Interviewing in two‐sided matching markets

• DOI: http://doi.org/10.1111/1756-2171.12193
• Author: Robin S. Lee,Michael Schwarz
• Published date: 01 August 2017
• Date: 01 August 2017

RAND Journal of Economics

Vol.48, No. 3, Fall 2017

pp. 835–855

Interviewing in two-sided matching markets

Robin S. Lee∗

and

Michael Schwarz∗∗

We introduce the interview assignment problem, which generalizes classic one-to-one match-

ing models by introducing a stage of costly information acquisition. Firms learn preferences

over workers via costly interviews. Even if all firms and workers conduct the same number of

interviews, realized unemployment depends also on the extent to which agents share common

interviewing partners. We introduce the concept of overla p that captures this notion and prove

that unemployment is minimized with perfect overlap: that is, if two firms interview any common

worker, they interview the exact same set of workers.

1. Introduction

The theory of two-sided matching generally assumes that agents knowtheir tr ue preferences

over potential partners prior to engaging in a match.1However, in many matching markets,

information acquisition plays an important role: in labor markets, firms interview workers; in

marriage markets, men and women date; and in real estate markets, buyers attend open houses.

Such interviews, dates, and meetings are often costly and scarce—for example, firms pay up to

a third of an employee’s annual salary as commission to headhunters just to narrow down the

potential field of candidates to interview (cf. Coles et al., 2008)—and because these interviews

affect the formation of preferences, their assignment can crucially affect the outcome of the

eventual matching process.

Our article generalizes the one-to-one matching model of Gale and Shapley (1962) to allow

for a stage of costly information acquisition. To our knowledge, this article is one of the first to

analyze the interview assignment problem in the context of two-sidedmatching. Throughout this

article, we will refer to agents as “firms” and “workers,” but this label can be changed to men

and women, colleges and students, hospitals and doctors, and so forth. Firms and workers do not

ex ante know their idiosyncratic preferences over potential matching partners, and must discover

them through a costly interviewing process.

∗Harvard University and NBER; robinlee@fas.harvard.edu.

∗∗Google and NBER; schwarz.m@gmail.com.

We thank Neil Thakral for exceptional research assistance, and Itay Fainmesser, Kyna Fong, Rachel Kranton, David

McAdams, Michael Ostrovsky,Al Roth, Lones Smith, two anonymous referees, and the Editor for helpful comments. All

errors are our own.

1For a survey,see Roth and Sotomayor (1990).

C2017, The RAND Corporation. 835

836 / THE RAND JOURNAL OF ECONOMICS

We analyze a two-stage game: in the first stage, firms simultaneously choose a subset of

workers to interview, and in the second stage, firms and workers are matched one-to-one using

a firm-proposing deferred acceptance algorithm in which firms make “job offers” to workers.

We primarily focus on the first-stage interviewing decisions and use standard results from the

one-to-one matching literature to analyze the second-stage assignment. Even so, the interview

assignment problem is generally difficult and possiblyintractable. To allow for analysiswhile still

maintaining a model rich enough to yield meaningful results, we make the followingassumptions:

firms bear the full cost of interviewing; a firm and worker must interview in order to be matched;

workers prefer being matched to anyfir m than to being unemployed;firms may find some workers

unacceptable and choose to remain unmatched; and workers and firms are ex ante homogeneous,

with preferences over partners independent and idiosyncratic to each agent.2

Even if all firms and workersare ex ante identical (prior to the realization of their idiosyncratic

preferences), our model emphasizes that agents are not indifferent overwhom they interview with.

As interviews are costly, firms care about how many interviews a potential interviewee has: as

the number of interviews a worker has increases, the probability of a job offer being accepted

declines as the worker might obtain and accept an offer from another firm. All else being equal,

workers who havefew interviews are more attractive to interview because they are more likely to

accept if an offer is made. As a result, even though there are equilibria in which firms all conduct

the same number of interviews, firms would prefer not to randomize over workers but instead

coordinate so that all workers receive the same number of interviews. We prove that for any

number of interviews conducted by all firms, there are values of interviewing costs where firms

randomly choosing workers to interview comprise an equilibrium of our game;additionally, there

are (potentially different) values of interviewing costs so that all firms and workers conducting

the same number of interviews is also an equilibrium.

Wethen investigate a more subtle form of coordination which also proves to have significant

effects on equilibrium employment. For our analysis, we focus on symmetric interview assign-

ments, which we define to be interview assignments in which each firm and worker has the same

number of interviews, and even if two firms or two workers swap their interview assignments,

the original interview assignment can be obtained via a renaming of other agents. Although there

may exist many equilibria in whichall agents conduct the same number of inter views,the number

of expected hires in the match can be very different, depending on whether or not the interview

assignment exhibits greater overlap—a partial ordering that we define formally, which captures

the number of common interview partners among agents.

To illustrate why overlap matters, consider two firms, fand f, who are the only firms that

interview workers wand w:iffhas an offer rejected by w, it must be that the worker accepted an

offer from f; consequently, fwill then face no “competition” for wand obtain him for certain

if it makes him an offer. If fand fdid not interview the same set of workers, then fcould

possibly be rejected by both wand wand not be matched, despite making offers to both workers

(because being rejected by wno longer implies obtaining wfor certain). Thus, a firm’sexpected

payoff depends not only on the number of interviews its workers receive, but also the identities

of the other firms interviewing those workers.

The main result of this article is that if the ex ante probability that a worker is found to

be unacceptable to a firm is sufficiently small, then among all symmetric interview assignments

in which every firm and worker conducts the same number of interviews, any assignment with

perfect overlap—that is, if any two firms interview the same worker, they interview exactly the

2Although homogeneity is a strong assumption to apply for an entire market, it is potentially plausibleif a market

is partitioned into subsets of workers and firms of similar quality. For example,although workers in general may have

a greater likelihood of preferring a “top-tier” firm in the entire market over a “bottom-tier” firm, within a tier, worker

preferences may be fairly evenly distributed; this also may be true with firm preferences over workers within a tier.

Thus, in the sense that workers and firms of similar quality are the only ones that interview and match with each other,

and—conditional on all available information—worker and firm preferences are generally uniform and i.i.d. among a

particular subset of agents, our model is less restrictive than it might appear.

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