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2018 | OriginalPaper | Chapter

Varying the Number of Signals in Matching Markets

Authors : Meena Jagadeesan, Alexander Wei

Published in: Web and Internet Economics

Publisher: Springer International Publishing

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Abstract

In large matching markets between job candidates and organizations, organizations may be unable to effectively identify interested candidates due to a large volume of applications. The resulting congestion makes it unlikely for candidates to receive offers from their most preferred organizations, leading to significant mismatch. We study how signaling mechanisms can be used as a market design tool to reduce the congestion in such markets. Specifically, we look at how the number of signals available to market participants affects welfare and the number of matches using a large market model. We show that for sufficiently many signals, candidate welfare and the number of matches decrease as a function of the number of signals, while the behavior of organization welfare depends on the extent to which organizations value top candidates. Furthermore, we describe a class of firm utility functions for which these limiting effects start to hold at realistic numbers of signals S.

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Footnotes
1
While Coles et al. [5] also study the case of multiple blocks of firms, some of their welfare trends become indeterminate for more than one block of firms in their model. For this reason, we focus on the case of one block in our paper.
 
2
In Coles et al. [5], each firm is only allowed to make an offer to at most one worker, and each worker is allowed to accept at most one offer from at most one firm. In our model, we maintain that each worker can accept at most one offer. However, we instead set the maximum measure of offers that a firm is permitted to send to \(\gamma \). While this offer structure does not precisely model the dating market (where candidates can “accept” multiple dates) or college admissions (where colleges can select the number of students to accept based on yield rates), the simplicity of the game, in both the setting of Coles et al. [5] and in our setting, enables the analysis to be tractable.
 
3
One difference between the dynamics of our model and the dynamics of the model of Coles et al. [5] is whether \(c = 1- \gamma \) is an equilibrium if worker signal truthfully, while in our model, for any \(S < F\), the cutoff \(c = 1 - \gamma \) is never an equilibrium. On the other hand, in [5], the cutoff \(c = 1 - \gamma \) is always an equilibrium in the game with signals. The difference arises because in our model, firms send offers to more than one candidate, and the margin now matters. One consequence is that in our model, shifts to strategies based on signaling are more likely to endogenously occur given the existence of a signaling mechanism.
 
Literature
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Metadata
Title
Varying the Number of Signals in Matching Markets
Authors
Meena Jagadeesan
Alexander Wei
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-030-04612-5_16

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