Tiered Housing Allocation with Preannounced Rankings: An Experimental Analysis

• Author: Saurabh Singhal,Juan D. Carrillo
• Published date: 01 March 2016
• DOI: http://doi.org/10.1111/jems.12143
• Date: 01 March 2016

Tiered Housing Allocation with Preannounced

Rankings: An Experimental Analysis

JUAN D. CARRILLO

Department of Economics

University of Southern California Los Angeles

CA 90089 and CEPR

juandc@usc.edu

SAURABH SINGHAL

UNU WIDER

saurabh@wider.unu.edu

We study in the laboratory a variant of the house allocation with existing tenants problem where

subjects are partitioned into tiers with hierarchical privileges, and they know their position in

the priority queue before making their decision. We evaluate the performance of the modified

versions of three well-known mechanisms: Top TradingCycle (TTC), Gale-Shapley, and Random

Serial Dictatorship (RSD) with Squatting Rights. For all three mechanisms, we find low rates

of participation (around 40%), high rates of truth-telling conditional on participation (around

90%), high proportions of fair allocations (above 90%), and significant efficiency losses. We also

observe differences across mechanisms: RSD is ranked highest in efficiency and TTC is ranked

lowest in fairness. We then show that position in the queue has a positive and significant impact

on participation whereas tier has little effect on behavior. Finally, the individual analysis reveals

that the majority of subjects who do not play according to the theory still follow discernible

patterns of participation and preference revelation.

1. Introduction

This paper studies a version of the house allocation with existing tenants problem. In this

problem, a set of indivisible goods must be allocated to a number of agents. Money

exchanges are not feasible and some agents may be endowed with some of the goods.

Examples include the assignment of offices or classes to faculty members, on-campus

housing to students, parking spaces to employees, schedules to crew in the transporta-

tion industry and others. Following the existing literature, we refer to the indivisible

goods as “houses.”

We investigate the class of one-sided matching problems where agents are par-

titioned into tiers with different privileges. Indeed, in many cases individuals belong

to groups with privileges that are identical within tiers and different across them. For

example, in university departments, offices are sequentially allocated to full, associate,

assistant, and adjunct professors.1Undergraduate housing is sequentially allocated to

We thank Ricardo Alonso, Manuel Castro, Arya Gaduh, Brijesh Pinto, Smriti Sharma, and the audience at

various seminars for helpful comments, and Chris Crabbe for developing the software. We thank the LUSK

center for Real Estate and the Microsoft Corporation for financial support. Juan D. Carrrillo also gratefully

acknowledges the support of the National Science Foundation, grant SES 1425062. All remaining errors are

our own.

1. For example, see the office assignment procedure at Providence College, RI (http://www.providence.

edu/academic-affairs/Faculty-Resources/Documents/FacultyOfficePolicy.pdf) or at the Department of

C2015 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume25, Number 1, Spring 2016, 133–160

134 Journal of Economics & Management Strategy

students in their senior, junior, sophomore, and freshman year. Crew members choose

their preferred schedules as a function of their seniority. Similar tiered structures are

present in other situations such as firms, fraternities, or the armed forces. In those en-

vironments, individuals within a stratum are on a level playing field, but have rights,

which supersede the rights of agents in the strata below.

A house allocation mechanism is a systematic procedure that assigns houses to

prospective tenants, allotting at most one house to each agent. At the outset, some agents

are endowed with a house (existing tenants) and some others are not (newcomers).

Similarly,some houses are occupied by an agent whereas others are vacant. An allocation

mechanism can be evaluated on four desirable properties: (a) Pareto efficiency (the houses

should be optimally allocated given the preferences of the agents), (b) fairness (the

assignment should respect the priority order), (c) individual rationality (an agent should

be no worse-off by participating in the mechanism), and (d) strategy-proofness (agents

should not benefit from misrepresenting their preferences).

Three leading allocation mechanisms have been proposed in the literature, each

with different advantages. The most commonly used mechanism in real life applications,

the Random Serial Dictatorship with squatting rights (RSD), satisfies properties (a,b,d) but

not (c), thereby discouraging participation, which can imply substantial losses. To get

around this problem, Abdulkadiro˘

glu and S¨

onmez (1999) propose the TopTrading Cycles

(TTCs), a mechanism that satisfies properties (a,c,d) but not (b). Under this procedure, an

agent may end up with a worse allocation than someone below in the priority queue, a

feature that may create tensions between agents due to issues related to envy or fairness.

Finally, the well-known Gale-Shapley mechanism (GS) of two-sided matching theory

(Gale and Shapley, 1962) has a natural counterpart in the housing allocation problem.

Guillen and Kesten (2012) show that a mechanism used at one of MIT’s undergraduate

dormitories (the NH4) is theoretically equivalent to GS in the context of the housing

allocation with existing tenants problem. This rule satisfies properties (b,c,d) but not (a).

Naturally, Pareto inefficiencies create ex post incentives for swaps.

With the imposition of a tiered structure, an individual in a higher tier can always

expropriate the house of an individual in a lower one. As a result of this new hierarchical

structure, two of the four above-mentioned properties need to be adjusted. First, fairness

must apply only to agents in the same tier. We call it tiered fairness. Second, because

property rights across tiers are compromised, individual rationality can no longer be

globally guaranteed. Following Title (1998), we consider the weaker notion of tiered

individual rationality, which incorporates the fact that an agent may be forced to switch

to another house if her endowment is preferred by another agent who belongs to a higher

tier. The first step of our analysis consists in extending the three mechanisms discussed

above to a multi-tiered structure, which we denote tSD, tTTC, and tGS, respectively.2

Under the proper modification of fairness and individual rationality, it is straightforward

to show that the multitiered mechanisms keep the same theoretical properties as their

single tier counterparts: tSD satisfies all but tiered individual rationality, tTTC satisfies all

but tiered fairness, and tGS satisfies all but Pareto efficiency (Proposition 1). Therefore,

in tSD some agents should rationally opt out.3As for tTTC and tGS, we should observe

Educational Psychology, Counseling, and Special Education at Penn State University (http://www.ed.psu.

edu/educ/epcse/forms/epcse-office-assignment-policy).

2. Because we inform the subjects of the priority queue before they make any decision, we choose to call

it tiered Serial Dictatorship (tSD) instead of tRSD.

3. Following the literature, Pareto efficiency is defined from the point of view of the participating agents

only.This means that tSD may result in Pareto inefficiencies over the set of all agents.