Team Incentives and Reference‐Dependent Preferences

• Date: 01 December 2016
• DOI: http://doi.org/10.1111/jems.12166
• Published date: 01 December 2016
• Author: Kohei Daido,Takeshi Murooka

Team Incentives and Reference-Dependent

Preferences

KOHEI DAIDO

School of Economics

Kwansei Gakuin University

1-155 Ichiban-cho Uegahara Nishinomiya, Hyogo Japan 662-8501

daido@kwansei.ac.jp

TAKESHI MUROOKA

Department of Economics

University of Munich

Ludwigstr. 28 Rgb, 80539 Munich Germany

takeshi.murooka@econ.lmu.de

We investigate a multi-agent moral-hazard model where agents have expectation-based reference-

dependent preferences `

alaK

˝

oszegi and Rabin (2006, 2007). We show that even when each agent’s

probability of success in a project is independent, a principal may employ team incentives. Because

the agents are loss averse, they have first-order risk aversion to wage uncertainty. This causes

the agents to work harder when their own failure is stochastically compensated through other

agents’ performance. In the optimal contract, agents with high performance are always rewarded,

whereas agents with low performance are rewarded if and only if other agents’ performance is

high.

1. Introduction

Teams and team incentives have become popular in workplaces.1Why team incentives

have so prevailed is one of the main themes in organizational economics. Existing

literature has studied team incentives from the view of competition, cooperation, or

mutual monitoring, and the literature has investigated under which condition team

incentives are optimal. Why firms sometimes reward low-performance employees as

well as high-performance ones, however, is still under-investigated. This paper offers

a new rationale by focusing on a prominent behavioral aspect, loss aversion: agents are

This paper was circulated under the title “Loss Aversion,Stochastic Compensation, and Team Incentives.” We

thank Stefano DellaVigna, Ernst Fehr,Ben Hermalin, Daisuke Hirata, Hideshi Itoh, Michihiro Kandori, Maciej

Kotowski, Sheng Li, Rosario Macera, Toshihiro Matsumura, Fumio Ohtake, Aniko ¨

Ory,Matthew Rabin, Dan

Sasaki, Steve Tadelis, Jidong Zhou, and especially Fabian Herweg, Botond K˝

oszegi, the co-editor, and two

anonymous referees for helpful comments. We are also grateful to participants at Nagoya University, UC

Berkeley, University of Tokyo, Contract Theory Workshop, Contract Theory Workshop East, the 4th annual

meeting of Association of Behavioral Economics and Finance (ABEF), and PET14. This paper received the

incentive award of the 4th annual meeting of ABEF.Daido thanks UC Berkeley and UC San Diego for hospi-

tality and MEXT/JSPS KAKENHI Grant Number 23730259 and 15K03529. Murooka gratefully acknowledges

financial support from the Murata Overseas Scholarship Foundation.

1. Lazear and Shaw (2007) introduce evidence of the popularity of teams and team incentives. For example,

from 1987 to 1996, the percentage of large firms that have 20% or more of their employees in teams increased

from 37% to 61%, and those that have more than 20% of employees working with some kind of group-based

incentive increased from 26% to 53%. Che and Yoo(2001) also provide evidence of the successful adaptation

of teams in workplaces. We use the term “team incentives” to refer to a wage payment scheme where an

employee’s wage depends on performance of other workers.

C2016 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume25, Number 4, Winter 2016, 958–989

Team Incentives 959

more sensitive to losses than to same-sized gains. Building upon and complementing the

literature on moral-hazard problems under loss aversion (Daido and Itoh, 2007; Herweg

et al., 2010), we analyze a multi-agent moral-hazard model with limited liability in which

agents have expectation-based reference-dependent preferences `

alaK

˝

oszegi and Rabin

(2006, 2007). The agents feel a psychological gain–loss from comparing their realized

outcome with their expected outcomes. Under loss aversion, team incentives can serve

as a device that alleviates the agents’ expected losses from their wage uncertainty,

even when their projects are independent. We show that, in the optimal contract, both

successful and unsuccessful agents are equally rewarded if their total performance is

high; otherwise only successful agents are rewarded. Our result helps explain why firms

sometimes pay high wages to all employees even though some of them fail to achieve

their projects, especially when the firms earn high total profits.

In our model, a principal designs a contract that minimizes expected wage pay-

ments to agents subject to the constraints that each agent exerts effort in his own project

and he is protected by limited liability.2The agents’ effort is not verifiable, but the princi-

pal can condition the payments on whether each project is successful or not. The success

probability of the projects is independent across the agents. Each agent’s utility consists

of an intrinsic “consumption utility” which corresponds to the standard utility, and a

psychological “gain–loss utility” which is defined as the difference between his realized

outcome and his reference point. The agent is loss averse: he dislikes losses more than he

likes same-sized gains relative to a reference point. Because the agent is loss averse, he

has first-order risk aversion to wage uncertainty, which is qualitatively different from a

standard concave utility.3To determine reference points endogenously, we assume that

the agent’s reference points are formed based on his rational expectations. Specifically,

we assume that each agent’s reference points are updated to his chosen action before

the outcomes of the projects are realized. Because the agent knows his reference points

will be updated based on his chosen action, he takes this into account when he chooses

his action. This notion is called the choice-acclimating personal equilibrium (CPE) and is

developed by K˝

oszegi and Rabin (2007).4

We first analyze a symmetric two-agent model in which each agent’s limited lia-

bility constraint binds but his participation constraint to the project does not bind. We

derive when the optimal wage scheme exhibits independent performance evaluation

(IPE), relative performance evaluation (RPE) or joint performance evaluation (JPE).5We

show that the principal may adopt team incentives in order to compensate an agent

contingent on his colleague’s performance. In particular, team incentives based on JPE

2. We use male pronounsto refer to an agent and female pronouns to refer to a principal.

3. As an illustrative example, suppose that an agent expects to work hard and to receive either $0 or

$30 with equal probabilities. Suppose also that he actually works hard. In the wage dimension, his expected

gain–loss utility consists of a weighted average of the following four cases with equal weights. There is no

gain–loss in two cases: he expects to receive $0 and actually receives $0, and he expects to receive $30 and

actually receives $30. In the case where he expects to receive $30 but actually receives$0, the agent feels a loss

of $30. Similarly, in the case where he expects to receive $0 but actually receives $30, the agent feels a gain

of $30. Because the agent is loss averse, his feeling of a $30 loss looms larger than that of a $30 gain. Hence,

his expected gain–loss utility for wage is negative and represents his aversion to wage uncertainty. In the

effort-cost dimension, he feels neither gains nor losses because he expects to work hard and actually works

hard.

4. CPE is plausible when the action is determined long before the outcome is realized, and the agent’s

reference points are acclimated before he knows the actual outcome. K˝

oszegi and Rabin (2006, 2007) develop

another equilibrium concept, the preferred personal equilibrium (PPE). We discuss properties of equilibrium

wage schemes under PPE in Section 6.1.

5. IPE, RPE, or JPE denotes that an agent’s wage is irrelevant to, decreases in, or increases in the perfor-

mance of other agents, respectively.

960 Journal of Economics & Management Strategy

are optimal when the agent’s loss aversion is moderate and the probability of success in

the project is low.In addition, optimal contracts based on JPE appear in a broader range

of the degree of loss aversion than those based on RPE. We also investigate a case in

which the principal hires many agents, and show that the optimality of team incentives

based on JPE is still valid: an agent is rewarded either when he succeeds in his project or

when the total performance is higher than a certain threshold. Note that in the latter case,

both successful and unsuccessful agents are equally rewarded. We further characterize

a case in which each agent’s participation constraint may bind in the optimal contract,

and show that how the property of the optimal contract is robust to this extension.

The crux of our result is that the principal faces a trade-off between the standard

incentive effect in the intrinsic consumption utility and the loss-reducing effect in the gain–

loss utility. On the one hand, the standard incentive effect leads each agent to work less

under team incentives than under IPE because his incentive to work hard decreases if

the principal compensates for his failure through team incentives. On the other hand, the

loss-reducing effect can work as the opposite. Because the agent is first-order risk averse,

working hard may increase the agent’s expected loss. This is more likely to occur when

the probability of success in the project is low.By adopting team incentives, the principal

can reduce each agent’s expected loss when he works hard, and she can also increaseeach

agent’s expected loss when he works less. As a result, team incentives become optimal

when the loss-reducing effect outweighs the standard incentive effect. Importantly, the

principal compensates for the agent’s failure only partially in the optimal contract: low-

performance agent is compensated for his failure only when other agents succeed. This

is because if each agent’s failure is always compensated, the standard incentive effect

always dominates the loss-reducing effect under limited liability.

Notice that if the principal can commit to stochastically compensate for the agent’s

failure individually (i.e., independent of other agents’ outcomes), our results do not

need to be team incentives. However, team incentives based on JPE seem moreplausible

than such individual stochastic compensation in practice. In Section 4.4, we show that if

the principal has a possibility of facing a credit constraint, then she prefers to adopt JPE

rather than to adopt any type of individual stochastic compensation. Intuitively, under

individual stochastic compensation, the principal cannot afford to pay high wages if all

agents fail in their projects because of her credit constraint. In contrast, the principal can

afford to pay high wages through the revenue of successful projects under JPE because

low-performance agents get paid such high wages only when other agents succeed in

the projects.

Last but not least, our model does not have classical team-production aspects such

as common noise shocks, production externalities, help, sabotage, or mutual monitor-

ing. In this sense, our model differs from the existing literature on team incentives.

However, we show that even when we do not explicitly incorporate such aspects of

team production, forming teams and introducing team incentives may be beneficial for

principals. It helps explain why teams and team incentives are ubiquitous even when

some workplaces do not seem to have the above aspects of team production.

This article is organized as follows. The related literature is summarized in

Section 2. In Section 3, we set up a two-agent model. In Section 4, we analyze the opti-

mal wage schemes of the model. In Section 5, we extend our model to the many-agent

case and investigate the effect of incorporating the agents’ participation constraints. In

Section 6, we discuss other extensions: a case applying a different solution concept and

a case where the agents are not only loss averse but also have a concave consumption

utility. Section 7 concludes.