A
HD28
.M414
no. 3375"
ALFRED
P.
Human
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
Relations in the Workplace
Julio J.
Rotemberg
*
WP# 3375-92-EFA
January 1992
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
Human
Relations in the Workplace
*
Julio J.
Rotemberg
WP#
3375-92-EFA
January 1992
Abstract
This paper seeks to understand wliat motivates workers to be friendly towards one another and studies whether firnis benefit from encouraging these
workplace.
The paper
first
three situations.
The paper then
The
second relationship
I
first
relations" in the
proposes that feelings of friendship, or altruism, can be
dividually rational in certain settings
strategically linked.
"human
where the variables controlled by the workers are
studies
has workers
consider
is
in-
who
what
this implies for equilibrium altruism in
are paid as a function of joint output.
The
that between subordinates and their supervisors while
the third heis workers paid as a function of their relative performance.
'Sloan School of Management, M.I.T. I wish to thank Deborah Ancona for helpful conversations, Bob Pindyck, Rob
Matthew Rabin, Garth Saloner and Jeremy Stein for comments, and the NSF for research support.
Porter,
LIBRARIES
j
pre
2
1
1992
Human
Relations in the Workplace
Julio J.
Rotemberg
People have feelings for those they work with. This raises two questions. The
these feelings affect performance on the job and the second, whose interest
to the
first
question
is
affirmative,
what
is
is
first is
enhanced
gives rise to these feelings. In this paper
I
if
whether
the answer
consider both
the effects and the causes of one particular set of feelings, namely feelings of friendship and altruism.
Having answered both questions,
I
give conditions under
which a firm would increase
its profits
by
spending resources to enhance the friendliness of employees towards each other.
The
is
idea that feelings of friendship (or
an old one, dating back at
least to
Mayo
"human
(1933).
relations") affect
performance
in the
workplace
The famous "Hawthorne experiments" reported
of Roethlisberger and Dickson (1939) appeared to confirm the importance of these personal relations in industrial settings.
Subsequently, a large
number
of empirical studies were conducted
relating productivity in small groups to the feelings reported by the
members
particular feature of groups that has been explored in several studies (see
Schminke (1985)
for a discussion)
means the extent
to
is
of the group.
One
Goodman, Ravlin and
group cohesiveness, whose definition varies but which often
which members of the group express that they
like
other
members
of the group.
Unfortunately, these studies of the relation between cohesiveness and productivity have delivered
mixed
results.
In this paper,
I
equate people's expression of liking for each other
to be classified as highly cohesive) with feelings of altruism.
between cohesiveness and productivity
take actions
who
then not surprising.
is
benefit fellow employees,
(i.e.,
(i.e.,
those which lead groups
The ambiguity
If
employees who
work
little
or to
work hard.
It
fellow employees to reduce their
effect
if,
has the former effect
own
effort while
by working harder an employee
like
each other
act altruistically), the effects on firm output
firm profitability depend on the setting. Altruism towards fellow employees
to
of the relationship
if
may
lead an employee
a cutback in an individual's effort allows
keeping their income constant.
raises the
and
income of
It
has the latter
his or her fellow employees.
This
would occur
individual output
if
unobservable and each employee
is
is
paid as a function of group
output.
This ambiguity
is
the
same
of "collusion" in organizations.
to collude
i.e.,
ais
that analyzed by
They focused on the
when the
firm's best
way
employees to exert lower
so that compensation
efiFects
if
is
On
tied to
the other hand,
if
is
are similar to those of contracts.
is
One reason
that altruism works even
to arise are not the
Finally,
my model
that, as
is
same
I
will
is
is
when
make them
to
for the firm
is
to
because
compete with
it
leads both
beneficial to the firm.
why one should study
a result of the repeated nature of the interaction.
Another difference
profitability of allowing workers
the firm can only observe collective output
altruism in the workplace
if its
that contracts between workers, particularly
they hurt the employer are not enforceable by the courts.
is
bad
group performance, collusion
issue that arises at this point
and altruism
study
Like altruism, these binding contracts
of inducing effort by employees
effort.
in their
enhance each other's welfare. Holmstrom and Milgrom show
each other, as in Lazear and Rosen (1971), collusion
One
on firm
effects
to write binding contracts with each other.
also lead workers to take actions that
that,
Holmstrom and Milgrom (1990)
One key
The
contracts might be self enforcing as
difference between this self-enforcement
the relationship between workers
is
about to end.
argue below, the conditions under which altruism
as those under which workers profit
is
likely
from contracting with each other.
of altruism generally has a unique equilibrium whereas equilibria in self-enforcing
repeated interactions are typically non-unique.
A
second issue
whether the mixed results
is
in the empirical relationship
between the cohesive-
ness of groups and their productivity can be explained by equating cohesiveness with a high degree
of altruism. In other words,
cally
towards them?
I
do people who express that they
like their
co-workers behave altruisti-
argue below that some of these empirical studies are indeed consistent with
the view that cohesion has the same effect on output as altruism. However, there are
many
other
empirical studies of this relationship which do not provide sufficient details to verify whether they
are consistent with the
If
model developed
here.
mutual attraction, and altruism, are indeed relevant
workplace,
it
becomes important to ask what brings these
in affecting
performance within the
feelings about.
of attraction between individuals are generally "backwards looking"
.
They
The
existing theories
treat the liking of an
individual for another as a reaction to what.kas gone on before. Thus, there exist large literatures
Aronson (1984)
(see
people
whom
Along similar
showing that,
for references)
in
experimental settings, people tend to
they perceive to be similar to themselves and people
lines,
Romans
(Romans
(1961).
Thus
us confer the reward of
is
are physically attractive.
(1950) and Thibaut and Kelley (1959) posit that attraction
consequence of having pleasant interactions with people.
from these observations
who
that people like individuals
A general conclusion
who
give
them
is
large rewards.
utility? In this
when
this
is
paper
large "rewards" at low "costs"
physically attractive people confer aesthetic rewards, people that agree with
making us
feel
that
we
are right etc.
who
give
In other words, are feelings of affection instrumental in raising one's
own
I
pursue this possibility;
in their self interest.
an individual starts with a
utility
a natural
that seems to emerge
This general conclusion raises the question whether people benefit by liking those
them
like
Formally,
I
develop a model in which people become altruistic
I
treat the degree of altruism
utility defined over his
function and become altruistic.^
If
own
a choice variable:
zis
welfare and chooses whether to change his
he does change
his decisions
it,
from then on take into
account the welfare of another individual.
The assumption
that people choose their altruism, which
of in two other ways.
First,
may be
controversial, can be thought
one can think of the individual as taking actions (such as inviting
the other to dinner) which modify his attitude towards the other person. Viewed in this way, the
model
is
akin to the rational addiction model of Becker and
knows that the
initial
Murphy
consumption of an addictive substance
substance in the future.
will
change
Second, one can think of natural selection
change their emotions whenever that
is
(1988) where the individual
cis
his attitude
towards the
favoring individuals
who
useful to them. In this cjise, the individual might feel
no
control over his emotions even though these are changing in self interested ways.
I
now turn
to the benefits that the individual derives from his altruism.
that, unless this altruism can be credibly demonstrated,
it is
It
should be clear
not in the individual's self interest.
Altruism leads the individual to take actions which maximize a combination of his own and the
'The sort of opportunistic change in tastes I consider is also featured in Akeriof (1983) who shows how people benefit
from becoming loyal, in Frank (1987) who shows that they benefit from having feelings of guilt when they take advantage of
others. Coleman's (1990) self-interested change in tastes is somewhat different since it involves an actor who becomes happy by
"changing himself to be satisfied with the world" (p. 517). Coleman (1990) also considers actors who relinquish control of their
actions to groups of individuals. This is more similar to what is considered here since these groups have potentially different
objectives from those of the narrowly conceived individual.
and
other's utility function
been purely
On
A
B
this,
knows that A's behavior
B
is
this occurs
is
modify
led to
to feel altruistic towards
which
A
the other hand, consider the case where
affect B's behavior. If
by
own
utility
than
if
the individual had
selfish.
Knowing
him.
this results in a lower level of
B
will
his
will
behavior
if
B
be different.
in
that he feel altruistic towards
This, in turn, will sometimes
a way that benefits A, the
have been a smart one.
related to the strategic
(1985). This condition requires that,
can prove to
I
will
initial
decision
show that the condition under
complementary of Bulow, Geanakoplos and Klemperer
each individual takes one action and these are normalized
so that increases in one person's action raise the other person's welfare, a marginal increase in A's
action leads to an increase in B's.
Since altruism
is
only beneficial
if it
can be proved,
degree.^
This irreversibility seems natural
a person
is
altruistic
if
it
must be
irreversible, at least to
one thinks of altruism as a change
in tastes.
towards another, he stops having an incentive to alter the
selfishness (unless that
somehow made both
better off).
In practice,
utility
some
Once
towards
one does see people who
stop liking one another. These further changes in emotions seem to arise as conditions within the
relationship change, usually in ex ante unpredictable ways.
hcis
To keep the
analysis simple,
my model
individuals interacting only once so that these later changes in emotions play no role.
This
baisic
idea that altruism can be privately beneficial
is
closely related to Becker (1974a).
Becker's (1974a) "rotten kid theorem" establishes that the interaction between a selfish and an
altruistic individual
will,
can lead to Paireto Optimal allocations.
In particular, the selfish individual
under certain circumstances, take actions which maximize joint income. This result hinges
on three assumptions.
First, the altruistic individual
must be so
rich
and so
altruistic that, in
equilibrium, he makes positive transfers to the selfish one. Second, the altruistic individual must
act after the selfish one. These assumptions imply that the altruist will lower his transfers to the
selfish individual
be linear
The
in
when
the latter reduces joint income.^ Finally, the selfish individual's utility must
the ex post transfers by the altruistic one. (Bergstrom (1989)).
"rotten kid theorem" does not establish that the altruist gains from his altruism.
closely related paper, Becker (1976) argues that altruistic individuals can, indeed,
is thus a form of commitment.
^Further discussion of these two assumptions can be found
^It
in Hirshleifer (1977).
In a
end up better
off
than
selfish ones.
His argument
is
largely informal,
though
the altruist would, ex post, punish the selfish individual
benefit the altruist.
selfish individuals
On
I
To avoid some
With
the latter failed to take actions which
change
this
I
devote Sections
1
and 5 to clarifying when altruism
in the
it
applications in the workplace. This boils
variables of different employees tend to be strategic
When
and
in Section 5
do
I
discuss
move games
down
in Section 1,
I
to an analysis of whether the strategic
complements or substitutes
in different settings.
they are complements, friendship should arise endogenously.
The
their
players take actions
remains a force which promotes such altruism.
After considering rational altruism within abstract simultaneous
its
is
timing of moves, strategic complementarity ceases to be
although
sufficient for equilibrium altruism,
turn to
when
of the asymmetries introduced
games with simultaneous moves. Only
focus mostly on
sequential moves.
based on an example where
is
altruists.
Given these contradictory findings,
sequentially,
too
the other hand, Bernheim and Stark (1988) provide an example where
do better than
individually rational.^
if
it
first
relationship
consider
I
payment depends only on
raise productivity.
that between two employees
their joint output.
Thus the
friendliness of their employees
is
is
from altruism among employees,
issue
I
show
who work
as a
team
in that
that, as a result, altruism tends to arise
whether firms benefit by spending resources to increase the
a subtle one. In the case of joint output, where the firm benefits
it
arises
anyway
as a consequence of the dependence of employee
compensation on total output. Moreover, the firm can make sure the employees
changing the group's incentive payment. Nonetheless,
I
like
each other by
show that there are circumstances where
additional payments to foster altruism are beneficial to the firm.
Section 2 also contains an extended discussion of some of the "Hawthorne experiments"
re-
ported by Roethlisberger and Dickson (1939). These experiments suggest that changing the incentive
payment together with the creation of an atmosphere conducive to friendship help productivity
more than
either
change on
its
own.
I
also discuss additional evidence
on the relationship between
cohesiveness and productivity which shows that altruism and measures of group cohesiveness are
closely linked.
In Section 3,
''Altruism
is
I
consider a second relationship within the workplace and that
rational in
my model
in the
same sense that addiction
5
is
rational in Becker
is
the relationship
and Murphy (1988).
of authority.
Several authors including
Homans
authority tend to be less friendly than relations
the case of supervisors
whose main
role
is
compensation, such absence of friendship
is
(1950) have pointed out that relationships of
among more
equal co-workers.
show
I
that, in
to monitor their subordinates' cictions for purposes of
to be expected.
I
also consider
an authority relationship
described in Crozier (1964) in which a "team leader" has no authority to set compensation but does
have some control over the pace of work.
The workers
feature.
I
focus on this relationship because
in this setting generally
reported that they did not
it
like
has an unexpected
each other (which
I
equate with lack of altruism). The exception was that team leaders liked their co-workers. This
assymetry seems hard to explain with the backwards-looking models of altruism but
my own
fits
well with
model.
Third, in Section
4,
I
consider two workers whose individual output
Lazear and Rosen (1971) there
is
a
common
shock to productivity which
is
As
observable.
is
in
not observable by the
Thus, payment schemes that pay workers as a function of the rank order of their output,
firm.
Yet, Lazear (1989) shows that they are relatively rare.
are quite desirable.
I
show
Section 4
in
some
that these schemes often encourage altruism between the affected workers and thereby lose
of their desirable incentive effects. Section 5 considers sequential
games while Section 6
offers
some
conclusions.
Rational Altruism
1.
In this section,
I
I
show how individuals can benefit by changing
their tzistes towards altruism.
take up separately the general case of continuous choices and the classical prisoner's
dilemma
problem.
1.1.
Continuous Choices
A
There are two individuals,
utility
functions of
A
and
B
and B, who carry out actions a and
are, respectively, a(o, 6)
thought of as being the "true" welfare
of
A
in
my
and
effort.
B
so that
a depends
(or, in the
and
/9(a,6).
only on what happens to
generally, particularly
'Assuming that the
disutility of effort
is
if
These
utility
The
initial
functions can be
terminology of Rabin (1991), "material payoff')
A
individually and similairly for
simple settings a depends on A's income and on his
More
6 respectively.
own
effort
but not on
fi's
/3.
Thus,
income or
one takes an evolutionary interpretation of changing
tastes,
separable from whatever pleasure the individual gets as a result of his altruism, the
one could define a and
If
as the ultimate fitness for survival of the
/?
the utility functions remain
a and
0, the
two agents.
Nash equilibrium pair of actions a", 6"
solve the
following standard equations
a,(a",6")
=
(1.1)
;9fc(a",6")
=
(1.2)
where subscripts denote partial derivatives. The Nash equilibrium
generally not Pareto Optimal.
is
Pareto optimality requires that, for some positive A the pair of actions
a^{a,b)
+
X0^{a,b)
=
aj(a,6)
+
A^i(a,6)
=
(a, 6) satisfy
(1.3)
Thus, Pareto optimality holds at the Ncish equilibrium only
I
assume that, before
A
chooses
a,
utility functions are given
a(,(a",6")
=
he chooses a taste parameter 7^ while
choosing these parameters, the choices of a and b maximize
post
if
U^ and
C/j
and
B
l3a{a'^,b")
chooses
respectively
—
-^b-
where these ex
a{a,b)
+
'^AUB
(1.4)
UB^0{a,b) + ^BUA.
(1.5)
Thus, the parameters 7^ and 7^ represent the degree of altruism chosen by
respectively.
/3
equivalent results by having
After
by
UA =
maximize a and
0.
A
and
B
to
Instead of having people choose parameters, one could obtain
them choose actions such
that, as in Becker
and Murphy (1988) the
preferences are changed by the actions.
Equations
(1.4)
and
(1.5)
Ub
can be solved for Uy^ and
yielding
Q + 7A/g
^ ^
1 - lAlB
rr
= ^ + ^^"
Ua
1 - 7A7B
It is
apparent from
one. Before maximizing
measurement of a and ^
is
(1.6) that this
a and
problem
is
not well defined unless 7^ and 75 are
with respect to the 7's
relatively straightforward.
I
s
f
^^
^
less
than
develop intuition for the effects of changes
in tastes
asking
by analyzing the
how U^
or
assume that the
Ub respond
to changes in 75.
(1988) and
This raises the question of whether one should
instead of
a and
Montgomery (1991)
since they
assume that agents
maximize the
future outcomes with the utility function that
them using the period
evaluating
obviously different from
is
f/'s
7's are picked to
Murphy
Becker and
changing 75 on both a and 0. This
effect of
(
The former
/?.
at
modified by the actions taken at
is
utility function itself.
is
t
closer to
evaluate
instead of
t
pursue the latter approach for two
I
reasons.
having people choose 7 to maximize
First,
B
friends with
some number
or not to have any friends at
of friends
U
implicitly treats
A
all.
if
one equates
occur
if
Ia^b
as choosing whether to be
more plausible view
B
and that he must decide whether
Thus, one can imagine that A's total benefits from
A
A
that
else)
A
is
sure to have
should be
from
his friendship
maximize a even though
his ex ante evaluation of
outcomes
is
7^ even
with B.^ This would
a higher 7^ reduces the utility from friendship with other people. In this case,
pick 7^4 to
in this set.
friendships are independent of
all his
with the psychological benefits to
someone
(or
is
the
same
A
ought to
as his ex post
evaluation.
Second, and perhaps related to this weakness, having people choose their 7's to maximize the
f/'s
has several unpleeisant implications. As Bernheim and Stark (1988) show, changes
can have paradoxical
people
to
—00
who
is
effects
on the
f/'s
because of their
are free to choose their 7 would set
he
in (1.4)
and
(1.5), the
Comparing
(1.3), (1.7)
and (18),
the Nash equilibrium with altruism
(1.8)
+00
if
their partner
is
(1.6). Also,
happy and equal
when 7^ = 7^
is
is
Nash equilibrium actions
satisfy
=
(1.7)
A + iBC^b =
(1.8)
aa
and
equal to
it
on the denominators of
unhappy.
is
Given the preferences
(1.7)
effect
in the 7's
it is
+
7A/5a
apparent that,
in the limit
Pareto Optimal. Supposing
monotone
in the
common
in
where 7^ and 75 equal one,
addition that the solution to
value of 7,
it
follows that increasing 7
^ Using Rabin's (1991) terminology these would be the "psychological payoffs" from the relationship
The benefits from
friendship are probably more complex than an expression like Ia^b
I use this formulation as a starting point because it is
standard
in
the literature on altruism.
^Montgomery (1991) avoids this problem by postulating that the t'a depend on previous
that makes infinite values either impossible or very undesirable to the individual.
choices of consumption in a
way
leads to actions that are closer to the Pareto
in
Optimum. This
altruism are beneficial to the individuals.
individual would unilaterally decide to
To study
this,
now
I
become
However,
I
explains
am more
why simultaneous
increases
concerned with whether an
altruistic.
analyze the effect of changes in 75. Consider
first
unaware of B's change of heart. Then, a remains constant and the change
in b
the case where
A
is
can be obtained by
differentiating (1-8)
{Pbb
The second order conditions
tiplying dh
for the
as
7^ hurt B. The reason
increases in
that maximizes
Now
As long
negative.
is
+
maximization of
that they
consider the effect on A's ex ante
I
B
is
now
loses
move
always better off when
=
--z-^
B
cares
+
his affection
is
known only
can demonstrate
more
towards
And what
The
first
a person
type,
is
movements
From
be
to
difficult (if
mimic the
signals should
A
body language,
is
feeling,
we take
of his hands,
these wholes
we
irritation, sympathy...
people, and
A
it
given by
(1.10)
him.
for
B
can demonstrate his affection.
to him, any gains to
his affection credibly, so that
credibility requires that
is
d^B >
to the changes this affection induces in A's behavior.
feel altruistic
and further away from the point
ISOibb
turn to the more plausible case where
when
ensure that the expression mul-
utility
h further
This
utility.
Pbb
A
(1.9)
/9.
aidh
so that
-OLid'^B
does not change sign as one varies 7^, this implies that
a\,
is
=
lBOtbb)db
A
is
But,
A
from
change
will
must be due
his affection
his actions only
who
if
B
Such
sure that S's actions will be affected.
not impossible) for a person in 5's position
does not
signal emitted by a true altruist.
somewhat
credible signals.
"In deciding
what sentiments
believe? There are at least two types of
stressed by
Homans
(1950)
who says
:
notice of slight, evanescent tones of voice, expressions of his face,
ways of carrying
his
body, and we notice these things as part of a whole...
infer the existence of internal states of the
[Yet]
B
Given that
we
we do not always
act on our inferences,
is
pursued
9
in
call
them
anger,
on our diagnoses of the sentiments of other
act ineffectively" (p. 39).
through favors and presents. This idea
human body and
Another way
B
can signal his affection
Camerer (1988) who
gives several reason
is
why
can be credible signals of affection. One of these reasons
gifts
is
that
may
it
be more difficult for a
person that does not actually care for another to deliver equally touching favors and
For simplicity,
I
neglect the costs of signaling altruism in
signaling, the effect of a
change
in
7b on both
gifts.
most of my discussion. With
costless
actions can be obtained by differentiating (1.7) and
where
\ Pab
Thus, the
effect
on a and
6 is
+
iBOlab
Pbb
+
iBO^bb )
given by
da
=
af,[a^i
+
(1.12)
'^A0^t,\/\D\
dh=-at[aaa + lA^aa\/\D\
(1.13)
and, using the equilibrium conditions (1.7) and (1.8) to substitute for
and
/?
and
a<i
ySj,,
the effects on
a
are given by
J
J
Ji —
da
+ a^db
=aada
—
-lA^aOtblo^ab-^-lA^ab]- O^lWaa
,
dp =Pada
+
To obtain a determinate
Pbdb
lA^aa]
,,
|Z)|,
I
,,,
(114)
-—
=
sign for
+
.
(1.15)
suppose that the solution
is
stable under the usual
tatonnement process where da/dt depends positively on dU^/da while dh/dt depends positively on
dU/db. This
stability,
which can be viewed as implying that people converge to the N2ish equilibrium
when they
act in a fairly myopic manner, implies that the matrix
as long as
D
is
not singular,
its
determinant
where 7^ and 7^ both equal zero (so that
A
of ah^aO^ab-
By appropriately normalizing the
same
In other words,
sign.
'The reason
where a* and
is
that, locally, the
we
set
system of
is
B
we can ensure
up the problem so that increases
governing o and
(da/dt\
(a-a-\
\ db/dt )
\b-b'
6* are the equilibrium values.
10
negative semidefinite.
are selfish) the sign of
actions,
differential equations
is
So,
This means that, starting at the point
positive.
and
D
)
b is
that
in
d0
aj,
is
and
equal to the sign
/3a
both have the
both actions are good
then given by
for
the other player. Then, the sign d/3
A
would want to increase a
if
the sign of aab- This second derivative
is
he knew that
B
had increased
Klemperer's (1985) terminology, a positive aab makes a and
B
point of view. This strategic complementarity then leads
The
move
intuition for this result
6 in
the direction a
A
the direction in which
A
complements,
instead,
A
now
effects are
straightforward.
must move
A
this leads
B
Then,
B
when he
loses
to adjust a in the direction that
B
if
this direction
ambiguous, although clear
effects
is
thus better off as
complements, the
In this case, a
7b can be
benefits from liking A.
lets
A know
finds deleterious.
first
B
likes
term
and
b
is
do
arise
when the altruism
da has
zero so
him more. However,
in (1.14) is negative.
both increase as
This
the
if 'ia
is
that he cares for
^°
same
is
purely one-sided so that
sign as
positive,
easiest to
is
—aaa which
and a and
understand
goes up. Once
A
likes
B
if
positive.
is
6 are strategic
one imagines that
for
both individuals.
a great deal, further increases
it is
plausible that
7^
is
ever so large that
75 hurt A.
altruism to maximize his
a.
I
this question
own ex ante
a and
b,
by assuming that each individual picks
level of utility.
Thus 7^
is
his
own
chosen to maximize
/?
level of
while
then ask whether a small increase in 7b starting from this point hurts A.
further simplify this analysis,
for all
7;,
be large. So the question becomes whether
attempt to answer
maximized
If,
deleterious to A's welfare because they induce excessive increases in a. This requires
itself
increases in
I
also
the actions are strategic
and ^a are both positive and that the two actions are strategic complements
7x
is
turn to the effects of B's increased altruism on A's welfare. Perhaps surprisingly, these
A
that
toward A.
altruistic
starts to feel altruistic towards A, he will
does indeed move his action in this direction and
does not care for B. In this case, 7^
in
become
his action to benefit B.^
A
ai,
B
If
a selfish
complements" from A's
6 "strategic
Suppose we normalize the actions so that
views the actions as strategic substitutes,
him because
I
likes.
is
if
Using Bulow, Geanakoplos and
b.
to
positive
is
a{a,b)
—
I
assume that the interaction between
A and B
is
7^1
To
symmetric so that,
^{b,a). Then, at a symmetric equilibrium, the 7's are set so that (1.15)
*In Bulow, Geanakoplos and Klemperer (1985)'fl work on Btrategic interactions between firms, there is no natural analogue to
For this reason, their results depend not only on whether actions are strategic complements or not. Instead,
they depend also on whether prices or quantities are the strategic variable, whether there are economies or diseconomies across
markets etc.
"'Bernheim and Stark (1988) provide an example where increased altruism by B makes B worse off for this reason. Their
example is based on the "Samaritan's Dilemma" B's altruism leads A to expect larger transfers in the future. This expectation
in turn induces A to consume more in the present period (which is inefficient).
this norn:ialiEation.
,
11
equals zero. Letting 7
= 7a =
7B, we have
+ labbh +
{ctaa
where the
first
term
is
a^b{l
negative while the second term
variables are strategic complements).
On
is
+
l)
=
(1.16)
positive in the case of interest (where the
the other hand, the sign of da/d'iB
is
the opposite as the
sign of
{oLaa
Comparing (116) and (117)
term
is
is
+
aabl
there to be too
little
The Discrete
payoff's in this
is
is
positive at the
and g are
smaller than one, the negative
strictly smaller. Therefore,
symmetric equilibrium. This
something that tends to benefit others as well as
result
oneself. So,
(117)
makes
one expects
Dilemma
Prisoner's
consider the standard model of conflict, namely the Prisoner's dilemma.
I
game
are given by
C
t
is
is
altruism in equilibrium, not too much.
In this subsection
where
(117)
bigger in (117) than in (1.16) while the positive term
intuitive sense; altruism
The
lOibb)
apparent that, as long as 7
it is
negative. This implies that da/d-^B
1.2.
+
D
C
1
D
\+g, -i
strictly positive. ^^
I
,1
\+g
-t,
(1.18)
0,0
will treat the
row player
A
cis
and the column player
as B.
Since each player's optimal eiction {D) does not depend on the other player's action, there
appear to exist no strategic complementarities
to play C, he
zero. But,
is
strictly
worse
in this
off if his altruism is
endogenous altruism can
still aff"ect
game.
If
B
starts liking
not reciprocated.
become proportional
and
this leads
ends up with
the outcomes. Suppose that
given by (1.4) and (1.5). Then, using (118) to obtain the values of
U
B
A
a and
A
and
B
—i
him
instead of
have
utilities
^, their perceived payoff's
to
D
C
C
1
D
l+g-iA^, -t +
+ 7A
,
1
-^ + 7a(1+p),
+ 7B
iBil
+
g)
1+5-7b^
,
"The zeros and ones are simply normaliiations. In any symmetric Prisoner's Dilemma, one can always subtract the same
amount from each entry to make the {D,D} entry equal to {0,0} and then multiply all the entries by a positive constant to
make the {C,C] entry equal to {1, 1}. The resulting game is strategically equivalent.
12
Consider
the symmetric situation where
first
7a
= 7b =
7-
Then {C,C}
a Nash equilibrium
is
as long as
Since 7 must be below one, this
Playing
C
7>l + (7-7£
+
l
possible only
is
becomes a dominant strategy
+
g/{l
if
(1.19)
t) is less
(so that {C,
C}
is
than one.
Nash equilibrium)
the only
if,
in
addition
^{l+g)-e>0
which
is
<
possible with 7
1
only
if
Suppose that condition (119)
i/{l
is
+ g)
also smaller than one.
is
satisfied while (1.20)
9
-^
< 7 <
i+e
Whether there
such a 7 exists
If
7
exists a
\{
t
satisfies
>
7 that
satisfies
(121)
is
violated. This implies that
is
f-
(1.21)
l+g
^
what
crucial in
follows. It
is
'
thus worth noting that
g and not otherwise.
(121), both {^C,C} and {£>,£)} are Naah equilibria.
C}
are not equally plausible since {C,
Farrell
(1.20)
is
and Saloner (1985). The reason
Pareto dominant. So, {D,
that
is
A
if
B make
and
than simultaneously, the only subgame perfect equilibrium
is
D}
However, both equilibria
is
not robust in the sense of
their choices sequentially, rather
{C,C}.
If,
A
say,
chooses
first,
he
knows that he guarantees himself the superior outcome {C,C} by choosing C.
Now
goes only from
aff'ection
is
selfish
>
B's altruism
is
-yg
=
(1-21)
costless.
7b
io A.
him
Now
1
unless
A
slightly
If £
<
affection cost
is
g,
above
(121)
him
satisfied for this
Somewhat more
7 at no cost to himself even
costly to
7^ <
g,
sets
B
and plays D, B's
instead, i
If,
B
suppose that
if
A is
i;
(//(I
+
£)
<
1
7b = 7 and
fails for
he could have gotten
73 and the only
generally,
if
not altruistic.
a
7
If
A
while
B
sets
plays
7^
C
to zero so that
for sure. Since
by remaining
Ncish equilibrium
is
selfish himself.
{D,
D}
so that
B
can set
exists such that (121) holds,
no such 7
exists,
A
B's affection
generally
is
reciprocates.
consider the initial stage where each individual picks his level of altruism,
then (1.21) can be satisfied for some 7
less
than one and choosing such a 7
strategy for both players. This choice gives a player the outcome {C,
chooses a 7 in this region while
it
costs nothing
if
C}
if
is
g
<
i
and
a dominant
the other player also
the other player chooses a lower 7.
13
li
On
the other
hand,
if
£,
the only equilibrium has the players remaining selfish.
By doing
strategy.
if
>
g
so one gains
1
+^
if
This
is
now
the other player becomes altruistic, while one loses nothing
the other player remains selfish.
The
result
is
intuitively appealing since
this result
is
that,
i
if
>
g, there are strategic
towards the other. In particular,
responds to
benefit
D
from playing
D
D
is
So
D
when
far,
I
of the
likes
A and
t
>
g,
B
rather than
g whereas
plays
C
it is
in
if
B
plays D. So
when
responds to
C
feels altruistic
with
C
while he
turn be traced to the fact that A's
B
does depend on whether
£
B
then
causes
t
C
plays
or not.
A
exceeds g,
If
B
plays C, A's
has a lower incentive
C
have considered abstract games with payoffs given either by the standard Prisoner's
Dilemma or by
of the payoffs
B
What
selfish.
complementarities once one player
with D. This strategic complementarity can
gain from playing
to play
if
when
says that people will tend to like each other
it
not doing so will hurt the other more than one would gain oneself by remaining
a and
arbitrary continuous functions
a and
/?
/?.
In the next sections,
that arise inside firms. These payoffs are
two people within the organization. Before developing
made
this
to
I
study specific features
depend on the relationship
theme,
it is
important to stress
that personality also plays a role in the determination of the equilibrium values of
particular, the private costs of the actions a
instance, an individual
who
his leisure very valuable)
is
a dominant
is
and
h are likely to
a and
/?.
depend on the individual.
In
For
not very interested in career advancement (perhaps because he finds
would have a
different attitude towards
changing
his effort
than one who
very keen on professional progress. Thus, one should not expect the pattern of friendship and
altruism to depend solely on the nature of the interactions in the workplace. With this caveat,
keep personality factors constant and analyze the
2.
effect of these interactions
I
on sentiments.
Joint Production
Often,
it is
not possible to disentcingle the effort two employees
Holmstrom (1982) shows,
their effort
is
if
subobtimally low. The reason
phenomenon. The
first
in
producing a good. As
they are paid as a function of total output alone and they are
is
selfish,
that each employee neglects the positive effects on
the other employee's compensation of an increase in his
this
make
own
effort.
I
will consider
two models of
subsection deals with the case of continuous actions and a differentiable
production function relating output to these actions.
14
The second subsection
considers instead a
case where output depends only on two discrete levels of effort.
show that
I
emerges endogenously though the social optimum can only be achieved
in
both cases altruism
in the
second setting. The
third and fourth subsections consider experimental evidence on cohesiveness and productivity and
relates
2.1.
it
A
to the
models of the
two subsections.
Differentiable Production Function
Suppose output
and
first
given by the symmetric, monotone and increasing function f{a,b) where a
is
once again represent the two actions.
b,
for their
output and they
If,
together, the two employees receive a price of one
split evenly the resulting revenue, the individual payoffs are
a(a,6)=/(a,6)/2-e(a)
/3(a,6)=/(a,6)/2-e(6)
where the
e functions
The
derivatives.
capture the cost of effort and with
selfish
Nash equilibrium then has
that fa and /j be equal to
effort
is
If
e' itself.
f^
=
(2.1)
>
e'
ft
=
>
0, e"
2e'
where primes denote
whereas the optimum requires
Since the marginal product of effort
is
smaller at the optimum,
higher there than at the selfish Nash equilibrium.
the two employees act as
if
they had preferences given by (1.4) and (1.5), the equilibrium
effort satisfies instead
1
+ 7A
e'
= 7—
1 + 7B
/*
so that the marginal product of each type of effort declines as the 7's
two
7's equal one,
we obtain the same outcome
Since aat equals jah,
we can be
as at the
sure that there
now
chooses his
This equilibrium must satisfy (1.16). Thus
{ha
As long
to one.
as /
We know
is
-
2e"
+
7/66)7
+
concave, the expression on the
this
where the
in equilibrium
if,
as in the
consider the symmetric equilibrium where each person
caise, /aj, is positive.
7.
In the limit
optimum.
some altruism
is
Cobb-Douglas
I
rise.
/a6(l
left
because concavity implies that
15
+
7)
hand
ha +
=
(2.2)
side of (2.2)
fhh
+
2/a6
is
is
negative for 7 equal
negative while (— e")
is
On
negative as well.
the other hand,
By
positive for 7 equal to zero.
is
between zero and one. There
is
if
on the
fah is positive, the expression
left
hand
side of (2.2)
continuity, the solution to (2.2) therefore involves a 7 strictly
some altruism
in equilibrium
but not enough to reach the
first best.
Because equilibrium altruism raises output and traditionally measured productivity,
The
to be in the firm's best interest as well.
output (which
I
normalized to one)
firm benefits
if
the price
have
I
2.2.
the employees like each
no mechanism
for the firm
I
consider this in the next subsection within
Discrete Levels of Effort and the Firm's Role in Promoting Cohesiveness
a cost, than changing
give an
I
its
example where the firm
incentives for effort.
will
is
better off promoting cohesion, even at
To demonstrate
payment per unit of output which was exogenously
far.
of
somewhat simpler model.
In this subsection
I
is
if
some
looked at the tradeoff between promoting cohesiveness and
raising the price paid employees per unit of output.
the context of a
or even the use of
better off
is
other than at the selfish Neish equilibrium. In this subsection, there
this cohesiveness nor
pays the team per unit of
it
some proprietary knowledge
the firm's capital, this will generally be true so that the firm
promote
tends
than the value to the firm of an addition to output. As
is less
long as the production of output involves
to
it
fixed at
1
this,
in the
I
determine endogenously the
previous subsection. In addition,
incorporate explicitly the costs of signaling one's affective state which
For simplicity,
individual
now
I
makes an
eissume that the actions a and
parameter
effort so that his effort
h
I
have neglected so
can take only two values. Either the
e is set
equal to one or he doesn't and
e
remains equal to zero.
If
both employees set
employee sets
1
—
n.
If,
e
=
1,
e
output
equal to zero, output equals zero with probability one.
is
instead, both employees set e
zero with probability (1
Q
equal to
— m)) where
=
m
only one
with probability n and equal to zero with probability
1,
>
If
output
n.
is
equal to
Q
An employee who
with probability
sets his
own
e
m
(and equal to
equal to one bears
a cost equal to d.
Supposing that the value at which the firm can
employees d
in
exchange
for their effort,
it
sell
the output
Q
is
p and the firm could pay
would ask one of them to make an
np- d>
or
n>P
16
effort
if
(2.3)
the firm also benefits from asking the second to
If (2.3) is true,
(m — n)p > d
Together
(2.3)
and
m—
or
make an
effort if
n > P
(2.4)
imply that
(2.4)
m
d
> 2-
(2.5)
P
make an
so that the firm benefits from asking both to
one of the two conditions
is
true,
which
in
individual effort
a bonus
w
(2.4)
Suppose,
is false.
is
effort
if
output does equal Q.
can achieve the same outcome as when payments
an extra d/n
his
output
would on average gain np
The
The
risk neutral.
if
in particular, that (2.3)
even though a single employee's
situation
is
is
—
more
in
If (2.3) is satisfied
exchange
is
indeed Q.
interesting
if
e
—
e
=
(2.4)
if
not, the firm
is
him
the effort and the firm
1
(2.6) that
to
mw —
nw
d,
,
=
but (2.3)
e
mw —
nw —
nw —
d
d,
will set e
he assumes the other employee sets
e
=
{m-n)>
=
set e
not.
Given
cannot exceed p/2.
=
nw
(2-6)
1 is u; is
=
1
set sufficiently high.
With
unless
this
if,
Aw
equal
a single individual
nw > d which
requires that
(2.7)
1,
he would set
e
=
unless
(m — n)w > d
or
d
2P
17
is
This
,0
d
would not
u;
effort.
by
1
both employees
the other worker sets e
satisfied
two employees, the bonus
selfish individuals are given
=
is
make an
d
n > 2P
Similarly,
Then, the firm
for effort are feasible as long as its
to p/2 may, however, be insufficient to generate individual effort.
who assumes
and
the firm wants both employees to
now making bonus payments
from
2n.
(2.5)
would not be worthwhile.
The employee would than make
e
clear
>
and
if
d.
For any w, the payoffs to two
It is
m
false
is
firm would contract with just one employee and offers to pay
occurs when, either (2.4) and (2.3) are both satisfied or (2.5)
that the firm
effort
be true even
(2.5) could
not observable, the firm can provide incentives for effort only by paying
to each employee
employees are
Note that
turn requires that there be economies of scale so that
would ask both to make an
If
and
(2.3)
effort.
(2.8)
Obviously
and
(2.7)
(2.4) hold simultaneously.
when w
game
obtains a
positive
is
cis
that
is
By
allowable rate p/2.
comparable to (1-18) where
(2.5) holds
if
In either of these cases, (2.6)
maximum
set at its
is
can both be violated even
(2.8)
is
(2.3) or
a standard Prisoner's
dividing
t equals
without
all
entries in (2.6) by
—^^ while g equals —~
if
and
(2.3)
dilemma even
mp/2 —
Jm
d one
(which
long as (2.5) holds).
If
- np > 2d- [m-
2d
the resulting t
is
bigger than
Then,
g.
will
be at least as large as what
will
make
this
7
is
if
n)p
necessary to
the effort. Since that 7 equals 5/(1
depends on
because only
(2.9)
if
> 2n
(2.9)
altruism can be signaled costlessly, each individual's 7
make
+ t),
it
(1-19) hold with equality
\m-n)p
equals
positive while the failure of (2.8) implies that
is
m
or
it
is less
rpj^^
validity of (2.4) implies
than one.
there are increasing returns to scale so that
and both employees
Equilibrium altruism
m
is
bigger than 2n do
the losses to the other worker from abstaining from cooperation exceed the private benefits from
defection.
Now
(2.9)
is
satisfied
Spence (1974) and Camerer (1988),
in
a
suppose that
gift)
which
is
more expensive
but that there
a cost x of signaling one's altruism.
is
must be the cost to the
this
for a selfish individual.
A
altruist of
selfish individual
As
an action (typically
must
find the cost so
high that he does not gain by masquerading as an altruist and later getting the defection payoff
nw.
To
A
may
In the presence of this cost x, altruism
see this, suppose that
mp/2 — d —
gains
equilibrium
when
x.
If
A knows
that
B
is
7 to
sets his
this is positive, there
affection
not emerge in equilibrium even
is
.
_'?
like
both his and his co-workers 7
equality.
instead, either of their 7's
Goods that might have such a
events as well
eis
The reason
changes
is
satisfied.
altruistic himself,
(this
is
the unique
differentially affect the welfare of
each other. In other words a firm that spends 2z can add
if
utility.
(2.9)
chosen and demonstrated sequentially).
each worker
If,
By becoming
an equilibrium with altruism
Suppose that, by spending some resources the firm can
employees who
if
in the
is
is
at least
cis
large as the
to the utility of
7 that makes (119) hold with
lower, the firm's expenditure adds only
differential
4>z
t/'z
to each worker's
impact include expenditure on parties and sports
job that allow the employees to have more social interactions.
these expenditures can be useful
is
18
that they induce the individuals to choose high
For any
7's.
is
w
nw
negative while
mp/2 — d — X
them
d/m and
between
is
d/n, (2.6) has a prisoner's dilemma structure because
mw —
exceeds
d which
Supposing that
positive.
is itself
nw -
(2.9) is satisfied
d
but
smaller than zero, the individuals remain selfish and the firm cannot get both of
Without spending
to exert effort.
most get np
2z, the firm can at
—
d hy inducing the effort
of just one employee.
Now consider
paying both employees a bonus of
number. To induce the individuals to become
which equals [mS
—
x
+
[<f>
workers can expect to get
a base wage that
—
<f>z
\l))z) is
where 8
must be
altruistic, z
is
an arbitrarily small positive
set so that
{mw — d — x-\-{4> — xli)z)
This requires that z be equal to
positive.
in amenities,
d/m+8
x/[<j>
seems reasonable to assum ethat they they
it
lower by 0z so that the total cost of friendship-enhancing activities
is
—
ip).
Since
is
will accept
2(1
— <p)z.
Total profits are then
mp Given that
2{d
+ mS) -
2(1
-
(^)z
= mp -
(2.9) is satisfied, these profits are positive
only one employee exerting effort) as long as 8 and
as
<f>
IS
than
Next,
I
X as long as
7
=
sets e
1
is
A
violated.
The
failure of (2.9) implies that
him nw instead
would be willing to
set his
of
mw —
own 7 equal
{4>-
If
are small. This latter ratio
the firm chooses z to satisfy (2.10)
employees
like
each other. This
is
to
ip)z
it
d.
7
A
is
B
that
it is
will
<i>
is
small as long
substantially larger
an individual, say 5, whose 7 equals
thus better off by keeping his 7 equal to
With the expenditure
eis
long
+ mw -
d>nw
(2.10)
thus ensures that there
is
a Nash equilibrium where the
indeed the unique Nash equilibrium
respond to A's altruism by setting his
also in A's best interest to set
7 equal to
19
own 7
7.
of 2z by the firm, however,
eis
their 7's in sequence (and before they set their effort).
that
and
is
of z can be valuable even in the absence of signaling costs
regardless of the sentiments of A.
zero since this gives
d (the profits of having
overcomes the costs of signaling friendship.
show that the expenditure
(2.9)
—
promoting friendship). The expenditure of 2z helps
(so that the expenditures are useful in
it
2
and bigger than np
j^
-6
-x
1
+ mS) -
close to one (so that the z expenditures are not too wasteful)
the firm here because
to
2{d
If
A
if
chooses 7
the two individuals choose
first,
he can be confident
equal to 7. Equation (2.10) then implies
now show
I
cannot be satisfied without
(2.5)
inducing only one individual to
(2.10)
satisfied
is
As a
(2.3).
make
z in this way. Since (2.9)
= m{p —
2tv)
—
—
2(1
the effort. Suppose that, instead, the firm sets
set high 7's
<l>)z
is
result, the firm has the option of earning
with equality. As long as the prisoner's dilemma structure of
by the choice of w, the workers then
TT^
w and
that the firm can benefit from setting
and cooperate. Expected
if
violated,
np — d hy
and
z so that
(2.6) is preserved
profits,
tt^
are then
-
2d—- 6
1
= mp — 2 w
rp
(2.11)
4>
Before we can evaluate the advantages of making z positive, we must determine whether the
bracketed term in (2.11)
is
positive. If
negative, profits are increasing in the
it is
employees. This means that the firm cannot do better than setting
xv
zero profits even with z set equal to zero. Since the firm could have
made
np
—
not
wage paid
equal to p/2 which leads to
positive profits equal to
d by having only one employee, the strategy of keeping two employees with a positive
make
Now
2
does
sense in this case.
consider the case where the bracketed term
rp
Since profits are
now
preserves the prisoner's
d/m +
6
dilemma
= mp —
2d
—
where 6 equals zero,
(2.12)
n
makes sense
namely
slightly
^
-
this
—
d
to set
wages
above d/m.
at the lowest level that
I
will
thus assume that
w
Using (2.11) this gives profits of
6 goes to zero.
2(1 -<i>)n
{4>
In the limit
it
structure,
and consider the limit as
Kz
4>
declining in wages,
positive which requires that
is
^^
— < m—
equals
to the
26
tp)m
is
greater than
np
—
d
if
1-6
p
--^<(m-n)5-l
—
xp
So, the expenditure of z to induce the employees to
as long as (2.12)
2.3.
and
(2.13) are met.
(2.13)
d
<p
Both require that
become
j^
friends with each other
is
profitable
be small.
The Evidence from the Hawthorne Experiments
In the previous subsection
we saw that
diture of resources to facilitate friendship
incentives for group output in addition to the expen-
may be
20
necessary to raise productivity. In this regard,
the experiments at Western Electric's Hawthorne plant reported by Roethlisberger and Dickson
(1939) are particularly relevant because they varied both the incentives under which groups of
workers operated and their opportunity to socialize (and therefore the ease with which they could
become
friends).
sustained rise
My
interpretation of these experiments
when groups were
is
that output had the largest and most
given both strong incentives and opportunities to socialize. Either
much
the opportunity to interact or strong incentives, by themselves, had a
smaller impact.
Room
Before being placed in the experimental conditions of the "Relay Assembly
Experi-
ments" the payment to the participating workers depended on the aggregate output of a group of
who were
approximately 100 operators
located in a large room. In the experiments, 6 workers of
which 5 were assemblers and one was a layout operator, were separated into a small room and paid
as a function of the output of this smaller group.
worker who
In the experimental conditions, a
produced an additional unit thus received an additional l/5th of the group's piece rate whereas,
in the initial conditions, she received only 1/lOOth.
Not
surprisingly, given that the
payment per
marginal unit rose, output rose as soon as the payment system was changed. ^^ After this change in
compensation, there were several experimental changes
in the
amount
of rest the workers were
al-
lowed to take during the working day. During these rest pauses the workers socialized. Rest pauses
were
first
introduced, then increjised, then reduced again.
and Dickson (1939)
change
in
output
is
is
The
principal finding of Roethlisberger
that output increased permanently by about
attributed by
them
30%
to the fact that the 5 workers
supervisors. There were better relations between
after these changes.'^ This
became
friendly with their
management and workers.
Roethlisberger and Dickson (1939) conducted two additional experiments.
In the "Second
Relay Assembly Experiment" the compensation scheme was changed and the experimental subjects
,
were put in close proximity but the method of supervision stayed as before and there were no
rest
pauses. This group's output also increased but only by 12.6%.^* Thus, the opportunity to socialize
also contributed to productivity, as the
model of section
3.3 predicts
if
one regards
offering a disproportionately valuable opportunity for socializing to the people
In the final
who
rest pauses as
like
each other.
experiment a group of workers originally paid on the basis of individual piecework
was segregated and given the same
rest
'^See what occurred in Period III on the Figure on
'^See Roethlisberger and Dickson (1939) p. 160.
pauses as
p. 56.
'*Jbid., p. 129-132.
21
in the
"Relay Assembly
Room
Experiments".
This experiment, called the "Mica Splicing
system was the same
15%
but, unlike
in
it
Experiment" had the advantage that the payment
the original and the experimental conditions. Output
what was observed
of the experiment
Room
in the
Relay Assembly
was only 4.4% higher than
of section 3.3 the incentive system also
initially.^^
Room
first
rose by about
then declined so that, by the end
Thus, again consistent with the model
promoted productivity.
Roethlisberger and Dickson's (1939) emphasize the change in supervisory methods as explaining the change in productivity in the "Relay Assembly
not seem consistent with the results of the Mica Test
experiment
is
more consistent with a model
like
Room
Experiments". This explanation does
Room, however. Their own
the one presented in this section which emphasizes
why attendance was much more
the interpersonal relations between employees. In explaining
ular in the later stages of the Relay
Assembly
discussion of this
Room
experiment, they say
it
was
"...more probable
that the difference in attendance was due to a difference in attitude... Among the
was no pressure
there
for
reg-
Mica operators
attendance except that which came from the individual's own personal
situation"
In addition,
hours.
"The Mica operators did not join
They had no
in
common
"parties" similar to the gatherings of the relay assembly
no willingness to help one another... The Relay Assembly Test
Mica
Splitting Test
relation
social activities outside
Room was
a story of "individuals"".^
Room was
girls...
working
There was
a "group" story, the
The authors own explanation
is
"the
between the type of payment system to the question of morale was overlooked. ..Under
group piecework, the operators
in the
Relay Assembly Test
Room
which they could organize. Under individual piece-work each
girl
had a common
was
interest
self sufficient; there
under
was no
need of working together".
What
also the
Roethlisberger and Dickson (1939) are suggesting
is
that not only the rest pauses but
group piece work encouraged the friendship among the "Relay Assembly Room" workers
and that
this friendship
was
in
turn instrumental in raising output. This
provides evidence for the view that friendship arises endogenously
interest rather
than being simply a reaction to
rest
pauses and the
when
like.
is
it is
important because
it
in the worker's best
To explain the
increase in
friendship with the model in this section, one needs to argue that the actions of the operators were
'^/bid., p. 148.
'*/bid., p
155-6, quotes in original.
^''
158.
Ibid., p.
22
strategically
least
all
complementary. While most operators
initially
two potential sources of complementarity. The
assemblers.
The marginal product
first is
of each assembler
operator's effort. Second, the assemblers found
it
worked independently, there were
at
that the layout operator had to help
was thus a
positive function of the layout
possible to increase joint output by helping each
other.
2.4.
Other Evidence on Cohesiveness and Productivity
Stodgill (1972) surveys 34 studies of the connection
report liking each other (cohesiveness) and productivity.
between how much members of a group
The
results are quite mixed,
about 1/3
of the studies find no relationship, 1/3 find a significantly positive relationship while 1/3 find a
negative one.
is
A
more recent study that
Gladstein (1984).
The question
assuming that cohesiveness
is
I
also
shows a
explore here
is
trivial correlation of
output with cohesiveness
whether these mixed results are consistent with
equivalent to altruism.
One study which does obtain both
and positive correlations between cohesiveness and productivity and which
view
is
is
negative
consistent with this
Berkowitz (1956).
Berkowitz (1956) studied the behavior of individual experimental subjects
selves to be producing output together with a co-worker (even
Each subject's output was supposedly used by
who
believed them-
though no co-worker actually existed)
their co-worker to
make
a finished product.
The
perceived production function thus exhibited strong complementarities between the effort of the
two workers.
While
first telling
the subjects about their task, Berkowitz (1956) also induced favorable or
unfavorable feelings for the co-workers. This was done by telling the subjects either that the co-
workers were
existed.
The
likely to
be compatible with the subject or by telling them that no such compatibility
subjects then briefly
met
their "co-workers"
(who were just confederates of the exper-
imenter). Those told that their co-workers were compatible did later express
for their
The
much
greater liking
co-worker than those told that they were incompatible.
subjects then carried out their assigned task in isolation. During this period they received
messages which they were told had been written by their co-workers. The key result of the study
is
that the subjects
their effort
when
who
expressed that they liked their co-workers were
these messages said that the co-worker needed
23
more
much more
inputs.
likely to raise
They were
also
more
likely to
reduce their output
if
with materials. Thus, workers
the messages said that the co-worker w£is either tired or inundated
who
express that they like their co-workers in questionnaires also
choose their output taking into account the desires of their co-workers.
What
problem
is
is less
that
that there was
strategic
clear
we do
some
is
whether the theory correctly predicts the sentiments of the subjects. The
not
know what
the subjects believed to be their payoff. Insofar as they
benefit in producing a high level of final output, each subject's effort
complement with the
effort of their co-workers.
will tend to like their co-workers.
"incompatible" co-workers
structure as in Section
if
1.2.
The theory can
the subjects
felt
is
not expect to be liked by.
24
was a
Thus, the theory predicts that the subjects
also explain the lack of affection
between the
that their personal payoffs had a prisoners's
In that setup, there
felt
dilemma
no benefit from liking someone that one does
3.
Relations of Authority
In this section,
I
I
study the relationship between employees
argue that, unlike what
will
(1986),
is
in
authority with their subordinates.
predicted by the models of collusion in hierarchical agency (Tirole
Holmstrom and Milgrom
model predicts
(1990)), the current
relatively little
between superiors and their subordinates against the firm as a whole.
strategic variables that they control
consider three models.
I
The
two
different employees.
previous two models,
example
last
that the
first is essentieilly
The
the model of Tirole (1986) which deals with
to report on the employees' effort.
is
third involves a relationship of
some authority
The second
but, unlike the
involves no ability by the "supervisor" to affect the employee's pay. This
it
based on a
is
is
do not tend to be strategic substitutes.
a single employee whose supervisor's only role
involves
The reason
ganging-up
described by Crozier.
real-life interaction
The
"supervisors" Crozier
interviewed expressed that they liked their fellow employees even though they were not well liked
in return.
common
This seems hard to reconcile with the view that friendship
experiences but,
The Supervisor
3.1.
is
on a
to report
will argue,
it fits
I
is
single subordinate's productivity.
^A
is
e[a).
The parameter e^ can
Employee
+
The subordinate's output
is
given by
a
(3.1)
take two values
observes the realization of e^ before choosing his
realization of e^
and sometimes doesn't.
management
manner that
can verify
of rational altruism.
a productivity parameter outside the agent's control while a represents his effort.
cost of effort
it
an automatic response to
consider the problem posed by Tirole (1986) of a supervisor whose sole
QA =
where e^
my model
well with
as Performance Evaluator of a Single
In this subsection,
role
I
is
in a
its validity.
is
When
effort.
and
e'
with
e''
>
e'.
The employee
The supervisor sometimes observes
the
he does, he can convey this information to top
credible. In other words,
The supervisor
e'*
The
when
the firm
is
given this information
thus has only one opportunity for lying, he can say that
he observed nothing when he actually knows the state of technology.
Both the supervisor and the employee are
g{e))
where
E
is
the expectations operator,
risk averse.
t/ is
The
latter's utility
a concave function and p
is
is
given by
EU[w —
the employee's wage.
Thus, as Tirole (1986) shows, the firm's optimal contract without collusion has the supervisor
25
receiving a constant
wage and always making a truthful
the optimal contract,
simply describe intuitively
I
report.
its salient
Rather than deriving the
where the supervisor does observe
subordinate should be the same
Now
is
high.
always claim that the state
to produce
that
1^3
the supervisor
if
is
and wage of the
truthful, effort
Denote these by wi and
in these states.
>
is
the
wage were
state
is
high, he
make the marginal
> wi >
wi
also
low so that he can
more when the
W2- And, to
contract sets W3
If
in these
make
ei.
a low effort in the high state.
utility of the individual
is
the
let 3
be
two states, the subordinate would
must be paid more
W2- Finally, effort in state 3
is
and 4 describe the two states
1
consider states 2 and 3 where the supervisor does not observe the outcome and
the state where ex
him
Then,
e^-
For details, the reader
features.
referred to Tirole's (1986) Appendix. Following Tirole (1986), let
rest of
same
sls
in state 3
vary as
than
little
in states 1
To induce
in state 2 so
as possible, the
and 4 because the
firm has nothing to gain from distorting effort in state 3.^*
Because W3 > wi the subordinate would gain
when
is
ex
=
if
the superior claimed not to
This would allow the subordinate to receive W3 instead of wi.
f
thus willing to pay something to the superior to distort his report.
of this benefit from collusion, endogenous altruism
is
I
know the
state
The subordinate
now show
that, in spite
not sufficient to induce cooperation between
superior and subordinate.
First, the
the superior
and
is
is
subordinate has nothing to gain from feeling altruism towards his superior. Even
paid a
flat
if
wage, the subordinate's affection does not lead him to change his report
thus of no benefit to the subordinate.
By being
altruistic
towards the subordinate, the
superior makes the subordinate better off (since the superior will dissemble in the state where he
observes
to
e
become
).
However,
altruistic
This interaction
this provides
no benefits to the superior. Thus, the superior
choose
towards the subordinate.
is
actually a special case of the following
C
D
C
f,
z+g
0,
z
D
f,
z
0,
z
Each player benefits from the other playing
is
will not
C
+
g
(3.2)
but has no control over his own outcome. The result
that one's strategy depends on one's affection for the other player but not on his affection for
'^It does stand to gain from lowering effort in state 2 below the first best because this underproduction in the low
accompanied by a corresponding reduction in tuj reduces the attractiveness of claiming that f^ = '' when e = f''.
26
state,
oneself or even his action. There
that,
if
is
then no private benefit from altruism.
cooperation in the workplace arises only as a result of
arise in settings such as Tirole (1986), even
What
have shown
I
self interested altruism, it will
though cooperation
is
is
not
beneficial in such settings.
Tirole (1986) provides several examples of superiors distorting the information they pass along
to the central office
common. For
trial
and regards these as suggesting that collusion of the form he models
instance, he cites Dalton (1959 pp. 80-85)
who
illustrates several ccises
ently,
such accidents could have been avoided
regarded these as cumbersome.
somehow
Thus,
is
them
to
bribe the foreman to allow
it
the workers had
if
worn
own
where indus-
pocket.
Appar-
safety shoes but the workers
where the workers
possible to read this case as one
wear regular shoes. But,
quite
who had broken
accidents are not reported. In the most vivid case the foreman took a worker
several toes to a private physician and paid for his medical bills out of his
is
it is
just
possible that the
cis
foreman himself expects higher productivity (and thus more personal income) from workers who
wear regular shoes.
It
might then be
in his
own
self-interest (leaving eiside
with the workers) to evade the rule on safety shoes even
bills
when
if
this
means he has
any implicit contract
to pay certain medical
accidents do occur.
Crozier (1964) provides additional evidence on what motivates supervisors to
do.
When
talking of the immediate supervisors (or section chiefs) he says
bias the information they give in order to get the
favors with which to run their sections smoothly."
maximum
^^
lie -
is
interpreted
lie
they
they are likely to
"...
of material resources
This lying
and
cis
and personal
self interested
the workers. In response to the question "whether the supervisor would go to bat for employees"
worker responds: "Supervisors defend us inasmuch as they think
eventually trample on the employees.
Our own
section chief
is
whom
will help
them.
very self seeking"
that supervisors do not feel warmly toward their subordinates
own statements. Crozier
it
is
If
.^°
by
,
a
not they would
The perception
consistent with the supervisors'
reports that supervisors "do not have high regard for production workers,
they consider neglectful, irresponsible and careless".'^
The
picture that emerges
vated by affection.
What
is
is less
consistent with
clear
is
my model
whether, and
in
in that the lying is certainly
what
not moti-
sense, these self-seeking supervisors
are colluding with the workers. These examples certainly do not involve direct quid-pro-quos where
">/bid., p. 45.
^"Ibid., p. 42.
2' /bid., p. 92.
27
workers induce their supervisors to
exchange
lie in
pervisors do appear to feel that their sections would run
this suggests that they are in a position to increase
In the formal
output when given more resources. Whether
model of
given
The
first
some small bonus
the supervisor's information
why supervisors
verifiable,
is
and
from
liking their
will generally be better off
b
when he
actually reveals the state of nature.
such a contract
feasible.
is
in state 1
Now, altruism towards
his
know
the
he would claim not to
for the supervisor to lose
from
his altruism arises
when
one subordinate, the supervisor has several. In this case, one important role
instead of having
for the supervisor
maintain incentives for his subordinates by inducing them to compete with each other as
I
show
in the next subsection that this
one subordinate more than he
The Supervisor
3.2.
as
becomes more
difficult
when
Performance Evaluator of
Qb,
is,
With
-|-
probability n, the firm
compensate them as
to top
only their sum.
analogously given by e^
in section 2.
A
and
B
and that, as
in section 4.1, the supervisor
The output
A
of
is
in
let
the super-
other cases, he and
again given by (4.1) while that of B,
where e^ *nd eg are positively correlated random variables.
6
and the supervisor observe only Qa
With
probability
I
—
n, the
+ Qb
to penalize the worker
who
has produced
less
so that they
must
supervisor knows, and can prove
management, which worker produced the most. To provide incentives
makes sense
in section
Two Employees
sometimes know the ranking of the two subordinate's outputs while,
know
to
the supervisor starts liking
sometimes knows the true state of nature while he sometimes doesn't. In particular,
the firm as a whole,
is
the others.
likes
Suppose that there are two subordinates
visor
Since
lose his bonus.
The second reason
4.
without
can be seen by modifying the model slightly so that
subordinate makes the supervisor worse off because,
state
they do, this should be viewed as
this subsection supervisors neither gain nor lose
altruism for their subordinates.
is
if
an open question.
employees. There are, however, two reasons
the supervisor
the other hand, su-
more smoothly with more resources and
these resources are used to "pacify" the workers and whether,
"collusive" remains
On
for personal favors. ^^
for effort,
it
then
and give a bonus to the worker who
58 does provide examples of cliques which lie for each other in order to ensure the promotion of all the
what is implied by the Tirole (1986) model, the verbal description of this interaction does seem
consistent with strategic complementarity.
^^Dalton (1959)
members
p.
of the clique. Unlike
28
I
has produced more. This
is
generally better, for insurance purposes, than simply paying
more productive worker.
the
now
I
more
to
ignore employee friendship to focus on the altruism of the
supervisor for one employee. Incorporating friendship between the subordinates would not affect
the analysis as long
that friendship was not so intense as to destroy the incentives from the
eis
tournament component of compensation.
If
the supervisor starts liking one person, he ceases to reveal his knowledge in the cases where
his favorite is second.
is
This eliminates the incentive
not the favorite (since he never
officially wins).
effect of the contract
The
favorite
from the tournament component since he only
an
effort
be
verified.
on the employee who
has some incentive to make
still
collects the prize
when
his victory can
Nonetheless, the reduction in the effort of the non- favorite employee also reduces the
favorite's effort (as
I
show below
positively on output, he
is
in Section 4). So,
output
falls.
If
the supervisor's income depends
thus worse off by liking one employee. Not surprisingly, favoritism can
be quite detrimental for supervisors.
3.3.
The Team Leader
In this subsection,
work
French
in a
I
will consider
an authority relation based on Crozier's (1964) account of
clerical agency. In this agency, the actual
whose job was to process customer's requests. The
records.
the
The next two processed the
team checked the whole
set the
member
wcis
done by teams of four people
of the
team checked the customers
requests that were approved by the
transaction.
The
first
member was the team
first.
The
final
member
of
leader in the sense that she
pace even though she did not have any formal authority nor ability to set compensation.^*
What makes
attitudes
their
first
work
among
this relationship interesting
the
members
of these groups.
workmates. As Cozier says: "Only 20%
friends" ^^
And, most of these
from our point of view
is
the difference in affective
The employees had very few
feel positively
feelings of affection flowed
ties of affection
about their workmates
cis
with
potential
from the team leaders to the other members
'^This can be seen as follows. Suppose that we are considering a state of nature where, in the absence of information, they
both get u;. Suppose that the contract then says that, with information on rank, the most productive worker gets w + z while
the other keeps getting w. With concave utility, one can always improve on this by offering a slightly higher wage in the
absence of information and a slightly lower wage in the case where the employee comes in second. The individual, and the
firm, are indifferent to small perturbations of this sort (because utility is locally linear). This change allows the difference in
utility between the winner and loser (which is what generates the effort) to remain the same at a substantially lower wage when
the employee wins. This lowers utility in those states of nature. Nevertheless, expected utility rises if average income is kept
constant by increasing the income the individual gets in the states with no information. The reason is that, with concave utility
the marginal utility of income is higher in those states.
2* See Crozier (1964) p. 18.
2^ Ibid. ,35.
29
of the team:
"The middle-class
friends were
team
I
that
to
now
is
the model
who made
comments about
positive
their
workmates as possible
leaders (half of them) and a few senior employees from the special
workroom".^
present a model of a relationship between a team leader and a single other team
loosely based
become
girls
altruistic
is
that
it
on Crozier's account.
I
show
that, in this model, the
team leader
member
will choose
towards the other team member but not otherwise. Thus, one nice feature of
can explain situations where only one person chooses to
In this model, the
team
the other.
like
gets paid as a function of their joint output Q; each
member
vQ. The payment v per unit of output should not be regarded as a piece rate which
production takes place. Rather,
it is
delivered large quantities of output
is
paid
is
set before
an ex post payment which depends on whether the employees
when
it
was important. Thus, teams who perform
regard might get promoted, might be favored
when
comes
it
well in this
to allocating better office equipment,
etc.
The
will
The other team member (whom
leader sets the pace in the sense that she picks Q.
term the follower)
hcis
He can
a more restricted choice.
agree to the pace
practice complaints about the behavior of co-workers (including the leader) were
Q
I
or complain. In
common and
they
led to an investigation into the appropriate behavior of the co-worker.
The
leader's cost per
document depends on
document that are being handled.
variable
known only
I
idyosincratic factors as well as the features of the
assume that the
would
to the leader. Thus, a leader
{v
leader's total cost
like to set
Q
zQ where
is ^^
so that
it
z
is
a
maximizes
+ z)Q-Q'
and would thus choose
V
+
z
Q^-yassuming
this is positive.
optimal output
The
is
I
assume that the mean of
positive for the
follower's cost
is
mean
a better position to
.
+
z), (v
+
z), is positive so
that the leader's
realization.
given instead by
Q^ — rQ where
the key assumption that the follower does not
in
{v
,
(3.3)
know when production
know
is
28 Ibid., 36.
30
v
r is
and
important.
z.
common
The
While
knowledge.
idea
this
is
I
will
make
that the leader
is
asymmetric information
is
not
made
explicit in Crozier (1964) he does say that the role of the leader falls to the
experienced operator and that, unlike what the
among employees. To ensure
of any information about
For simplicity,
payoff of zero.
It
level.
might be more
its
mean, we must have v
I
assume that the
realistic to
do not pursue
and thus high
this
is
Q
optimal for the follower
on the follower's part
effort
+
r
>
not rotated
0.
follower's payoff
depends on the
this because the follower's response
he should complain whenever the output
The reason
is
assume that a complaint by the follower gives him a (suitably normalized)
I
of the ensuing investigation.
cases:
guidelines require, this job
that the follower wants to produce positive amounts in the absence
except for
t;
official
most
chosen by the leader
is
that high values of
is
Q
is
the
same
results
in
both
above some threshold
suggest that z
is
high
only in the leader's interest. To see this assume that
is
and V are independently distributed with normal distributions defined by N(z,a^) and N{v,al)
z
Then,
respectively.
+
V
Q
rrfra
(<5
~
v
—
if
z).
the leader chooses
Q
using (3.3), the follower's expectation of v given
Therefore, the followers expected payoff
if
Q
is
he goes along with this choice of
is
/
<^l
+
v
„
^";^l«
Assuming the leader
the follower's cutoff
to zero.
Thus the
is
picks
Q
cutoff
Q'"^
Q
(other than zero) that
makes the expression
in (3.4) equal
satisfies
and pick Q"^^ otherwise. Thus,
minimum
(3.4)
and that the follower gets zero when he complains,
Given any cutoff Q"^^ the leader's best choice
the
^2
+ rQ
Q -Q'
2
as in (3.3)
that value of
z
is
to pick
Q
as in (3.3)
in equilibrium, the cutoff is
of the quantity in (3.3)
and that
whenever
this is
below Q"^^
given by (3.5) with output given by
in (3.5).^^
Consider now what happens when the follower chooses to become altruistic towards the leader.
This leads the follower to pick a higher
interest.
There
is
now
level for the cutoff
have no
is
clearly in the leader's best
a larger set of realizations for v and z such that he chooses
However, the follower does not benefit from
in the cutoff
Q'"^. This
effect
this
change
in
if
(3.3) gives a negative
31
as in (3.3).
emotion. Indeed, while small changes
on follower welfare, large increases are
^^This ignores negative outputs. Obviously,
Q
Q, the optimal
strictly deleterious.
Q
is
lero.
The reason
is
that output doesn't change except in states of nature where the follower would have expected to
be better
off
with an output of Q'"^. The follower thus
hcis
no incentive to
feel altruistic
towards
the leader.
Finally, consider an increase in the affection of the leader for the follower.
chooses
Q
to
if
+ 1a){vQ - Q^) +
(^
+
the follower believes that
leader), his expected value of
^+
his payoff
if
t;
>
<rl
Q
is
given
+
.
Q
make
this to zero
it
+
,_-,,,.
{'^l/{l
—^
[Q
+ lA)'\
.
Q
f^
+ lA)'\
^
and solving
comparable to
(3.5)
2
is
to
is
+
in the
+ lAr
2(1 + 7a)
z
is
Q -Q^ +rQ
of the cutoff which, after
her strictly better
off.
On
+
/
az
r) is positive,
which
is
required for the follower
in 7^1
(u) is high.
32
Because
has no effect on her welfare when she
the other hand, an increase in
Intuitively, the leader benefits
for the follower.
7^ does
raise the cutoff
from her affection because
the follower to trust her more and, as a result, they both increase their effort
doing so
some manipu-
absence of any information.
maximizes leader welfare, a small increase
constrained by the cutoff.
in the affection of the
7a)
This implies that the leader benefits from small quantities of affection
(3.3)
^
given by
increasing in 7^1 as long as (v
want to produce positive output
2(1
given by (3.6)
new value
gives the
2ct?
This expression
2
—^{Q-::-
{<^l/{i
^
7a)
is
he goes along with the choice of
<rl
Equating
+
'rxr
chosen in this way (so that he believes
<^u
^+ ,..,",.
lation to
+ lAr)Q
^> + ^ +
2(1
Thus,
{z
he were unconstrained, he would pick output to ensure that
=
If
now
leader
maximize
[i
so that,
The
and
this
is
not
makes
this affection leads
when the payoff from
4.
Relative Performance Evaluation
A
Suppose
B
and
are correlated. Thus,
independently carry out similar tasks but that the outcomes of the two tasks
if
individual
t's
output
is
denoted by Qi, the two outputs are given by
QB =
QA^h{a,tA)
where the h function
random
increaising in
is
h{b,eB)
(4.1)
both arguments while e^ and cb are positively correlated
variables outside of the control of the individuals.
observe the random disturbances and the two employees are
a compensation scheme which makes their
Then, assuming the firm does not
selfish, it
makes sense
own wage depend not only on
their
to offer
them
own performance,
but also on the other agent's performance (Lazear and Rosen (1981), Holmstrom (1982), Green
and Stokey (1983)). The reason
the
common component
the
C
function
compensation
is
is
is
of the two
that the other agent's performance conveys information about
f's.
Thus, the compensation of
increcising in the first
given by
argument and decreasing
A
is
given by
C[QA,Qb) where
in the second.
Similarly, B's
C{Qb,Qa)-
Let e(a) and e[b) be, once again, the private costs of
effort.
The
resulting payoff for
A
is
a = c[h{a,eA),h{b,eB))-e{a)
and similarly
It
is
for
then
(4.2)
/?.
apparent from this formulation that aj (and 0a) are both negative so that employees
benefit each other
when they
cut
down on
their effort.
As shown by Holmstrom and Milgrom
(1990), collusion between employees thus reduces effort. But, will altruism arise naturally?
be sure that
it
will arise
if
aat
is
positive
-
which requires that C12 be positive
-
We
can
but this need not
be part of the optimal contract.
To
illustrate the ambiguities involved,
I
analyze a particularly simple contract that has been
shown by Lazear and Rosen (1981) and Green and Stokey (1983)
this setting.
With
this contract each employee's
to have desirable properties in
payment depends only on the rank of his output.
Let the worker with the highest output be paid W2, while the one with the lower output
is
Wi where Wi < W2.
sum
Specializing further to the ceise where the h function
is
given by the
paid
of
^*Note that such a tournament does indeed make payments insensitive to the other employees output when the difference
between the two outputs is large.
33
=
the effort and the disturbance (so that /i(a,e^)
a
+
A
e^) the payoffe to
a = Wi + {Wi - Wi)G{a -
b)
-
e{a)
Wi)G{a -
6)
-
e(6)
and
B
are
(4.3)
^Wi-{W2where
G
the
is
c.d.f.
of €a
—
(b-
At the Nash equilibrium without altruism we have
Q„
Thus dab has the same
a
mode
at zero, the
no incentive
sign as —g'.
{W2
- Wi)g -
e'
=
the distribution
If
G
(4.4)
is
changes
in
7
at this
that, in this ccise, the slope of expected
Thus, there
is
symmetric equilibrium. The intuition
for this result
is
compensation with respect to
second derivative of g with respect to
that relatively large drops in
b
its
7 are attractive.
argument
lower g and,
something from relatively large increases
if
A
behaves as in
7^
in
at its unique
B
benefits
This
is
of
G
and
e
will
what goes on
win but also lower the
= 6^
insight into
respectively.
for e(a).
In the
Taylor approximation of
G
This
still
twice differentiable, the
is
is
negative.
This implies
lower a as well. Thus,
B
and lead to reductions
gains
in a).
so that one cannot be sure that
that large reductions in b not only raise
sensitivity of the probability of
what determines whether
An
e{b)
and similarly
B
G
Nash
winning to A's
a.
increeise in
approximation, the resulting value of
=
new
e is
e{b^)
7b
B
benefits,
I
consider a Taylor expansion
in the "selfish"
lowers 6 (since at
is
Nash equilibrium. These
negative). Using the Taylor
then
+
e'(6
-
6^)
+ -{b -
b^)^
(4.5)
equilibrium, b will be below a so that a
—
6 is positive.
The
can thus be written as
G{a -
6)
=
G(0)
+
3(a
-
6)
+ ((a Z
^*
is
around the values that their arguments take
and a^
are
A
what reduces
To gain further
effort is highest at the
mode
(since these lower 6
course, these large reductions in b also lead to direct costs for
his altruism. Intuitively,
If
(4.4),
Of
effort.
g'
does not change for small changes in the other person's action.
it
the probability that
=
heis
0.
leaves open the question whether larger changes in
from
symmetric, differentiable and
symmetric Nash equilibrium occurs at a point where
for small
equilibrium so that
:=
6)^
+ ^(a -
These conditions on the distributions are obviously met when the distribution of each
(1981).
34
b)'
(4.6)
b
t is
normal as
in
Lazear and Rosen
where
equal to zero. Using these approximations, the
g' is
remains
selfish,
becomes
{W2
Using
order condition (4.4) for A, which
first
- W^)
(g
+
^-[a
- hf\ -
e'
-
- a^) =
e"(a
(4.4), this implies
a-a'' =~{W,-W,){a-h)''
Because g"
from
its
selfish
negative while e"
is
Nash equilibrium
difference between
^ and
its
is
(4.7)
positive, this equation says that,
value, a declines.
Using
-{W, - W,) [g{a -b) + ^(a -
6)^)
-
e'{b
-
—
—
a
a
+
b), this difference
e'ia""
As
B
-
a)
-
{W,
raises 7^, b falls so that (a
-
W,)^-^{a
—
b)
(meaning that
long as
or equivalently {W2
—
B
Wi)g,
is
B
benefits
Tournaments
from
also
-
6)^
B
gains) while the last
we shrink
promote altruism and cooperation
6^)^
and that
[a
(6
e'
-
— 6^)
is
equal
b])'
(4.8)
(4.7) a falls.
term
e",
may seem
in the case
rather special,
falls
reductions in b create a range of realizations for eg such that
is
Thus the
first
negative. However, as
the positive terms dominate
and g" /e" constant, we can be
A
it
where the
illustrates
when
6 falls.
e's
-00
The reason
f{eA)f{eB)deAdeB
is
/+00
f{b-a +
00
35
is
why
that
wins whether he changes a slightly
r+00
/
Jb-a+fB
have independent
another reason
t^ and £b are independently distributed, with density function /,
/oo
SO that g
and
e" keeping
the sensitivity of A's probability of winning to his effort
When
the resulting
liking A.
uniform distributions. While this case
or not.
(4.4),
- ^(a - a^ -
large relative to g"
gains from his altruism. Similarly, as
sure that
- ^(6 -
6^)
becomes positive and, given
in (4.8) are positive
and
(4.6),
sufficiently
equals
two terms
e',
changed
is
Given that these expressions are evaluated at the Nash equilibrium
to (a
and
(4.5)
(4.3),
value at the selfish Nash equilibrium
if 6 is
€B)f{€B)d€B
G
becomes
In the case
(1
—
(a
—
where /
the uniform distribution between
is
6)) so that,
from
(4.4), aab
is
positive. ^°
zero. This then leads to a decrease in effort.
and
Thus,
1,
is
it
The model thus
and
in
6 is
smaller than
a, this
equals
B's interest to raise ib above
explains why, in
some circumstances,
altruism and friendship between employees rises endogenously and hurts firm profitability.
The model
also helps explain
why
expect from Lazear and Rosen (1981).
firms appear to shy
my
competition.
It
in place
would
Indeed, Lazear (1989) provides several examples where
From
the point of view of firms, such competition
might be argued that some competition
is
Personality matters
outcomes very
to tournaments as one
setting because individuals respond by liking each other
problem, however,
who put
much
away from having people who are near each other compete even though such
competition would appear optimed.^*
attractive in
firms do not resort as
is still
likely to
is
not
and thereby blunting the
remain
in equilibrium.
One
that the personalities involved affect the degree of friendship and altruism.
if it
affects a, ^, or the direct benefits
from the friendship
tournaments subject individuals to additional
sensitive to the personality of the
worker with
risk since
whom
reduces the ex ante welfare of workers, and tournament-using firms
they
itself.
Thus, firms
make
individual's
they are matched. This risk
who wish
to attract workers
must therefore pay higher wages.
^"Note that g is actually equal to (1 - |a - b\) so the sign of Oat depends on whether a is bigger than or smaller than b.
However, as required for B to benefit, if B starts liking A, b falls so a - b becomes positive and a responds by lowering a.
^'Lazear's (1989) theory of this stresses the opposite of altruism. He notes that employees who compete with each other are
likely to sabotage each other's work, to the detriment of their employer.
5.
Moves
Sequential
So
far
somewhat
I
have generally assumed that
artificial, this
this section,
I
my
B select their actions a and
and
A
modelling device does ensure that
briefly consider the case
the robustness of
A
where
A
B
and
his choice of b
always makes his move
first.
I
do
this
both to study
conclusions and to relate this work to that bzised on Becker (1974a).
with
full
knowledge of
condition which gives the resulting value of
and 7^- Denote
as a function of a
simultaneously. While
are treated symmetrically. In
Consider the continuous action model of section 2 and zissume that
makes
6
For any value of
a.
Since a
6 is (1.8).
this function
by $(0,7^).
75
A
chooses a
first.
(including zero), the
B
first
then
order
known
at this time, (1.8) gives h
We know
the local behavior of this
is
function from the second line of equation (111), which can be rewritten as
dh
From
(5.1)
follows that,
it
if
a selfish
A
is
would
nothing to gain by being
of
what one
is
altruistic.
The reason
to zero.
likely to do.
since he already
d76
(5.1)
IbOLhb
when
a
B
will
choose
b using the function
$. Thus,
set a such that
+
should now be apparent that, because
7^ equal
+
positive, b rises with 75.
is
he chooses a knowing that
different;
aa
It
^66
a and h are strategic complements for both players, b rises
does. Also, given the normalization that aj
A's problem
"^
= J-^^±J^^da
Pbb + 76 "66
is
ai^a
b
=
(5.2)
does not depend on 7^ but only on a
In other words, he achieves the highest value of
itself,
A
has
a by keeping
that altruism has value by influencing the other players' perception
But, in the case where
knows the action
B
moves
last,
B's perception doesn't matter,
a.
This result, that any altruism that occurs in equilibrium must be B's, accords well with the
timing of moves in Becker (1974a, 1976) where the altruist moves
last.
It
therefore suggests that
Becker's order of moves need not be an assumption but a conclusion from letting altruism be
endogenous.
This result does hinge, however, on a predetermined order of moves.
realism of this
affection,
I
I
is
questionable, and because
it
Because the
has such a pronounced effect on the pattern of
concentrated mostly on simultaneous moves.
now study whether B
benefits
from becoming
37
altruistic
i.e.,
whether d^/d^B
is
positive.
Using
and
(5.1)
(1.8), d/3 is
d/3
=
Ma + Mh -
The second term
ditions.
I
given by
represents the "direct" effect which
and 7^. This
changes
itself.
0.
where 75
will consider the case
term then has the same sign
b
Ua + lBO^,~-^P^]
da.
eis
some
plays
(5.3)
The
first
differentiate (5.2) with respect to a,
the coefficient of da in (5.2), responds to
is
apparent from (5.2) that $3 depends not only on 75 but also on
is
clearly not enough.
I
affects the desirability of altruism, strategic
thus proceed to show only that strategic complementarity
To do
role in generating altruism.
this,
I
assume that a and
db/da varies only with 7^- The derivative db/da with respect to 7b, ^a^B
^aiB
=
are quadratic so that
^^
^^^^
aab + Otbb^a
-^-—
Phb
+
.^
,(.
(5'*)
IbOibb
that the denominator of (5.4)
The second order conditions imply
6
a function of the third partial derivatives of a and
Thus, because the sign of these partial derivatives
is
—l^^^d^s
negative given the second order con-
is
must
da, one
how $a, which
Moreover, the extent of this dependence
complementarity
+
small so that this term can be neglected.
To obtain
raises the question of
in these variables. It is
is
da
positive as long as aab exceeds —a^b^a- In the normal ccise where
is
on,b is
negative.
Thus, ^ais
^^
negative, this requires a
strong strategic complementarity.
Ignoring the dependence of $a on
6,
differentiation of (5.2) gives the following expression for
da
{aab
da=
+
^aabb)db
^
+ ^aigdlB
T
,^ ^^
\y-^)
\
Combining
(5.1)
and
(5.5), the
da
=
change
in a
{-ab^i'a-^B^hb
when 75
+
Oibiaab
small
is
+
is
^aahb)/D'
(5.6)
where
D'
The denominator D' has
terminate
if
=
[aaa
+
Otab^a)^bb
"
{^ab
+
a generally ambiguous sign.
one assumes the system
is
stable.
Olhb^a)^J>
As
In particular,
before, this sign can be
suppose that
B
made
always chooses
deb to
maximize
his utility (so that b satisfies (1.8))
Assuming that the change
It is
in a
A
but that
has the same sign as aa, the system
,
make ^aig
the numerator of (5.6) are positive so that a increases with
7b from zero
ism
is
apparent from (5.4) that, with a positive D' the expression
the strategic complementarities are sufficiently strong to
I
has to grope towards his optimal a.'^
is
when D'
in
Then, both terms
game
ideas to the "merit good"
the former, the
visiting often.
first
mover (the
closing this section,
how much money
generating altru-
game"
of Becker (1974a). In
good" such as studying hard or
child) picks the level of a "merit
is
in
increcising in the
amount
of the merit good
to transfer to the child. Becker (1991) shows that
children of altruistic parents will tend to pick relatively high values of the merit good
point of view of the parent, transfers and the merit good are complements,
utility of transfers
in this ccise
when
goes up
the child behaves well.
where altruism leads the kid to behave
In the "transfer
income and,
how much income
What my
well, altruism
it
affects the
to transfer to A.
must determine whether the
i.e.,
analysis shows
if
if,
from the
the marginal
that precisely
is
in the parent's self interest.
is
game" of Becker (1974a) the action taken by the
in particular,
a.
briefly discuss the application of these
of Becker (1991) and to the "transfer
After this, the parent, whose utility
picked by the child, chooses
I
in
turn implies that increasing
have now established that strategic complementarities are also important
move games. Before
whenever
then has the same sign as the change in
attractive since the increase in
in sequential
positive.^
is
in (5.6) is positive
positive.
This
'ib-
stable
first
mover
A
aff"ects
only
second mover's wealth. The second mover, B, then decides
To determine whether altruism
resulting increeise in transfers to
A
is
leads
good
A
for
B
in this
to generate
game, we
more income
for B.
now argue
I
that the existence of this strategic complementarity depends on whether A's action
generates mostly income controlled by
income
later decides
how
it is
A
or mostly
to be spent. Suppose
income controlled by B. Whoever controls the
first
that A's action, a, requires costly effort to
generate income only for himself and that b represents the fraction of
to
a.
An
increase in b then lowers a since
it
and use
(5.1) to
determine
(b
-
b')
income that
lowers A's marginal utility of income.
^^This makes some sense since A can't be sure what b will be, while B does know
^^To see this, note that (5.2) then implies that da/dt is proportional to
(oaa
fi's
+ aat*a)(a -
a')
+
from (a - a').
39
(a<,t
+
Q:66*a)(*
-
o.
b*)
is
transferred
The
actions are
strategic substitutes
Now
suppose, as
and
is
B
loses
from
his altruism.
implicit in Becker (1976), that A's action generates only
control of B. Then, letting 6 be positive rather than zero raises a because
income generated by
fraction of the
for A,
and
B
his effort.
Thus,
in this case, a
does benefit from his altruism. His altruism leads
and
A
income under the
now A
gets at least a
b are strategic
to produce
complements
and he gets to keep
a fraction of this income.
6.
Conclusions
This paper has shown that altruism can be rational and that this can explain certain observa-
tions
from industrial
By becoming
settings.
altruistic
The
towards you,
actions induce you to change your
is
central idea
am
I
own
led to
fact that the theory predicts
change
is
my
behavior.
way that
If
benefits me,
the resulting changes in
my becoming
altruistic
rich in refutable implications. This richness
comes
both the emotions that people have and their actions. Insofar
as emotions can be measured, there are thus
alone. Here,
that strategic complementarity breeds affection.
actions in a
smart. This idea, while extremely simple,
from the
is
more implications than
in theories that predict actions
have only focused on measurements of emotions that are based on self-reports and
I
have found some concordance between these and the emotions predicted by the model. To be more
convincing, this evidence would have to be supplemented with evidence from physical and chemical
changes which are supposed to accompany changes
In this concluding section,
I
in
emotions.
deal with two issues.
altruism with Homans' (1950) idea that people tend to
which they receive large rewards at low
settings.
I
will
argue that
many
this idea are also consistent
than
my own
costs.
The
my
a comparison of
like (or feel altruistic
The second
is
of the findings that have led
with
first is
own. In addition,
my
theory of
towards) those from
the applicability of the theory to other
Homans
(1950) and others to embrace
this traditional theory is less consistent
with the observed features of authority relations.
Using anthropological data from the Polynesian island of Tikopia and data from the Hawthorne
experiments as evidence,
Homans
(1950) stresses that the friendliness
among co-workers
is
much
^*One interesting feature of this example is that the outcome is Pareto Optimal (so that the "rotten kid theorem" holds)
whether B is altruistic or not. The example is not wholly in the spirit of Becker {1974a) because a affects only A's income.
However, the conclusion that a and b are strategic substitutes for A so that altruism is bad for B extends also to the case where
the effort a also raises the income controlled by B as long as this effect is sufficiently small. Pareto efficiency of A's effort is
still assured by the "rotten kid theorem" as long as A's utility is linear in income and B's altruism is sufficiently intense.
40
more pervasive than between workers and
much more
friendliness between brothers
their supervisors.
(who work together
In the island of
Tikopia there
is
than between sons and
in the field)
fathers (where the latter are the central authority figure). This seems problematic for the view that
friendliness
depends only on the frequency of interaction or even on the happiness of the outcomes.
Indeed, Romans' (1950)
is
led to posit that friendliness
from repeated interaction
arises only
when
the participants are relatively equal, or, in his words "when no one originates the interaction with
much
greater frequency than the others" (p.
difference in affective attitudes
and
One advantage
my
of
theory
is
that this
explained endogenously as one can see by comparing Sections 2
3.
Moreover,
my
theory can explain
(such as people
who
those that give
them
it
is
243).
may
why people
are competent or attractive).
not be apparent what effect altruism has on one's
my
That
why people
them
large rewards
feel altruistic
own rewards from
dilemma case
of Section 1.2.
sometimes obtained only when both individuals
from
someone that already
liking
unknown
is
no formal quid pro quo).
who
an individual
rational; he
What
is
is
cis is
like
the other. In this case, an individual has
feels affection for
him than from
raising the
it
explains
more
proffering his affection
why
feelings of altruism
required by the fairness theory of Rabin (1991). Second,
feels altruistic
be seen
There, positive outcomes for either individual are
third party. This has two consequences. First
are often symmetric,
towards
the relationship. This
affection tends, endogenously, to flow towards those that like one already can
in the prisoner's
it
implies that
towards somebody whose company benefits him may actually be
odds of continuing to
profit
from the relationship.
more, the notion that one raises the probability of being liked by liking someone has
plenty of empirical support (See Aronson (1984)).
altruistic
give
theory implies that liking someone raises the likelihood
that one will be liked in return (even though there
to an
Explaining
who
large rewards might actually be regarded as something of a challenge since
mystery dissipates once one realizes that
to gain
like individuals
So, the idea that people benefit from being
towards those they benefit from interacting with
is, itself,
already proven by the existing
experimental evidence.
In this paper,
I
have studied interactions only within the workplace. While affection certainly
also takes place elsewhere,
I
have focused on the workplace for several reasons. First, firms create a
41
large degree of variation in the setting within which people interact. This allows one to study
Second, the benefits people extract from the workplace
relationships differ in different settings.
are relatively tangible.
members
are not only
By
how
contrast, the benefits one extracts from one's social friends and family
more
subjective, they are also
extensions of the model to relationships
among
more
family
likely to
members and
be unconscious. Nonetheless,
friends seems desirable.
The
endogenous creation of altruism within the family would seem to be a useful complement both to
Becker's (1974a and 1976) discussion of the consequences of altruism and to Becker's (1991) insight
that people
who
each other are more
like
Another potential application of the model
The question
related occupations.
or
among
chief executives,
is
is
marry.
likely to
is
to the ties of friendship that bind people in
the degree to which friendship and altruism
in their self interest rather
among
doctors,
than being only the result of their shared
experiences. This in turn raises the question whether the manifestations of these intra-professional
friendships, be they patient referrals or "Gary" dinners, are socially desirable.
7.
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o^9
44
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