of 18
Allocators
are more
prosocial
when
affected
agents
can
visually
eavesdrop
Stephanie
W. Wang
a
,
*
, Colin
F. Camerer
b
a
University
of Pittsburgh,
United
States
b
California
Institute
of Technology,
United
States
ARTICLE
INFO
JEL Classification:
C92
D91
Keywords:
Social
preferences
Social
image
Observability
Attention
ABSTRACT
In these
experiments,
participants
made
binary
choices
in
dictator
games
choosing
distributions
for themselves
and others.
All payoffs
are initially
hidden
and can be clicked
open
using
a mouse.
To study
the effect
of social
image
on attention
and choices,
we used
a novel
screensharing
technique:
One of the participants
receiving
the chooser
s allocation
can observe
the chooser
s
clicks,
so they can see if the chooser
is looking
up what
the impact
will be on their own allocation
(but they
cannot
observe
the chooser
s choices).
This change
in observability
increases
the
possible
impact
of social
image
concerns
on expressed
social
preferences.
It increases
the time
choosers
spend
looking
at the potential
payoffs
to the observer
and makes
their
choices
less
selfish.
This
finding
goes
against
the hypothesis
of
willful
ignorance
and suggests
other
behavioral
influences.
1. Introduction
In Plato
s Republic,
a character
called
Glaucon
tells of a myth
about
a ring that can turn a person
invisible.
Plato
s Glaucon
insists
that in general
even a good
person
could
not resist
the temptation
to behave
at least a bit antisocially
when
cloaked
in invisibility
(as
described
fictionally
in
Baker,
1994
). Put the other
way around,
knowing
that we are observed
puts us on our best behavior.
As Plato
writes
(
Plato
and Jowett,
1941
):
If you could
imagine
anyone
obtaining
this power
of becoming
invisible,
and never
doing
any wrong
or touching
what
was
another
s, he would
be thought
by the lookers-on
to be a most wretched
idiot,
although
they would
praise
him to one another
s
faces,
and keep up appearances
with one another
from
a fear that they too might
suffer
injustice.
(2.359a
2.360d)
Glaucon
s claim
that people
behave
less badly
when
being
observed
is a hypothesis
about
one way that human
nature
deviates
from
simple
selfishness.
While
the model
of pure
material
self-interest
will always
prove
to be a useful
benchmark,
social
and natural
scientists
are now establishing
a model
of human
nature
that is richer,
but also predictive.
Such useful
models
include
concerns
for the
distribution
of rewards
to other
people
(
Bolton
and Ockenfels,
2000
;
Charness
and Rabin,
2002
;
Fehr and Schmidt,
1999
) and reci
-
procity
(
Dufwenberg
and Kirchsteiger,
2004
;
Falk and Fischbacher,
2006
;
Rabin,
1993
). In these
models,
whether
a person
is observed
by others
does not make
any difference.
*
Corresponding
author.
E-mail
addresses:
swwang@pitt.edu
(S.W.
Wang),
camerer@hss.caltech.edu
(C.F.
Camerer).
Contents
lists available
at
ScienceDirect
Journal
of Economic
Behavior
and Organization
journal
homep
age:
www.el
sevier.com/l
ocate/jebo
https://doi.org/10.1016/j.jebo.2024.106772
Received
16 June
2023;
Received
in revised
form
23 September
2024;
Accepted
6 October
2024
Journal
of
Economic
Behavior
and
Organization
228
(2024)
106772
Available
online
25
October
2024
0167-2681/©
2024
The
Author(s).
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(
http://creativecommons.org/licenses/by-nc-nd/4.0/
).
However,
in other
models,
people
sometimes
help others
to increase
their
own
social
image
(e.g.,
manners
in
Andreoni
and
Bernheim,
2009
;
Benabou
and Tirole,
2006
;
Camerer
and Thaler,
1995
;
Rotemberg,
2008
,
2014
). In these
models,
people
derive
utility
when
others
believe
they adhere
to a norm
of pro-sociality
or are genuinely
altruistic.
Some
evidence
from psychology
and neuroscience
indicates
that being
observed
can influence
behavior,
including
prosociality
(e.g.
Guerin,
1986
). For example,
an early
small-sample
study
showed
that people
washed
their hands
in bathrooms
twice
as often
(80 % vs
40 %) when
they knew
somebody
was watching
them
(
Munger
and Harris,
1989
). This kind of behavioral
change
in response
to public
observation
indicates
that some
hand-washing
is done
to appear
like a hygienic
person,
rather
than to actually
be hygienic.
In our study,
participants
choose
allocations
of money
for themselves
and others.
All the monetary
payoffs
are hidden
in boxes
on a
computer
screen.
When
a cursor
moves
into the box area participants
can see the monetary
payoffs
(a method
called
Mouselab).
In the
Baseline
condition,
other
participants
don
t
see the payoffs
the decision
maker
is looking
at. In the social
image
(SI) condition,
an
observer
whose
payoffs
will be determined
by the decision
maker
s
choice
gets to see
through
screen-sharing
exactly
what
payoffs
the decision
maker
is looking
at. In both cases,
the affected
other
participant
does not observe
the actual
choices
made
by the active
participant
until the end of the experiment.
The goal of our experiment
is to contribute
new evidence
of observability
effects.
While
other
studies
have experimentally
changed
social
observation
(see the next section),
our study
is the first to vary actual
social
observation
of a person
s
attention
and decision-
making
process
visual
eavesdropping
by a social
observer
whose
payoff
is affected
by the person
being
observed.
This design
can establish
how social
observation
affects
both attention
and choice
at the same
time.
Changing
what
other
people
know
or see about
a person
s
decision-making
process,
and measuring
whether
the person
s
decisions
change,
is a method
that can discriminate
social
image
models
from distributional
or reciprocity
models
most clearly.
Specifically,
this paradigm
measures
three
interesting
empirical
properties
of observability
and social
image:
(1) Are people
more
prosocial
when
they are observed?
(2) Does their visual
attention
to
payoffs
change
when
they are observed?
And (3) Do people
deliberately
control
social
attention
when
they are observed,
and in which
direction?
That is, do they look
more
at others
payoffs
to improve
social
image,
or do they look
less
to create
deniability
or
moral
wiggle
room
?
Learning
more
about
the answers
to these
questions
is important
for economics
and social
science
for three
reasons.
First,
in recent
decades
a lively
debate
has arisen
in economics
about
which
models
of social
preference
are best for various
empirical
purposes
(
Camerer,
2003
;
Cooper
and Kagel,
2016
). Social
image
modeling
is newer
and more
complex
than the earlier
alternatives.
Knowing
more
about
the importance
and properties
of social
image
effects
is essential
to advance
the debate
about
whether
the social
image
models
are a workable
improvement
over simpler
ones (
Rotemberg,
2014
).
Second,
if social
image
concerns
are important,
and observability
therefore
matters,
then institutional
details
of how social
in
-
formation
is organized
and broadcast
will affect
choices
(and presumably
welfare).
One class of effects
is how observation
of actions
enhances
social
image.
An obvious
example
is how charities
use publicity
in acknowledging
donors
naming
buildings,
or putting
their
names
on a plaque
that is prominently
displayed
to advertise
their generosity.
Other
studies
indicate
that social
observation
changes
voting,
education,
and consumption
decisions
(
DellaVigna
et al., 2017
;
Bursztyn
and Jensen,
2015
;
Bursztyn
et al., 2018
). Social
signaling
has also been
used to motivate
prosocial
choices
such as childhood
vaccination
(
Karing,
2024
).
A second
class of effects
is how observation
of the information
used by decision
makers
reassures
economic
agents
that their
in
-
terests
are being
considered
(buttressed
by the decision
makers
desire
for a good
social
image).
For example,
in business
and man
-
agement,
law, and politics
there
are often
rules about
disclosure,
transparency,
and how the impact
on people
should
be considered
in
decisions.
These
institutions
include:
Public
corporate
shareholder
meetings,
the right of the accused
to physically
face one
s
accuser
in
court,
freedoms
of the press,
sunshine
laws
,
the Freedom
of Information
Act, widespread
reliance
on face-to-face
personal
interviews
in selection
and hiring,
etc. These
rules all promote
the right of a person
who is affected
by decisions
to get a chance
to socially
observe
a decision
maker
by directly
confronting
decision
makers,
or by seeing
their paper
trail. Some
of these
rules
are required
by law to
mitigate
agency
problems,
but others
are voluntary
actions
designed
to enhance
image
(e.g.,
WalMart
donating
goods
to Hurricane
Katrina
victims).
Thus,
the institutions
and practices
designed
to benefit
observers
presumably
do so in part because
they discipline
and
change
what
those
being
observed
do.
Many
studies
in social
psychology
and organizational
behavior
suggest
that workers
will more
readily
accept
unpleasant
outcomes
such as layoffs
and pay cuts
if they believe
their interests
are considered
during
a
procedurally
just
process.
(
Lind and Tyler,
1988
;
Taylor
et al., 1995
). A related
empirical
example
is that
apology
laws
”—
which
exclude
apologies
as evidence
of guilt in malpractice
cases
reduce
litigation
(
Ho and Liu, 2011a
,
b
). These
studies
suggest
that if observers
see that a participant
is looking
at their payoffs,
those
observers
will more
readily
accept
selfish
actions
(which
could
lead participants
to act more
selfishly).
Third,
technology
has rapidly
made
social
observation
easier
(e.g.,
through
Facebook
and other
social
media).
That is, the infor
-
mation
that people
pay attention
to and the options
they weigh
may have
become
more
apparent
to others
while
their
final choices
often
remain
private
and unknown
to anyone
else. This boom
has made
image-cultivation
a bigger
business
and changed
the modern
workplace.
Understanding
the underlying
motivation
for both observation
and image
are necessary
to understand
the development
and welfare
consequences
of these
technologies,
the market
activity
they catalyze,
and the new management
challenges
and oppor
-
tunities
they have
created.
2. Background
Previous
social
image
studies
fall into three
categories:
(1) Presentation
of abstract
cues of observation;
(2) Actual
observation
by
disinterested
people;
and (3) deliberate
image
management
by participants
(through
endogenously
choosing
what
others
know
about
their
choice
set and choice).
Abstract
cues:
Several
experiments
show
pro-sociality
is increased
by indirect
cues to being
watched
or heard
(
surveillance
cues
,
in
S.W. Wang
and C.F. Camerer
Journal
of
Economic
Behavior
and
Organization
228
(2024)
106772
2
evolutionary
psychology
language).
Cues in the form
of stylized
or abstract
human
eyes,
or a vaguely
human-like
robot,
have shown
modest
effects
on prosociality
in dictator
games
(
Burnham
and Hare,
2007
;
Haley
and Fessler,
2005
;
Rigdon
et al., 2009
), in a
workplace
pay-what-you-want
setting
(
Bateson
et al., 2006
), and in moral
condemnation
of crimes
and villains
in vignettes
(
Bourrat
et al., 2011
). However,
there
have
been
many
failed
replications.
For example,
Fehr and Schneider
(2010)
found
no effect
in a trust
game.
Most
effects
also appear
to be interactions
between
a trait or state variable
and surveillance
cues.
Effects
have
been
found
when
the eyes are in 3D rather
than 2D (
Kr
́
atký et al., 2016
), and when
eyes look directly
compared
to
being
averted
(consistent
with heightened
biological
activity
from
direct
eye contact)
(
Manesi
et al., 2016
). There
is also substantial
evidence
of effects
from
short
exposure
(
<
1 min)
and no effect
at longer
exposures
(several
minutes)
(
Sparks
and Barclay,
2013
).
A field experiment
on voting
measured
the effect
of sending
a postcard
encouraging
voting
(
Do your civic duty and vote!
) with
three
background
images
eyes,
an American
flag, or a palm
tree. The eyes increased
turnout
by 1
2 %, but the effect
was only
significant
among
Republican
voters
(
Panagopoulos
and van der Linden,
2016
)
As a whole,
these
results
demonstrate
the intriguing
possibility
that even simple
observation
cues
could
have an effect,
but the effect
is not well-established
(and could
be inflated
by publication
bias if non-effects
are either
unsubmitted
or rejected).
Human
observers:
Several
studies
have
found
that the presence
of actual
human
observers
influences
prosociality
(broadly
inter
-
preted).
Izuma
et al. (2010)
shows
heightened
activation
in well-established
reward
regions
(ventral
striatum),
and more
giving,
when
participants
are watched
while
giving
to charity;
autistic
adults
show
a diminished
observation
effect
(
Izuma
et al., 2011
).
Coricelli
et al. (2010)
find that having
your picture
displayed
to others
deters
an experimental
version
of tax evasion
(and arousal,
measured
by
skin conductance
response,
increases
more
during
an experimental
audit
when
your picture
is displayed).
An effect
of human
observers
on anti-social
cheating
was measured
by a natural
experiment
in Italy,
explicitly
randomizing
adult
examiners
to classrooms,
as Italian
2nd and 5th graders
took tests (
Bertoni
et al., 2013
). The examiners
watched
for cheating
and
transmitted
answers
when
the students
were done.
In classes
with examiners,
test scores
were about
5
8 % lower.
The effect
is probably
due to reduced
cheating,
because
students
did not report
feeling
more
anxious.
Endogenous
image
management:
Experimental
participants
sometimes
exhibit
a preference
to limit whether
or not they are socially
observed
when
they are making
prosocial
choices.
Limiting
social
observation
can create
deniability
or
moral
wiggle
room
to then
act selfishly
without
the emotional
burden
(perhaps
guilt)
of being
watched.
In a modified
dictator
game,
Lazear
et al. (2012)
and
Dana
et al. (2006)
found
that many
people
deliberately
opted
for a choice
which
had no scope
for prosociality
but gave them
less money,
in
order
to avoid
a choice
in which
they could
earn more
but another
person
would
know
they had acted
selfishly.
DellaVigna
et al. (2012)
found
that some
households,
when
notified
that a charity
would
be visiting
the next day, did not answer
the
door at the scheduled
visiting
time,
presumably
to avoid
observability
by the charity
solicitor
of the household
s explicit
decision
to
give nothing.
Dillenberger
and Sadowski
(2012)
and
Benabou
and Tirole
(2006)
provide
formal
models
of these
preferences.
Two other
field studies
looked
at reactions
of shoppers
to solicitors
asking
for charitable
donations
outside
of stores.
One was the
familiar
red kettle
of Salvation
Army
at Christmas
holiday
times.
Not surprisingly,
to anyone
who has shopped
and seen solicitors,
about
a third
of shoppers
avoided
the likely
guilt from not giving,
by walking
an average
of 70 feet extra
to go through
a door with no
solicitor
(
Andreoni
et al., 2017
). In a similar
experiment
in Alaska,
when
the temperature
dropped
below
0
F, the avoidance
dis
-
appeared,
indicating
that avoidance
is sensitive
to its price
(
Trachtman
et al., 2015
).
All these
studies
are important
for showing
how observation
can matter.
However,
they are generally
limited
on one of two di
-
mensions:
(1) Basic
internal
validity
i.e., we cannot
be certain
that the experimental
treatment
was applied
as intended
(i.e., that
participants
knew
they were being
observed).
In the abstract
cue studies,
participants
were
typically
not asked
if they noticed
the eyes
or the robot
picture
(and
their
attention
was not measured
in any subtler
way).
(2) Do observers
have
a stake
in the outcome?
Observability
effects
might
work
differently
presumably
more
strongly
if the observers
care about
how the participant
treats
them.
1
Our design
is different
along
both
of these
dimensions.
The decision
makers
know
that the observers
see exactly
what
they
themselves
see (as if the observers
are standing
over their shoulder
looking
at the screen).
They
also know
that the observers
payoffs
will depend
on what
they choose.
We measure
the decision-making
participants
attention
to their own and others
payoffs
directly.
3. Framework
and hypotheses
First,
we show
a highly
stylized
model.
This is a language
to express
some
hypotheses
about
the influence
of social
observation
on
lookups
and choice.
Our experiments
were not well-designed
to estimate
parametric
features
of this structural
model,
so we will not do
so. However,
other
papers
do so (e.g.,
Bruhin
et al., 2019
).
Player
roles and allocations
: We analyze
the case of two players,
the chooser
C and the observer
O. When
there
is an observer
and a
passive
third
player,
the analysis
is complicated
by whether
the observer
s utility
depends
on what
the passive
third
player
gets, and
what
the chooser
C believes
about
that utility.
We did not design
those
treatments
to test any theory;
they are purely
exploratory
to
generate
data that may provoke
future
theorizing.
Player
C chooses
between
two allocations
denoted
A
S
, A
F
. The allocation
payoff
pairs
are denoted
(
π
C
(A),
π
O
(A)).
In the design,
1
Studies
by
Dana
et al. (2006)
and
Lazear
et al. (2012)
are important
exceptions
because
they have
strong
internal
validity
and do have
financially-
interested
observers.
They
clearly
show
that some
participants
have a preference
for avoiding
social
observation
and choosing
selfishly.
Our design
goes
further
by exogenous
manipulation
of observation,
implementing
direct
observation
of information
gathering
through
screen-sharing,
and recording
visual
attention.
S.W. Wang
and C.F. Camerer
Journal
of
Economic
Behavior
and
Organization
228
(2024)
106772
3
these
are payoff
vectors
such as (400,400)
and (300,
600).
Without
loss of generality
(given
further
modelling
assumptions
below),
the
payoff
allocations
can be normalized
by subtracting
the lowest
role-specific
payoff
from
each of the two allocations,
which
creates
A
S
=
(100,0)
and A
F
=
(0,200)
for the previous
example.
We can further
normalize
these
to A
S
=
(1,0) and A
F
=
(0,y),
where
y is the ratio of
the payoff
advantage
to O from the allocation
A
F
over A
S
, relative
to the advantage
to C of A
S
over A
F
. The example
(400,400)
and (300,
600) allocations
then are transformed
to (1,0)
and (0, 2).
Player
private-information
types:
The O players
do not actively
choose.
Therefore,
for simplicity,
we assume
they are purely
selfish
so
that U
O
=
π
O
(A).
2
There
are two chooser
C types,
called
selfish
(S) and prosocial
or fair (F). In general
U
C
(A)
=
π
C
(A)
+
απ
O
(A). Their
utilities
put a
(weakly
positive)
weight
on the payoffs
of O. But S types
have U
S
(A)
=
π
C
(A) (i.e.,
α
=
0) and F types
have U
F
(A)
=
π
C
(A)
+
απ
O
(A) (with
α
>
0). The prior
proportions
of these
types
are 1-p and p.
Note
that F types
will choose
A
S
over A
F
iff 1
<
α
y.
The next part has three
steps.
In step 1, we describe
the general
utilities
which
can arise from social
image
when
O players
observe
what
the C players
look up. In step 2, we work
through
the logic
of what
happens
for all players
(C and O) and player
types
(S and F
types
of C players)
in the baseline
condition
where
there
is no observation
that is, the C players
can look at whatever
payoffs
they
want,
but the O players
will not know
what
was observed.
In the most complicated
step 3, we describe
equilibrium
conditions
when
C
players
both choose
what
to observe
and what
to choose.
Step 1: Judgments
of social
image
and disutility
from guilt
We make
assumptions
on social
image
and utility
such that the Observability
(Social
Image)
treatment
could
potentially
activate
a
social
image
judgment
by the O players,
about
the C player
s likely
type and therefore
O
s expected
payoff,
and which
also creates
potential
disutility
for C.
In both treatments,
S and F type Choosers
are assumed
to care about
their social
image.
Social
image
is defined
as their beliefs
about
the difference
between
what
O actually
gets and O expects
to get. Note that this is a socially
iterated
expectation
(C
s beliefs
about
what
O believes).
For the two types
of Choosers
the utilities
for S and F types
are assumed
to be
U
S
(A,
λ
)
=
π
C
(A)
+
γ
[
π
O
(A)-E
C
[E
O
[
π
O
(A)|
λ
]]
0
U
F
(A,
λ
)
=
π
C
(A)
+
απ
O
(A)
+
γ
[
π
O
(A)-E
C
[E
O
[
π
O
(A)|
λ
]]
0
An important
piece
of notation
is that [
π
O
(A)-E
C
[E
O
[
π
O
(A)|
λ
]]
0
, defines
a function
which
is upward
censored
at zero (i.e., positive
values
are set to zero).
The idea is that this term measures
only negative
guilt when
the chosen
amount
π
O
(A) is less than the Chooser
thinks
the Observer
expects.
3
When
the
π
O
(A) is above
the iterated
expectation
it is set to zero.
The first term is the Chooser
s personal
payoff.
The second
term,
for the F type,
is the altruism
weight
α
on the O payoff
π
O
(A). For
both types,
the last term is a social
sensitivity
parameter
γ
times
the difference
between
what
O will actually
get from choice
A, which
is
π
O
(A), and C
s expectation
about
what
O expects
to get. This is the iterated
expectation,
E
C
[E
O
[
π
O
(A)|
λ
], given
the choice
of lookup
λ
.
Step 2: No observation
(Baseline
Treatment)
In this Baseline
treatment,
player
O does not know
the lookup
values
λ
(A). We assume
the third
term in the specifications
does not
influence
choice
because
E
C
[E
O
[
π
O
(A)|
λ
]] cannot
vary with the unobserved
choice
of
λ
(A).
Denote
the lookup
function
λ
=
1 if C looked
up O
s payoffs
and
λ
=
0 if C did not.
4
Even
in the Baseline
treatment,
the fair-minded
type F always
looks
up (
λ
(A)
=
1) and chooses
A
F
iff 1
<
α
y. F types
will always
look
because
they need to know
if 1
<
α
y. Intuitively,
F is not looking
because
it affects
O
s judgments
in any way (and hence
F
s social
image
concern).
Instead,
F is looking
to find out if the payoff
y for player
O is sufficiently
high to trigger
preference
for A
F
.
The selfish
C type doesn
t look (
λ
=
1) because
that type does not take into account
O
s payoff
in the selfish
utility
when
social
image
doesn
t matter.
She compares
U
S
(A
S
)
=
1 and U
S
(A
F
)
=
0 and always
chooses
A
S
.
Step 3: Social
image:
Player
O observes
what the chooser
C looks up
The Chooser
s utilities
have
the following
values,
depending
on the S or F type and on whether
they look up or not Assume
that
1
<
α
y (otherwise
both F and S types
choose
A
S
)
F type
In the Social
Image
treatment
(as in Baseline
above),
the F types
always
look up because
they want
to know
if 1
<
α
y which
triggers
the choice
of A
F.
In this treatment
there
is an additional
motive
which
is utility
from social
image
(or guilt-avoidance,
see
Battigalli
and
2
The observer
O
s could
be altruistic,
for example,
and weight
C
s payoffs
positively.
But since
the O
s do not make
any choices,
there
is no
learning
based
on what
the O
s observe
or do (they
aren
t observed
by C in what
they choose
to observe
or do). This makes
it implausible
to consider
models
in which
players
want
to match
altruism
levels
(e.g.
Levine,
1998
).
3
Notationally,
[
π
O
(A)-E
C
[E
O
[
π
O
(A)|
λ
]]
0
=
[
π
O
(A)-E
C
[E
O
[
π
O
(A)|
λ
]]
<
0 if [
π
O
(A)-E
C
[E
O
[
π
O
(A)|
λ
]]
<
0 and [
π
O
(A)-E
C
[E
O
[
π
O
(A)|
λ
]]
0
=
0 if [
π
O
(A)-
E
C
[E
O
[
π
O
(A)|
λ
]]
>
0.
4
Empirically,
if C players
looked
at either
of the payoffs
U
O
(A
S
) or U
O
(A
F
) they also looked
at both so we treat
O-player
payoff
lookups
as one
variable.
S.W. Wang
and C.F. Camerer
Journal
of
Economic
Behavior
and
Organization
228
(2024)
106772
4
Dufwenberg,
2007
).
U
F
(A,
λ
)
=
1
+
γ
[0-E
F
[E
O
[
π
O
(A)|
λ
=
1]]
0
λ
=
1, choose
A
S
0
+
α
y
+
γ
[y-E
F
[E
O
[
π
O
(A)|
λ
=
1]]
0
λ
=
1, choose
A
F
Since
1
<
α
y, and the expectation
terms
above
are larger
for the choice
of A
F
than for the choice
of A
F,
the F type chooses
λ
=
1 and A
F.
Note
that in this case,
the F type behaves
in the same
way as in the Baseline
when
1
<
α
y (choosing
A
F
) but the F type
s utilities
are
different.
Psychobiological
measurements
of emotion,
attention,
or neural
activity
could
therefore
find differences
in underlying
sources
of utility
even though
the observed
A
F
choice
is the same.
S type
U
S
(A,
λ
)
=
1
+
γ
[0-E
S
[E
O
[
π
O
(A)|
λ
=
1]]
0
λ
=
1, choose
A
S
0
+
γ
[y-E
S
[E
O
[
π
O
(A)|
λ
=
1]]
0
λ
=
1, choose
A
F
Let
s unpack
the expression
U
S
(A,
λ
=
1)
=
1
+
γ
[0-E
S
[E
O
[
π
O
(A)|
λ
=
1]]
0
just to clearly
understand
the nature
of these
decision
util
-
ities.
This expression
describes
the utility
to a selfish
S type chooser
who looks
up payoffs
(
λ
=
1). The lookup
creates
an expectation
E
O
[
π
O
(A)|
λ
=
1] in the observer
about
their
earning
π
O
(A). The S type maintains
their
own iterated
expectation
E
S
[E
O
[
π
O
(A)|
λ
=
1]]
0
because
in equilibrium
type S
s expectation
about
O
s expectation
is correct
(that
is an imposed
assumption).
S
s second-order
expectation
creates
guilt
disutility
γ
[0-E
S
[E
O
[
π
O
(A)|
λ
=
1]
0
if they choose
A
S
so that the observer
O gets nothing
and is disap
-
pointed.
The guilt comes
from
S having
built up an expectation,
based
on lookups,
that the observer
O might
get y but only get 0.
The S type chooses
A
F
over A
S
iff
γ
y
>
1. Intuitively,
if avoiding
the
γ
-weighted
guilt of
leading
the observer
on
through
lookups
is
greater
than the gain of 1 from
the A
S
choice,
then the S type will choose
λ
=
1 and A
F
.
Willful
ignorance
(or plausible
deniability)
An interesting
and plausible
equilibrium
is one in which
the S type never
looks
up the observer
s payoffs
at all. Aspects
of this kind
of
willful
ignorance
(or plausible
deniability)
has been shown
experimentally
by
Dana
et al. (2006
,
2007
),
Lazear
et al. (2012)
and
extensively
in social
psychology
(
Vu et al., 2023
).
Remember
that all F types
look at all observer
payoffs
(
λ
=
1) because
they will choose
A
F
iff
y
>
1/
α
. They
look up (if costless)
because
they would
like to know
if this threshold
condition
is met. To compute
when
there
is willful
ignorance
of the observer
payoffs
among
the choosers,
we need to know
the overall
chance,
for the experimentally-designed
distribution
of y values,
that an observed
y
will lead the F type to choose
A
F
. Denote
this value
by y*
=
E
(y|
y
τ
)P(
y
τ
) where
τ
=
1/
α
. The second
term P(
y
τ
) is the probability
that the fair F type looks
up a y value
that makes
her choose
A
F
. The term E(y|
y
τ
) is the conditional
expectation
of the y values
that,
when
looked
up, lead the fair type to choose
A
F
.
Now
we
re back
to the S types.
If they don
t look up at all, they think
there
is a p chance
(the prior
probability
P(F))
that the
observers
expect
y*. The observers
unconditional
expectation
is therefore
E
O
[
π
O
(A)]
=
py*. Now if the S player
never
looks
up, and
always
chooses
selfishly,
the conditional
expectations
of the observer
is E
O
[
π
O
(A)|
λ
=
0]
=
0 and the iterated
expectation
is
E
S
[E
O
[
π
O
(A)|
λ
=
0]]
=
0.
In this willful
ignorance
scenario,
S gets 1
+
γ
0
=
1 from not looking
(
λ
=
0) and choosing
A
S
. If S does look up (but will always
choose
A
S
), then E
S
[E
O
[
π
O
(A)|
λ
=
1]]
0
=
py*. Then
S gets a guilt-adjusted
utility
of 1
+
γ
[0-py*]
which
is less than1.
If she plans
to choose
A
S
no
matter
what,
she prefers
not to look up at all; going
so just creates
an expectation
of possible
gain in O, which
creates
a little guilt in the
chooser
(the term -
γ
py*).
As is common
in signaling
games,
there
are other
equilibria.
In the next section,
we contrast
two of them
which
make
different
predictions
about
lookups
and choices.
Pooling
equilibrium
on
λ
=
1 and AF:
When
1
<
α
y, F type choosers
prefer
to choose
A
F
because
the altruism
weight
α
is sufficiently
large.
When
γ
y
>
1, there
is an equilibrium
in which
S types
choose
to look,
then choose
A
F
to avoid
guilt.
This combination
creates
a
pooling
equilibrium
in which
both
types
take the same
actions
looking
λ
=
1 and choosing
A
F
. Remember
that in the baseline
condition
the S types
always
choose
A
S
. Thus,
because
of this change,
the prediction
is that if the pooling
equilibrium
occurs
there
will
be more
overall
looking
and more
A
F
choice
in the Social
Image
treatment.
In this equilibrium,
both F and S chooser
types
look at the observer
payoffs
and choose
A
F
. When
1
<
α
y and 1
<
γ
y the pooling
equilibrium
exists.
This means
that the lower
of the two values
α
(fair players
altruism)
and
γ
(selfish
players
guilt)
determines
whether
this is an equilibrium.
Remark
.
In the willful
ignorance
never-look
separating
equilibrium,
S earns
the simple
payoff
of 1 and does not suffer
from guilt.
In
the pooling
equilibrium,
S earns
less, 0, because
otherwise
she would
earn A
S
from choosing
1-
γ
y
<
0, and
γ
>
1/y is a sufficiently
high
guilt parameter
to lead to an A
F
choice
and sustain
that pooling
equilibrium.
What
keeps
the pooling
equilibrium
together
is the off-
equilibrium
belief
(among
observers,
filtered
through
to choosers
given
assumed
rational
expectations)
that if a player
deviates
and
does not look (
λ
=
0), that player
is probably
a fair F type and the Observer
then expects
to get a payoff.
This perception
creates
guilt if
the deviating
S type chooses
λ
=
0, which
prevents
deviation.
Separating
equilibrium:
There
is also a separating
equilibrium
in which
the S and F types
do not
make
the same
λ
or A choices
that is,
the types
can be
ex post
separated
or Bayesian-distinguished
based
on observable
lookup
behavior.
This occurs
when
1
<
α
y (F types
S.W. Wang
and C.F. Camerer
Journal
of
Economic
Behavior
and
Organization
228
(2024)
106772
5
prefer
A
F
) but
γ
y
<
1, so that S types
choose
λ
=
0 and A
S
.
With
observation
(Social
Image):
O
does
know
λ
(A). The observer
updates
the belief
about
the chooser
s type if she observes
the
chooser
look up her observer
payoffs,
and depending
on what
is actually
chosen
after those
lookups.
The fair-minded
F type chooser
always
looks
up
λ
(A)
=
1 and chooses
A
F
. The selfish
S type chooser
chooses
λ
(A)
=
1 but chooses
A
S.
Anticipating
these
patterns
of lookup
and choice,
the observer
s expected
payoff
(given
the prior
P(F)
=
p
) is E
O
[
π
O
(A)|
λ
=
1]
=
py.
Rational
expectations
leads
to E
S
[E
O
[
π
O
(A)|
λ
=
1]
=
py. The S type chooser
compares
earning
1-
γ
E
S
[E
O
[
π
O
(A)|
λ
=
1]
=
1-
γ
py from looking
up and choosing
A
S
(feeling
py
units
of guilt),
and 0-
γ
E
S
[E
O
[
π
O
(A)|
λ
=
1]]
0
=
0. She separates
by choosing
A
S
iff 1-
γ
py
>
0, or equiv
-
alently,
γ
<
1/py.
Figs. 1 and 2
illustrate
some
of these
results
graphically.
(The willful
ignorance
result
is not shown
because
it is graphically
un
-
interesting.)
In
Fig. 1
, the x-axis
is O
s possible
payoff
π
O
(A
F
) which
is y. The y-axis
is the altruism
weight
α
which
the F type gives
to the
O payoff.
The hyperbola
α
y
=
1 divides
the parameter
space
into two: When
values
of y and
α
are low (to the lower
left of the thick
line),
both types
choose
A
S
. In this region,
O does not expect
any payoff
so there
is also no guilt for the choosers.
In the upper
right region,
when
γ
<
1/py the separating
equilibrium
can occur.
Both types
look up, F
s choose
A
F
and S
s choose
A
S
.
When
γ
<
1/py the pooling
equilibrium
can occur.
Both F and S types
look up payoffs
and choose
A
F
. The S types
are choosing
to avoid
guilt.
Fig. 2
illustrates
a simple
comparative
static
result.
If the prior
P(F)
=
p
and guilt weight
γ
fall in a combination
so that if 1/p
γ
increases,
the area of separating
equilibrium
is larger
so there
are fewer
λ
=
1 and A
F
choices
from the S type.
The reduction
in the prior
reduces
the observer
s expectation
E
O
[
π
O
(A)|
λ
=
1]
=
py, together
with the reduction
in
γ
, reduce
the S type
s weighted
guilt and create
fewer
A
F
choices.
The analysis
leads
to several
hypotheses
about
the possible
differences
between
observation
and choice
in the Baseline
and Social
Image
treatments:
1.
No effect:
One possibility
is that observability
makes
no difference
overall.
This is just a benchmark
null hypothesis.
2.
Willful
ignorance:
There
is an equilibrium,
as shown
above,
in which
the S type chooser
never
looks
up payoffs
and always
chooses
A
S
. In this equilibrium,
there
will be no difference
between
lookups
and choices
in the Baseline
and Social
Image
case.
The pre
-
diction
here is the same
as
no effect
but it emerges
from
equilibrium
reasoning.
3.
More
observation
and prosociality
in the Social
Image
condition:
The pooling
equilibrium
derived
above
is one mechanism
by
which
SI will increase
looking
and prosociality.
It depends
on the parametric
condition
γ
y
>
1. There
are other
intuitive
possibilities
which
fall outside
the analytic
framework.
Choosers
may simply
have a tastes
for non-instrumental
information
(curiosity)
about
the Observer
s payoff,
5
even if it does not produce
guilt or affect
their
choices
in other
ways.
4.
Lip service:
As noted
in the introduction,
it could
be that choosers
look at the observer
payoffs
because
they think
that merely
looking
generates
some
benefit
to themselves,
or to observers.
In the guilt-driven
model
above,
if payoffs
are observed,
but do not
affect
the chooser
s choice,
there
is a negative
utility
from
guilt.
Lip service
ignores
such utility.
Remark
.
Notice
that the no effect,
willful
ignorance,
and lip service
hypotheses
cannot
be distinguished
from
choices
alone.
However,
they have different
predictions
about
the chooser
s attention
to observer
payoffs.
Furthermore,
in the lip service
case it may
be that social
observers
derive
utility
from
knowing
that their
possible
outcomes
were
considered
(i.e., visually
attended
to by the
chooser),
and/or
that choosers
see the observers
utility
as enhancing
their social
image.
There
would
be no basis
for this conclusion
without
the visual
attention
data from
mousetracking
(
Table
1
).
4. Experimental
design
and procedures
We focus
on simple
binary
social
allocation
decisions
where
the decision-maker
often
faces
a tradeoff
between
her own payoff
and
the payoff
for others.
To study
the hypotheses
about
the impact
of an affected
observer
on the decision-maker
s attention
and choice,
we run a Social
Image
treatment
where
an observer
can see exactly
what
the decision-maker
pays attention
to before
her choice,
but
not the actual
choice.
In the baseline
condition,
there
are no observers.
The Deniability
hypothesis
predicts
less attention
to the ob
-
server
s payoffs
while
the Lip service
and Social
image
influence
hypotheses
predict
more
attention.
Not showing
the observer
the
decision-maker
s actual
choice
allows
us to distinguish
between
the Lip service
hypothesis
which
predicts
that decision-maker
will not
make
more
pro-social
choices
(because
they can signal
through
attention
alone)
and the Social
image
influence
hypothesis
which
predicts
that they will.
There
were
three
types
of allocation
games,
each offering
a choice
between
two possible
allocations.
(The full set of allocations
is
shown
in the Appendix).
We use allocation
games
from
Charness
and Rabin
(2002)
and
Engelmann
and Strobel
(2004)
as well as some
variants
of those
games.
In the first type,
S2O, the decision-maker
(DM)
decides
between
two allocations
to herself
and two other
people.
For example,
the
DM chooses
between
one allocation
where
all three
receive
575 and another
allocation
where
the DM receives
675 while
the other
two
receives
800 and 200. In the second
type,
S1O, the DM chooses
between
two allocations
to herself
and one other
person.
For example,
the DM chooses
between
one allocation
where
she receives
600 and the other
receives
300 and another
allocation
where
she receives
5
See
Eliaz
and Schotter
(2007
,
2010
),
Kang
et al. (2009)
,
Alan and Mumcu
(2024)
.
S.W. Wang
and C.F. Camerer
Journal
of
Economic
Behavior
and
Organization
228
(2024)
106772
6
500 and the other
receives
700. Finally,
in the third
type,
2O, the DM chooses
an allocation
for two others
only;
the choice
does not
affect
DM
s payoff.
For example,
the DM chooses
between
allocating
400 to both or 375 to one and 750 to the other.
In the first two baseline
sessions,
there
were
80 and 84 trials
respectively.
In the first 40 trials,
we alternated
between
blocks
of 10
Fig. 1.
Graphical
depiction
of choices
and lookups
and selected
equilibrium.
Choices
of fair and selfish
types
are C(F),C(S).
Lookups
are
λ
=
1 (hats
denote
observed
lookups
of Observer
payoffs).
Note:
A similar
graph
could
be constructed
to show
a willful
ignorance
separating
equilibrium
in
which
F types
choose
λ
=
1 and A
F
(
α
y
>
1) or A
S
(
α
y
<
1), and S types
always
choose
λ
=
0 and A
S
.
Fig. 2.
The effect
of reducing
the prior
p(F)
=
p
and guilt
γ
. Reducing
those
values
to p
1
,
γ
1
shifts
the (thicker)
vertical
line
y
=
1/p
1
γ
1
to the right.
This leads
to a larger
parametric
range
in which
is a larger
region
of the separating
equilibrium,
which
implies
fewer
choices
(by S types)
of A
F
.
Table 1
Summary
of theory
predictions
about
choices
and visual
durations
of payoff
looking.
The experimental
conditions
are
baseline
(B) and social
image
(SI), in which
the Observers
can see which
payoffs
Choosers
are looking
at.
Prediction
Hypotheses
Prosocial
choices
Visual
looking
durations
No effect
B
¼
SI
B
¼
SI
Social
image
influence
B
<
SI
B
<
SI
Willful
Ignorance
B
¼
SI
B
¼
SI
Lip service
B
¼
SI
B
<
SI
S.W. Wang
and C.F. Camerer
Journal
of
Economic
Behavior
and
Organization
228
(2024)
106772
7