GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.175

Autonomy and Motivation: A Dual-Self Perspective

Junichiro IshidaFebruary 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Autonomy and Motivation: A Dual-Self Perspective∗
Junichiro Ishida
ISER, Osaka University
February 17, 2011

Abstract
This paper provides a simple autonomy-based model of human motivation in whicha decision maker with divided selves must perform some task. The key presumption of
the model is that the brain is not a unitary system which is equipped to achieve a single
goal in a systematic manner; rather, it is more like an organization which is hampered byseveral constraints such as preference incongruence and incomplete exchange (or imperfect recall) of information. Due to these constraints, the model yields behavioral patterns
that are consistent with various stylized facts of human motivation, mostly found in social psychology. The main findings of the paper are: (i) more autonomy induces more
motivation; (ii) complex tasks are susceptible to motivation crowding out; (iii) small rewards are detrimental to motivation; (iv) intrinsically interesting tasks are susceptible tomotivation crowding out.

JEL Classification Codes: D03, D99.
Key Words: Autonomy, Intrinsic and extrinsic motivation, Dual self, Motivation crowding
out.
∗ Correspondence to: Junichiro Ishida, Institute of Social and Economic Research, Osaka University, 6-1 Mi-

hogaoka, Ibaraki, Osaka 567-0047, Japan. E-mail address: jishida@iser.osaka-u.ac.jp.

1 Introduction
In economics, the term “incentive” is almost a synonym to motivation, and the distinction
between them is rarely made clear. Economists typically emphasize the role of incentives
in guiding and shaping human behavior without making much reference to motivation perse, as if they are simply two different ways of representing the same thing. This is probably due to the fact that economists are primarily concerned about extrinsic motivation –the side of human motivation which is induced by external enforcers, or “incentives,” suchas contingent rewards, monitoring, surveillance and evaluation.1 To the extent that there
exists a one-to-one monotonic relationship between motivation and incentives, the distinction between them is merely semantic and mixing them up does not lead to any substantial
complications.
The problem is that human motivation is a far more complicated subject, and extrinsic
motivation seems to represent only a part of it. It is now widely accepted, not only amongsocial psychologists but also increasingly among economists, that to fully understand human motivation, one needs to understand the workings of intrinsic motivation, which arises
from sheer pleasure of engaging in an activity itself, as well as those of extrinsic motivation.
To further complicate the issue, abundance of evidence also suggests that these two conceptsof motivation do not exist in isolation: there seem to exist substantial interactions between
the two, where a change in one often leads to a change in the other. These findings imply that
intrinsic and extrinsic motivation are not additive in nature, and focusing solely on extrinsic motivation, with no specific reference to intrinsic motivation, might lead to misleading
predictions.
What we need is then a description of the underlying mechanism that can explain how
intrinsic motivation interacts with extrinsic motivation. To this end, although there seems
to exist no unified theory of human motivation to date, the recent literature in social psy1 Of course, the distinction between motivation and incentive would ultimately come down to how we define

them. A conventional view is probably that incentive is a means (to induce motivation) whereas motivation isan end. According to the Oxford Dictionary of English, for instance, it is defined as “a thing that motivates or
encourages someone to do something.” We take this view throughout the paper although we interchangeably
use extrinsic rewards and incentives.

1chology indicates several consistent patterns observed in a variety of settings, which potentially provide us with an angle to inquire into this issue. First, it is now well known andfirmly established that external enforcers, such as rewards, surveillance, competition andevaluation, often undermine intrinsic motivation, thereby yielding a counterproductive effect (Deci, 1971; Deci and Ryan, 1985; Frey, 1997). Second, many studies also point out that
autonomy, such as control over method or timing and discretion in setting goals, is a key
determinant of intrinsic motivation (Hackman and Oldham, 1976; Gagne and Deci, 2005).
Although this second fact is less known than the first, various sources argue that people
tend to be more intrinsically motivated in doing an activity when it is their independentand “self-determined” choice to do so. Third, the saliency of intrinsic motivation depends
on the type of task people do. In particular, intrinsic motivation seems to matter more for
non-routine tasks, e.g., complex tasks or tasks that require creativity (Amabile et al., 1990;
Oldham and Cummings, 1996). Forth, the hidden cost of incentives seems to be more salient
when extrinsic rewards are relatively small in magnitude (Gneezy and Rustichini, 2000a). Finally, the hidden cost is more likely to surface when the target task is intrinsically interesting(Ryan et al., 1983; Deci et al., 1999).
In this paper, we construct a simple dual-self model of human motivation which is parsimonious and tractable enough to capture these observations. The key presumption of themodel is that the brain is not a unitary system that is equipped to achieve a single goal in acohesive manner; rather, it is like an organization which is hampered by various constraints
such as preference incongruence and incomplete exchange (or imperfect recall) of information.2 We consider a decision maker (DM) with divided selves, called Cognition and Affect,
who must perform some task. Cognition is the sophisticated self who is endowed withcognitive ability to evaluate alternatives and make choice, whereas Affect is the primitiveand instinctive self who is endowed with motivational or affective energy to carry out anaction.3 These differences in cognitive and affective characteristics give rise to the following
2 One of the earliest works to model intrapersonal conflicts is Thaler and Shefrin (1981). Recently, there are
increasingly many works which model a decision maker with divided selves. See Benabou and Tirole (2004),
Bernheim and Rangel (2004), Fudenberg and Levine (2006) and Brocas and Carrillo (2008) for recent examples.
3 This mean that Affect must take some initiative for one to produce an action. On this point, Camerer (2005)
et al. note “our view is that cognition by itself cannot produce action; to influence behavior, the cognitive system2three features of the model.

• Decentralization/specialition: There are two stages in implementing an action: theplanning stage (what to do) and the implementation stage (whether to do it). Thissequence of choices is made in a decentralized way, where Cognition (mostly) does
the first while Affect does the second.
• Incomplete information: The values, both extrinsic and intrinsic, of the action chosen
in the first stage are not accessible to Affect who must infer them from the primitivesof the environment.
• Preference incongruence: Cognition is more patient and forward-looking than Affect,
because it requires a certain level of cognitive ability to expect and appreciate potential
consequences of an action. This difference in time preferences effectively results in a
conflict of interests between them, because the extrinsic and intrinsic values typicallyrealize at different points in time.
To be more precise, the model goes as follows. In the first stage, either Cognition or
Affect chooses an action to implement from a set of feasible alternatives, each of which ischaracterized by its intrinsic and extrinsic values. Initiative in this stage can be taken byeither agent, depending on the complexity of the target task. In the second, Affect thendecides whether to actually carry out the action chosen previously. The problem is that,
due to the incomplete exchange or imperfect recall of information, it is not clear to Affect
why that particular action was chosen in the first place and hence how rewarding the action
is to him. Environmental factors, such as the degree of autonomy given to DM, rewards
associated with the task, and the nature of the task, may then influence DM’s motivation
as represented by Affect’s effort choice. Using this framework, we obtain conditions underwhich those environmental factors raise or undermine DM’s motivation.
The paper is related to several strands of literature, both in social psychology and economics. The entire framework relies heavily on an insight developed in Self-Perception
must operate via the affective system.”

3

Theory (Bem, 1972).4 The theory posits that our attitudes and feelings are often uncertain
and, when they are, we make an inference about these states by observing our past behaviors and the situation in which it occurs. To the extent that this holds true, external enforcers
can inflict a negative impact on our intrinsic motivation. For instance, when people are paid
to do an activity, they reason in retrospect that they do it because of the reward that theyget. The unfortunate consequence is that when that happens, people often lose their interestin the activity which they initially do it for its own sake. In social psychology, this is often
called the overjustification effect: extrinsic enforcers make them underestimate the intrinsic
value of the activity. Alternatively, Cognitive Evaluation Theory (CET) argues that external enforcers diminish feelings of autonomy and undermine intrinsic motivation through achange in perceived locus of causality (PLOC) from internal to external. Not much is known,
however, about the underlying mechanism that gives rise to the overjustification effect ora shift of PLOC. It is in particular not clear why we ever need to overjustify, rather thansimply justify, our originating motives. Constructing a simple autonomy-based model, we
provide a microfoundation for what appears to be overjustification.
Recently, the role of intrinsic motivation in general and the “hidden cost of rewards andincentives” in particular draw attention from economists as well and are discussed rather
extensively (Kreps, 1997; Frey, 1997; Frey and Oberholzer-Gee, 1997; Gneezy and Rustichini,
2000a, 2000b; Fehr and List, 2004; Falk and Kosfeld, 2006).5 Theoretical investigations of
the hidden cost of incentives have also flourished. In a setting with an informed principal,
Benabou and Tirole (2003) show that contingent rewards may be counterproductive sincethose rewards are taken as a signal about undesirable features of the task to be performed.
Benabou and Tirole (2006) argue that rewards diminish the incentive for prosocial behavior
because they undermine its signaling value. Sliwka (2007) considers a setting where somefraction of agents are conformists who derive utility from conforming to others. When those
4 Hirshleifer and Welch (2002) provide a model with potential memory loss (actions are remembered well

but information signals are not) which is related to Self-Perception Theory when it is brought into an individual decision problem. They then show when the decision maker exhibits excess inertia (insensitivity to new
information) and excess impulsiveness (excess sensitivity to new information). Benabou and Tirole (2004) also
consider a case where past attitudes are not certain and inferences must be made from past actions.
5 Also see Frey (2001) for a survey.

4

agents do not know what fraction of agents are fair, trust emerges as a signal that mostagents are indeed fair, and the principal may choose to trust, rather than control, agents.
Ellingsen and Johannesson (2008) consider a similar setting to Benabou and Tirole (2006)
but assume that the payoff of social esteem depends on the audience to whom the agent
tires to impress. In that setting, they show that material incentives erode esteem incentives
especially when the principal has a choice of incentive scheme.
All of these models mentioned above are concerned about interpersonal situations where
things such as trust and esteem matter. In contrast, we focus on an intrapersonal mechanismof motivation crowding out as an alternative route. Since most experimental results are obtained in controlled laboratory environments, where interactions are mostly anonymous andsocial incentives are supposedly less renounced, we argue that the intrapersonal perspective
can provide an insight that can complement the existing literature which focuses more onsocial incentives.6
The paper proceeds as follows. We outline the model in section 2 and analyze it insection 3. In section 4, we discuss main results of the model, especially when and underwhat conditions motivation crowding out occurs in this context. Finally, we offer someconcluding remarks in section 5.

2 Model
2.1 Setup
Consider a two-stage model between agent C (cognition, she) and agent A (affect, he).
These two selves altogether comprise a decision maker (DM) who must engage in sometask, which we call the target task. The decisions are made in a hierarchical and sequential
manner, where an action is chosen in the first (planning) stage and is implemented in thesecond (implementation) stage.
First stage: In the first stage, DM “finds” or “invents” an action to be implemented. The
6 To clarify our stance in the paper, we do not mean to argue that interpersonal models cannot explain exper-

imental results observed in laboratory settings. We do believe that social incentives work, either consciously or
subconsciously, in those settings to some extent. See Ellingsen and Johannesson (2008) for a discussion on thisissue. Our approach is hence not exclusive: there are many factors that come into play on this issue of human
motivation, and the intrapersonal mechanism which we illustrate here possibly provides one such factor.

5task in this context represents a (vague) goal that DM would like to achieve (such as “sellmore” or “raise revenue”) whereas the action represents a particular way to achieve it (howto proceed the task). Initiative in this stage can be taken by either agent A or agent C,
depending on the complexity of the task. We assume that agent C is called upon to makethis choice with probability ρ ∈ [0, 1] which measures the complexity of the target task: ρis closer to one when the task is more complex and requires more cognitive resources; it iscloser to zero when it is simpler and/or more routine.
Every possible action is completely characterized by its values (v, y), where v and yrefer to the intrinsic and extrinsic values, respectively. The extrinsic value reflects a material
benefit of the action and is often associated with an observable consequence of the action,e.g., the level of observable output, which takes some time to materialize. In contrast, theintrinsic value refers to other immediate gains that are intrinsic to the environment or to
the action itself, such as the sense of achievement, responsibility, and job satisfaction which
typically comes from inside DM.
While there are presumably many ways to model this process of “inventing” an action,
we adopt an approach that is amenable to the standard consumption-choice framework.
Suppose that each agent is endowed with some cognitive resource R which the agent incharge can allocate at his/her disposal. The agent must expend more resources to find anaction with higher values, so that the cost of coming up with an action with (v, y) is simply
given by d(v + y) where d > 0 is some constant. The values can only be improved so that(v, y) ∈ R2+ . Define r := R/d as the parameter capturing the degree of autonomy given
to DM. The basic idea is that the larger r is, the larger the set from which DM chooses anaction. In the most extreme case where DM is given no autonomy at all (r = 0), she has no
choice but to implement the default action, possibly assigned by an outsider, whose values
are normalized at (0, 0).
Second stage: After the action is chosen, agent A chooses the effort level e ∈ R + . The(motivational) cost of effort, which is incurred entirely by agent A, is given by e2 /2. What is
critical here is that the values of the chosen action is not accessible to agent A, either because
it is simply forgotten or because there is no established channel of communication between
6the two selves.

2.2 Payoffs
The key to the entire analysis is the misalignment of preferences between the two selves.
In particular, we would like to emphasize the difference in time preferences between them,which originates from the difference in cognitive ability to evaluate potential future consequences of an action. We assume that agent C is more patient and forward-looking thanagent A because agent C can foresee future consequences better.7 This difference in time
horizon matters because each value materializes at different points in time. The intrinsic
value tends to be realized more immediately than the extrinsic value because it stems mostly
from sheer pleasure of performing the task itself. In contrast, the extrinsic value takes moretime to materialize because it is contingent on the observable consequence of the action
which may not be immediately available.
We specify each agent’s preferences under this presumption. Given the values of theaction and the effort level, the payoff for agent C is given by
U C (v, y, e) = uC (v, wy)e,
where w ∈ R + is the incentive rate which may be imposed from outside. The incentive
rate is the parameter of our utmost concern and should be interpreted broadly: it is meant
to capture the salience of contingent rewards and punishments, surveillance, monitoring,evaluation and so on. The payoff for agent A is, on the other hand, given by
U A (v, y, e) = uA (v, wy)e −e2,
2

We make the following assumptions on the payoff functions.
Assumption 1 The payoff functions u j : R2+ → R + , j = A, C, are twice continuously differentiable and satisfy the following properties:
j

j

j

j

(i) u1 > 0, u2 > 0, u11 < 0, u22 < 0;jj(ii) limv→0 u1 = ∞ and limy→0 u2 = ∞.
7 There is ample evidence that long-term and short-term rewards are processes in different regions of thebrain. Also, Dohmen et al. (2010) show the correlation between cognitive ability and patience, implying thatcognition plays some role in evaluating long-term rewards.

7

Assumption 2 For any (v, y) and w,
MRSA :=

uC
uA
C
1
1
>
MRS
:
=
,
uA
uC
2
2

Assumption 2 is particularly important, which states that at any combination of the values,
agent A is always more willing to trade the extrinsic value (a future benefit) for the intrinsic
value (an immediate benefit) than agent C, capturing the idea that agent C is more patientand forward-looking.

3 The analysis
3.1 The second stage
Since agent A has no recollection of what has happened in the first stage, she must makean inference from the primitives of the model environment about the values of the chosen
action. Let (v̂ j , ŷ j ), j = A, C, denote the expected choice of the values when the choice ismade by agent j. Agent A’s problem in the second stage is then defined asmaxe[ρuA (v̂C , wŷC ) + (1 − ρ)uA (v̂A , wŷA )]e −e2.
2The optimal effort, denoted by e∗ , is given bye∗ = ûA (ρ) := ρuA (v̂C , wŷC ) + (1 − ρ)uA (v̂A , wŷA ).
Of course, in equilibrium, these expected choices must coincide with the actual choices.

3.2 The first stage
Let (v j , y j ) denote the actual choice of the values when it is made by agent j. When agent j
is called upon to make the choice, the agent solves
max( v j ,y j )u j (v j , wy j )ûA (ρ),

subject tov j + y j ≤ r :=

8

R
.
d

Since u is non-satiated, one can immediately see that the cognitive resource constraint always binds at the maximum. The first-order condition is given byjj

u1 − wu2 = 0,

(1)i.e., the values are chosen so as to satisfy MRS j = w if there exists an interior solution. Notethat under Assumption 1, an interior solution always exists, where the optimal solution canbe written as v j (r, w) and y j (r, w).
jk

j

jk

j

Define u jk := u j (vk , wyk ), u1 := u1 (vk , wyk ), u2 := u2 (vk , wyk ) and so on. Then, (1)implies
uAC
uAA
1
1
>
w
=
.
AA
AC
u
u2
2
Figure 1 illustrates this for two extreme cases (ρ = 0 and ρ = 1).8 Defineµ(r, w) :=

C
C
uAC
uA
1 ( v (r, w ), wy (r, w ))
1
=
,
C
C
uA
uAC
2 ( v (r, w ), wy (r, w ))2

which we use as a measure of the degree of preference incongruence between the two agents.
The preferences are identical when µ(r, w) = w for any (r, w) and become more divergent
as µ(r, w) becomes larger.
[Figure 1 about here]

4 What factors enhance (or diminish) motivation
The present framework allows us to examine how a change in the underlying environment
influences DM’s motivation which is directly represented by e∗ = ûA (ρ).

4.1 Autonomy
While the role of autonomy in inducing motivation is less discussed in economics, many
theoretical hypotheses argue and corresponding experimental results suggest that autonomy plays a decisive role in determining the level of human motivation: people tend to be
8 The first-stage problem is equivalent to max
jv,y u ( v, y) subject to v + y/w ≤ r. The figures are illustrated
this way, where the slope of the cognitive resource constraint is equal to − w.

9

more intrinsically motivated in doing an activity when it is their independent choice to doso. For instance, Cognitive Evaluation Theory (CET) argues that external enforcers diminish
feelings of autonomy and undermine intrinsic motivation through a change in perceive locus of causality (PLOC) from internal to external. In contrast, giving choice about aspects oftask engagement tends to enhance feelings of autonomy, prompting PLOC from external tointernal. Similarly, Self-Determination Theory, a revised and broader version of Cognitive
Evaluation Theory, clearly identifies autonomy as a driving force of human motivation.9 Job
Characteristic Theory also emphasizes autonomy as one of five important characteristics toenhance motivation (Hackman and Oldham, 1976). These theories imply that the allocationof authority and control right has some impacts on workers’ motivation in a way that is not
typically considered in economics.
We now examine how a change in the degree of autonomy r affects DM’s motivation. To
this end, it is convenient to establish the following notion.
Definition 1 The intrinsic value is a normal good for agent C iff ∂vC /∂r > 0.
It is widely accepted that most goods are indeed normal, implying that the condition should
not be particularly restrictive: in fact, this property holds for a wide class of preferences,such as CES, typically used in economic analyses. When this condition is satisfied, we canestablish the following result.
Proposition 1 An increase in r raises DM’s motivation (the equilibrium effort level e∗ ) if the intrinsic value is a normal good.
P ROOF : See Appendix.

The intuition behind this result should be clear and obvious. It simply says that agent
A, who has no recollection of what has happened in the first stage, can reason that an action
which is chosen from a wider set of alternatives is more likely to be of some value. In
contrast, when DM is given less autonomy, an action is expected to be imposed more from
9 See, for instance, Gagne and Deci (2005) for a survey.

10

outside and there is little reason to believe that it accords well with agent A’s preferences.
Figure 2 illustrates this when ρ = 0. In the figure, an increase in r raises Agent C’s payoffClevel from ūC
0 to ū1 and moves the equilibrium point accordingly. One can see that thischange induces more motivation from agent A as her payoff level improves at this new
equilibrium point.
[Figure 2 about here]

4.2 Extrinsic rewards
We now turn to the main focus of the analysis, i.e., the effect of a change in extrinsic rewards
on motivation. For expositional purposes, we say that motivation crowding out occurs if
an increase in w reduces the equilibrium effort level e∗ or, equivalently, agent A’s expected
payoff. There is now abundance of evidence which documents the undermining effect of
extrinsic rewards (the case of motivation crowding out), both in social psychology and economics. The previous findings are so overwhelming that the relevant question to be asked is
not whether this undermining effect exists, but when and under what conditions the effectis more likely to surface. In what follows, we raise several factors and discuss them in turn.
4.2.1

Complex tasks are susceptible to motivation crowding out

Cognition plays a larger role in choosing what to do when the task at hand is complicatedand/or requires creativity in some sense. A number of observations in fact suggest that
intrinsic motivation matters more for those complex, non-routine, tasks. First, many argue
that high intrinsic motivation is a necessary ingredient for achieving creativity (Amabile,
1996; Shalley and Oldham, 1997). Moreover, it is also suggested that the complexity of tasks
and intrinsic motivation (and creativity) are closely connected (Amabile, 1996; Boomer andJalajas, 2002; Hackman and Oldham, 1980). Given this nature, it is understandable that
motivation crowding out is more salient for complex tasks or tasks that require creativity.
Amabile et al. (1990) show that external factors such as evaluation and competition can be
detrimental to creativity. McGraw and McCullers (1979) find that monetary rewards also
diminish cognitive flexibility in problem solving while Erez et al. (1990) find that monetary11rewards diminish performance on a complex task with difficult goals. Of course, complex
tasks and tasks that require creativity are not always the same. Baer et al. (2003) show thatextrinsic rewards lower creativity for employees in complex tasks. All of these studies indicate that extrinsic rewards make people think that they perform the task for the rewards thatthey get, thereby inhibiting intrinsic motivation that is necessary for enhancing performancein complex tasks.
To examine the undermining effect of extrinsic rewards, it is convenient to use the following notion.
Definition 2 The intrinsic and extrinsic values are gross substitutes for agent C if ∂vC /∂w < 0.
Two goods are said to be gross substitutes if the Marshallian demand for one good increases
when the price of the other good increases.10 Again, the condition for gross substitutability
is not particularly restrictive: in the case of preferences represented by CES, the goods aregross substitutes if the elasticity of substitution is greater than one.
In the present context, the complexity of the task is measured by ρ, where a larger ρmeans that the target task is more complicated and hence agent C is more likely to takeover the decision-making process. We then obtain the following result which shows that
motivation crowding out is more likely for complex, non-routine, tasks.
Proposition 2 Suppose that (i) the values are gross substitutes and (ii) the preferences are sufficiently divergent, i.e., µ(r, w) is sufficiently large. Then, motivation crowding out occurs if ρ issufficiently close to one.
P ROOF : See Appendix.

[Figure 3 about here]
The proposition indicates that motivation crowding out is more likely to occur when
the preferences are divergent (a large µ) and the target task is relatively complex (a large
10 Since the price of the extrinsic value can be regarded as 1/w, the two values are gross substitutes for agent

C if ∂vC /∂w < 0.

12ρ). These conditions are closely related and complementary to each other. When the task
is simple and the first-stage choice is made by agent A, there is little room for preference
incongruence to play any role, meaning that motivation crowding out is less likely to occur.
In contrast, as the task becomes more complicated, an increase in w sways the choice excessively towards the extrinsic value (overjustification), from the viewpoint of Agent A, thereby
lowering her subsequent payoff. The following result establishes necessary conditions for
motivation crowding out in the current context.
Proposition 3 Motivation crowding out never occurs if ρ = 0 or µ(r, w) = w for all (r, w).
P ROOF : See Appendix.

This result shows that preference incongruence within oneself is the driving force of motivation crowding out, which provides an answer to the question we set out at the beginning,i.e., why we ever need to overjustify, rather than justify, our originating motives. To see this,note that our model is the one of perfectly rational agents where agent A rationally forms
expectations about agent C’s behavior: a change in w changes agent C’s choice of the values,
but any change in the choice is always correctly anticipated by agent A. Our model showsthat what appears to be overjustification can be understood within the framework which
strictly rests on rational behavior, without relying on irrational overjustification, as long as
there is some degree of preference incongruence within one self. In contrast, one can also
argue that the presence of preference incongruence is the necessary condition for motivation
crowding out in the current setup.
4.2.2

Small rewards are detrimental to motivation

Some of recent experiments show that extrinsic rewards undermine intrinsic motivation especially when the rewards are small in magnitude, i.e., no rewards are better than small
rewards (Gneezy and Rustichini, 2000a). Intuitively, when no rewards are offered at all, theactivity must be done purely for intrinsic motivation. Small rewards are then detrimental
because they shift agent C’s attention more towards the extrinsic value, which makes pref-13erence incongruence more resounding.
Proposition 4 Suppose that the values are gross substitutes and limy→0 yuA
2 = 0. Then, motivation crowding out occurs for any ρ ∈ (0, 1] if w is sufficiently small.
P ROOF : See Appendix.

[Figure 3 about here]
This result stems from the fact that motivation crowding out is more likely when yA
and yC are relatively small. To see this, we need to consider both the direct effect and theindirect effect of changes in the incentive rate w. First, fixing the choice of the values, a unit
A AA
increase in w directly raise agent A’s payoff by ρyC uAC
2 + (1 − ρ) y u2 , which is positiveby design. Second, a change in w shifts the choice of the values and indirectly affects his
payoff. The second, indirect, effect is negative when the values are gross substitutes, andmotivation crowding out surfaces when the indirect effect dominates the direct effect. It isthen clear that when yA and yC are smaller, the direct effect is weaker and more likely to be
dominated by the indirect effect. Small rewards are then detrimental to motivation because
the marginal payoff from the extrinsic value is low when the incentive rate w is low, making
the direct effect less of a factor.
4.2.3

Intrinsically interesting tasks are susceptible to motivation crowding out

A consensus among social psychologists is that the target task must be intrinsically interesting to observe any effects on intrinsic motivation. Due to this widely held perception, mostexperiments in fact examine the effect of external rewards for interesting activities (Ryan etal., 1983; Deci et al., 1999). To examine this issue, we defineφ(r, w) :=yC (r, w),
wvC (r, w)

and φmax := max(r,w) φ(r, w). When the marginal return to raising y is small, agent C expends more resources to raise v. We thus take φmax as measuring how intrinsically interest14

ing the target task is: we say that the task is intrinsically interesting and challenging whenφmax is small.
Proposition 5 Suppose that the values are gross substitutes. Then, motivation crowding out occurs
for any ρ ∈ (0, 1] if φmax is sufficiently small.
P ROOF : See Appendix.

5 Conclusion
This paper provides a simple dual-self model of human motivation which allows us to inquire into the effects of various environmental factors on human motivation. The present
model shows that extrinsic rewards may indeed produce a counterproductive effect andclarify under what conditions this negative consequence of rewards is more likely to surface. The main findings of the paper are: (i) more autonomy induces more motivation; (ii)complex tasks are susceptible to motivation crowding out; (iii) small rewards are detrimental to motivation; (iv) intrinsically interesting tasks are susceptible to motivation crowdingout.
A natural next step is to take the present framework into interpersonal contexts. The
incentive rate w and the degree of autonomy r are noth likely to be under the principal’s
discretion. If the principal cares only about the extrinsic value, e.g., the output, then she
faces an interesting tradeoff. Giving more autonomy to the agent results in the action that isfun (a high intrinsic value) but not so productive. The cost arising from this distorted choiceof action may, however, be more than compensated by an increase in the agent’s motivation.
This in fact seems to be the tradeoff faced by many managers: the tradeoff between lesscontrol and more motivation. The present framework can be extended to shed light on this
aspect, and it is of some importance to address this issue in future.

15

Appendix: proofs
P ROOF OF P ROPOSITION 1: An increase in r raises DM’s motivation iff


A
A
C
∂vC
AA ∂v
AC ∂y
AA ∂y
+
(
1
−
ρ
)
u
> 0,
+
wu
+
wu
ρ uAC
2
1
2
1
∂r
∂r
∂r
∂r
∂y j
∂v j
+
= 1, j = A, C.
∂r∂r
This can be written as


C
AC ∂v
AC
ρ (uAC−wu)+ (1 − ρ)wuAA
> 0.
+
wu
2
2
2
1
∂r
AC , this condition holds if ∂vC /∂r > 0, i.e., the intrinsic
Since we already know that uAC
1 > wuvalue is a normal good.
Q.E.D.
P ROOF OF P ROPOSITION 2: An increase in w lowers DM’s motivation iff




A
C
A
∂vC
AA ∂v
AC ∂y
C AC
AA ∂y
A AA
+
(
1
−
ρ
)
u
< 0,
+
wu
+
y
u
+
wu
+
y
u
ρ uAC
2
2
2
2
1
1
∂w
∂w
∂w
∂w
where
∂v j
∂y j
+
= 0, j = A, C.
∂w∂w
It follows from these that


C
AC ∂v
C AC
)
−
wu
ρ (uAC< 0,+ (1 − ρ)yA uAA
+
y
u
2
2
2
1
∂w
As ρ → 1, (2) becomesAC(uAC
1 − wu2 )∂vC+ yC uAC
2 < 0,∂w

which is further reduced to(µ(r, w) − w)∂vC
+ yC < 0.
∂w

Given that the values are gross substitutes, this holds if µ(r, w) is sufficiently large.
16(2)

Q.E.D.
P ROOF OF P ROPOSITION 3: When ρ = 0, (2) is reduced to yA uAA> 0, so that this condition
2
never holds. When µ(r, w) = w for all (r, w), on the other hand, (2) becomesρyC + (1 − ρ)yA

uAA
2
< 0,
uAC
2

which never holds either.
Q.E.D.
P ROOF OF P ROPOSITION 4: Note that as w → 0, y j → 0. If limy→0 yuA
2 = 0, (2) becomesAC(uAC
1 − wu2 )

∂vC
< 0,
∂w

for any ρ > 0. It is immediate to see that this condition holds if the values are gross substitutes.
Q.E.D.
P ROOF OF P ROPOSITION 5: Motivation crowding out occurs if


uAA
∂vC
ρ (µ(r, w) − w)
+ yC + (1 − ρ)yA 2AC < 0.
∂w
u2

(3)

Dividing both side of (3) by wvC (r, w) we obtainρ µ(r, w) − w ∂vC
wvC (r, w) ∂w+ φ(r, w) + (1 − ρ)

uAA
yA
2
< 0.
wvC (r, w) uAC
2

Since yC (r, w) > yA (r, w) for any (r, w), it suffices to show that
ρ

uAA
2
+
φ
(
r,
w
)
+
(
1
−
ρ
)
φ
(
r,
w
)
< 0.
wvC (r, w) ∂w
uAC2

 µ(r, w) − w ∂vCAs φmax → 0, the condition becomes(µ(r, w) − w)

∂vC
< 0,
∂w

which holds if the values are gross substitutes.
Q.E.D.
17

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20

y( vC , yC )uC = ūC( vA , yA )u A = û A (1)u A = û A (0)v
Figure 1: The equilibrium choice of the values and the corresponding motivation level.

21yuC = ū1C

uC = ū0C

u A = û A (1)v
Figure 2: Autonomy enhances motivation (ρ = 1).

22

yuC = ū1C
uC = ū0C

u A = û A (1)v
Figure 3: The case of motivation crowding out (ρ = 1).

23