan, 2016). With monotonicity the choices only have to coincide at some of these sets of contracts.…”

Section: Equivalent Choice Functionsmentioning

confidence: 99%

“…3 In many applications of matching models with contracts, there is a natural ordering on contract terms and it is reasonable to assume that preferences are monotone with respect to the ordering: In the cadet-to-branch matching model of Sönmez and Switzer (2013) the contract-term is the service time in the military and it is natural to assume that cadets prefer a shorter to a longer service in the same branch. This assumption is for example made in the analysis of Jagadeesan (2016). In college admission problems (Hassidim et al, 2017;Abizada and Dur, 2017) with stipends, it is natural to assume that students prefer being admitted with a stipend to being admitted without a stipend at the same college, or more generally, being admitted with a higher stipend than a lower stipend at the same college.…”

Section: Introductionmentioning

confidence: 99%

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Equivalent Choice Functions and Stable Mechanisms

Schlegel

2018

SSRN Journal

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We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a choice profile under which contracts are substitutes and the law of aggregate holds is a necessary and sufficient condition for the existence of a stable and group-strategy-proof mechanism.Our result can be interpreted as a (weak) embedding result for choice functions under which contracts are observable substitutes and the observable law of aggregate demand holds. JEL-classification: C78, D47

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Section: An Embedding Resultsmentioning

confidence: 99%

Section: An Embedding Resultsmentioning

confidence: 99%

Section: Equivalent Choice Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Equivalent Choice Functions and Stable Mechanisms

Schlegel

2018

SSRN Journal

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“…Note however thatKelso and Crawford (1982), point out that their analysis can be generalized beyond the quasi-linear model since "all arguments are completely ordinal"(Kelso and Crawford, 1982, p.1492).5 The original analysis of the military match bySönmez and Switzer (2013) uses a model that does not directly fit into the Kelso-Crawford model. However, it can be shown(Jagadeesan, 2016) that the problem can be rephrased in an equivalent way using a Kelso-Crawford model.…”

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confidence: 99%

Virtual Demand and Stable Mechanisms

Schlegel

2016

Proceedings of the 2016 ACM Conference on Economics and Computation

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We study conditions for the existence of stable, strategy-proof mechanisms in a many-to-one matching model with salaries. Workers and firms want to match and agree on the terms of their match. Firms demand different sets of workers at different salaries. Workers have preferences over different firm-salary combinations. Workers' preferences are monotone in salaries. We show that for this model, a descending auction mechanism is the only candidate for a stable mechanism that is strategy-proof for workers. Moreover, we identify a maximal domain of demand functions for firms, such that the mechanism is stable and strategy-proof. In the special case, where demand functions are generated by quasi-linear profit functions, our domain reduces to the domain of demand functions under which workers are gross substitutes for firms. We provide two versions of the results for the quasi-linear case. One for a discrete model, where salaries are restricted to discrete units and one for a continuous model, where salaries can take on arbitrary positive numbers. More generally, we show that several celebrated results (the existence of a worker-optimal stable allocation, the rural hospitals theorem, the strategyproofness of the worker-optimal stable mechanism) generalize from the discrete to the continuous model.

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