Dynamic incentive effects of assignment mechanisms: Experimental evidence

• Author: Xiaocheng Hu,Thomas Gall,Michael Vlassopoulos
• Date: 01 November 2019
• Published date: 01 November 2019
• DOI: http://doi.org/10.1111/jems.12315

Received: 15 January 2018

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Revised: 20 November 2018

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Accepted: 5 March 2019

DOI: 10.1111/jems.12315

ORIGINAL ARTICLE

Dynamic incentive effects of assignment mechanisms:

Experimental evidence

Thomas Gall

1

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Xiaocheng Hu

2

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Michael Vlassopoulos

3

1

Department of Economics, University of

Southampton, Southampton, UK

2

European Centre for the Environment

and Human Health, University of Exeter,

Exeter, UK

3

Department of Economics, University of

Southampton, Southampton, UK and IZA,

Bonn, Germany

Correspondence

Thomas Gall, Department of Economics

University of Southampton, Southampton

SO17 1BJ, UK.

Email: t.gall@soton.ac.uk

Funding information

School of Social Sciences, University of

Southampton, Grant/Award Number:

SRDF 15/16

Abstract

Optimal assignment and matching mechanisms have been the focus of

exhaustive analysis. We focus on their dynamic effects, which have received

less attention, especially in the empirical literature: Anticipating that assignment

is based on prior performance may affect prior performance. We test this

hypothesis in a lab experiment. Participants first perform a task individually

without monetary incentives; in a second stage, they are paired with another

participant according to a pre‐announced assignment policy. The a ssignment is

based on the first‐stage performance, andcompensation is determined by average

performance. Our results are largely consistent with a theory: Pairing the worst‐

performing individuals with the best yields 20% lower first‐stage effort than

random matching (RAM) and does not induce truthful revelation of types, which

undoes any policy that aims to reallocate types based on performance. Perhaps

surprisingly, however, pairing the best with the best yields only 5% higher first‐

stage effort than RAM and the difference is not statistically significant.

KEYWORDS

assignment games, dynamic incentives, matching, performance, truthful revelation

JEL CLASSIFICATION

C78, C91, D23, M54

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INTRODUCTION

Individuals' payoffs depend on the economic environment they are placed in. For example, peers' attributes can affect

an individual's payoff in the workplace or the classroom, and one's spouse's attributes will affect marriage payoffs.

However, the attributes that determine payoffs are likely to be the consequence of prior choices made, in full

anticipation of the later assignment to other people, peers, tasks, or jobs. For instance, expectations about the future

assignment into colleges, firms, or teams may well provide powerful incentives for accumulating human capital. This

raises an interesting question: Does the manner of how individuals are assigned to each other or to tasks, jobs, schools,

and so forth, affect their prior choices, such as earlier stage investments and performance?

In the workplace, a wide range of methods to assign workers to tasks and to each other are used in practice. For

instance, some firms assign workers into teams that are heterogeneous in ability, by partnering stronger performers

with weaker ones, to facilitate learning or to provide role models that lead to productivity gains (Hamilton, Nickerson,

& Owan, 2003). More importantly, this pattern may also be promoted by managers who pursue social goals, such as

fairness or equality in remuneration, with an aim to boost morale (see, e.g., Bewley, 1999; Blinder & Choi, 1990; Pfeffer

& Langton, 1993) or job satisfaction (Card, Mas, Moretti, & Saez, 2012) among workers. Such organizational choices

may come at a cost, however, limiting an individual's desire to exert effort at an earlier stage. That is, there is a dynamic

J Econ Manage Strat. 2019;28:687–712. wileyonlinelibrary.com/journal/jems © 2019 Wiley Periodicals, Inc.

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trade‐off between equity ex post and efficiency ex ante. More subtly, distortions in early stage behavior will also make

observations of earlier behavior less informative of future performance, jeopardizing attempts to promote equity or

fairness through assignment that is based on past choices. Conversely, if the best performers are assigned to better

partners this will provide additional incentives for effort at an earlier stage. Depending on the degree of production

complementarity (Franco, Mitchell, & Vereshchagina, 2011) and the strength of incentives (Bandiera, Barankay, &

Rasul, 2013), this pattern will also arise when workers are allowed to choose their own teammates because workers will

tend to match positively assortatively in ability. Of course, team formation may also be left to chance, for instance, if

assignment is by sequence of arrival, follows a rotation system or is guided by alphabetic order of names (e.g., Bartel,

Beaulieu, Phibbs, & Stone, 2014).

Also outside the workplace assignment mechanisms of individuals vary widely, sometimes as the result of an explicit

policy, but often as the result of a decentralized market place. For example, in higher education, there is a marked

difference between the US and the UK where students self‐select by academic ability into universities guided by

detailed rankings, and continental Europe where students focus more on the city a university is located in. In the

secondary education, countries differ substantially in the degree to which they sort pupils by academic achievement,

that is, tracking (cf. Betts, 2011, Chapter 7; Hanushek & Woessmann, 2011, Chapter 2). Evidence on the marriage

market suggests that mating is assortative in educational achievements (see, e.g., Fernandez, Guner, & Knowles, 2005).

In all these examples, individuals who anticipate that their later assignments and outcomes depend on their earlier

stage choices will, therefore, respond to the assignment mechanisms used at later stages. This reasoning has been

considered in the theoretical literature, examining, for example, investments taken before marriage or business

partnerships (see, e.g., Bidner, 2010; Cole, Mailath, & Postlewaite, 2001; Felli & Roberts, 2016; Peters & Siow, 2002),

providing some insights into the incentive effects of different matching mechanisms (e.g., Booth & Coles, 2010; Gall,

Legros, & Newman, 2015, 2006), and mechanism design (Hatfield, Kojima, & Kominers, 2017). However, there has

been no comparable interest in examining empirically the dynamic effects of different assignment mechanisms.

1

The

aim of the current paper is to fill this void.

We design a real effort experiment with two stages: In the first stage, participants perform a task individually and do

not receive compensation. In the second stage, they are assigned to teams of size two based on their performance in the

previous stage, perform the task and receive compensation that depends on the average performance of the team.

However, the tasks worked on permit learning‐by‐doing, introducing a dynamic complementarity by increasing

individual productivity in the later stage. Given the novelty of examining the resulting dynamic incentive effects, we opt

for a clean design and shut down static complementarities or substitutabilities, that is, peer effects within teams in the

second stage. Thus, the design will allow some extrapolation of the results for the presence of positive or negative peer

effects.

The experimental variation stems from varying the rule that matches participants in the second stage. We examine

three salient forms of team assignment: Random matching (RAM), matching participants randomly ignoring their

performance in the first stage as a baseline treatment, positive assortative matching (PAM), in which the best performer

is matched with the second best and so on, and negative assortative matching (NAM), in which the best performer is

matched with the worst and so on. Besides the practical relevance, mechanism design theory would suggest that these

assignment policies are interesting for another reason: PAM rewards higher first‐stage performance with a better match,

and thus has a positive dynamic incentive effect on the first‐stage effort. Under RAM, the second‐stage match is

unrelated to first‐stage performance, thus shutting down the dynamic incentive effect. By contrast, under NAM higher

first stage yields a partner with worse first‐stage performance, yielding a negative dynamic incentive effect. However,

while PAM tends to induce investment behavior that is strictly monotone in productivity, thus revealing agents' types

through their investment choices, this is not necessarily the case with NAM, as there is a trade‐off between one's own

performance and the partner's performance in the second stage. Finally, as we are also interested in comparing the

efficacy of team formation policies as an incentive device in relation to explicit monetary incentives, we implement a

fourth treatment (R

I

&), in which participants also receive an individual piece rate for their first‐stage performance and

are randomly matched into teams.

We use a simple model to derive some theoretical pointers as to how outcomes in the individual‐work stage might

differ across the treatments. Individuals, who differ in their cost of effort, exert effort and invest through learning‐by‐

doing, and then are assigned into teams of size two with payoffs increasing in their partner's effort. The results we

obtain are largely consistent with the predictions. Intuitively, NAM leads to the lowest performance in the individual‐

work stage, substantially lower than in the other treatments (20% reduction in mean performance compared with RAM

and 30% compared with PAM). Perhaps surprisingly, RAM yields quantitatively similar performance outcomes as the

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