MOOD AND ECONOMIC DECISION MAKING: EXPERIMENTAL EVIDENCE
JUDD B. KESSLER
ANDREW MCCLELLAN
ANDREW SCHOTTER
September 6, 2015
ABSTRACT
In this paper we investigate the impact of short-term fluctuations in happiness (i.e. a
positive mood) on decision-making. The emotional fluctuations we analyze are
orthogonal to the fundamentals of the decision maker’s wellbeing and standard theory
suggests they should have no effect. We perform an experiment in a sports bar on the
Upper East Side of Manhattan while subjects watch an NFL football game. During
numerous commercial breaks, we monitor subjects’ happiness and ask them to perform a
set of standard experimental tasks involving charitable giving, risk taking, trust, and
willingness to pay. We find that the events of the game not only affect the mood of our
subjects but that these changes in mood lead to predictable changes in decisions. Our
experiment introduces a new method for inducing a dynamic mood sequence and
provides a model that can explain why changes in short-term emotions influence
economic decisions.
I. Introduction
Every day we face myriad opportunities to buy things, be generous, take risks,
and trust others. Between making these decisions, we face the outcomes of numerous
unrelated events: whether it is a sunny, whether the barista making our coffee is friendly,
whether the episode of TV that we are watching has an entertaining ending, or whether
our favorite sports team wins a game. While these events no doubt make us happy for a
short while, we know that they are orthogonal to the fundamentals of our wellbeing and
should not affect our decisions. Indeed, if such emotions were to systematically affect the
choices we make, we might want to be conscious of this relationship to avoid taking
actions we would later regret. Those who might potentially profit from our behavior
would also want to understand the relationship between our emotions and our choices.
Despite a rich literature in Psychology, Neuroscience,1 and Economics showing
that emotions affect decisions including: trust and trustworthiness (see, e.g., Capra
[2004]; Dunn and Schweitzer [2005]; Kirchsteiger, Rigotti, and Rustichini [2006]; Myers
and Tingley [2011]); risk (see, e.g., Johnson and Tversky [1983]; Nygren et al. [1996];
Lerner and Keltner [2000], [2001]; Loewenstein, Weber, Hsee, and Welch [2001]);
willingness to pay (see, e.g., Lerner, Small, and Loewenstein [2004]); and helping
behavior (see, e.g., Aderman [1972]; Isen and Levin [1973]; Rosenhan, Underwood and
Moore [1974]; Konow and Earley [2008]), and despite the urging of prominent
researchers to integrate emotions into economic models of decision-making (see, e.g., Jon
1
For the Neuroscience literature, see, e.g., LeDoux (1996), Lempert and Phelps (2013), and
Bechara et al. (1997).
Elster [1998] and George Loewenstein [2000]), Economics has generally ignored the role
of emotions on behavior.2
To the extent that Economic theory has considered emotions, it has tended to do
so in the framework of Psychological Game Theory — making specific emotions, like
guilt, a byproduct of beliefs or unfilled expectations (see, e.g., Charness and Dufwenberg
[2006], Battigalli and Dufwenberg [2007]; see Caplin and Leahy [2001] for a treatment
where the goods people contemplate have an emotional component). Other, more applied
papers introduce emotions into the calculus of decision making but do not provide an
associated model to explain this (see, e.g., Loewenstein and Ariely [2005] on willingness
to engage in risky sexual activity in response to sexual arousal; Edmans, Garcia, and
Norli [2007] on stock markets dips in response to a country’s elimination from the world
cup; Card and Dahl [2011] on spikes in domestic violence when a city’s football team
suffers a surprise loss).3
In this paper, we introduce a new experimental paradigm for investigating the
impact of fluctuations in one important emotion, happiness (i.e. a positive mood), on
behavior. Our design allows us to leverage naturally occurring short-term variations in
2
There is, of course, a now well established literature on the relationship between happiness and
utility (see, e.g., Kahneman et al. [2004]; Frey, Luechinger, and Stutzer [2008]; and the paper by
Kimball and Willis [2006], which presents a model describing the relationship between these two
concepts.). There is also a rich literature that looks at happiness as an outcome measure following
Bentham (1789). Much of this research focuses on how subjective well-being has changed over
time (see, e.g., Stevenson and Wolfers [2008] and Sacks, Stevenson, and Wolfers [2010], [2012]).
More recent work has found that individuals do not choose the things that maximize suggestive
well-being, identifying systematic wedges between suggestive-well being and utility (see, e.g.,
Benjamin et al. [2012], [2014]), and identifying an alternative way of measuring subjective wellbeing that could serve as a better proxy for utility (see, e.g., Benjamin et al. [2014]). While we
differ from this important research — we treat happiness as an input into the utility function
rather than a measure of its level — our findings complement the work by revealing another
rationale for measuring happiness, namely it can have a direct effect on economic decisionmaking.
3
While Card and Dahl (2011) do provide some theoretical structure in their paper, their model
tailored to fit the situation they are trying to describe.
happiness from exogenous events — orthogonal to the fundamentals of well being —
while holding all other aspects of the subjects’ lives constant.4 In particular, we leverage
the short-term fluctuations in happiness induced when subjects watch an NFL football
game. During commercial breaks of the game they are watching, we repeatedly measure
each subject’s mood and present the subject with a set of decision tasks.5
As will be described in detail in the following sections, watching the game
generated variation in self-reported happiness for the vast majority (81%) of subjects.
Swings in happiness were not random; events in the game lead to predicable responses in
happiness.6 For example, we observe a significant increase in happiness when a subject’s
favored team scores a touchdown, an even larger decrease in happiness when the
opposing team does so, a smaller increase when a favored team kicks a field goal and no
significant effect on happiness when the opposing team kicks a field goal.7
We find that changes in happiness affect the behavior of our subjects in each of
the four tasks presented to them: willingness to pay for consumer goods, risk taking,
willingness to donate money, and trust or trustworthiness. In addition, we find that all
effects are in the “same direction,” such that people are more willing to give up money
4
This method ensures we avoid changes in happiness that might come from more substantial
changes in economic or other conditions (e.g. performance at work, stock market returns, new
romantic relationships) that might have direct effects on economic decisions unrelated to mood.
5
In particular, to measure mood we ask: “How do you feel right now?” on a 7-point Likert scale
with answers ranging from: (1) “very unhappy” to (7) “very happy”. As will be described in the
experimental design section, we also ask subjects other questions about the game as controls to
ensure the changes in behavior we see result from changes in happiness (rather than from changes
in these other things about the game).
6
We log events of each game, which allows us to investigate how events that took place since
last subject data entry (e.g., whether there was a touchdown, field goal, etc.) affect subject
happiness.
7
This substantial variation in happiness arises despite the fact that subjects were not watching
games that involved their local team (subjects came from a New York City subject pool and
neither the New York Jets nor the New York Giants played in either of the games subjects
watched). Our results would presumably be stronger if subjects were more engaged in the game.
(including paying more for a consumer good, giving more to charity, and being
trustworthy) and take risks (including buying a lottery and trusting others) when they are
relatively happier. We present a simple model of decision-making under the influence of
emotions that puts mood into the utility function and can rationalize all our results about
how happiness affects decision with a very simple assumption that can be interpreted
simply as: being happy makes you feel richer.8
Our experimental design differs significantly from designs used by others. In a
typical experiment investigating the relationship of emotions to decision making, the
experimenter induces one or two emotions (e.g. happiness and sadness) at one point in
time by either: (a) showing a subject a happy or sad movie clip (see, e.g., Kirchsteiger,
Rigotti, and Rustichini [2006]; Zarghamee and Ifcher [2011]) or (b) having them
recollect in writing a sad or happy event in their life using the Autobiographical
Emotional Memory Task (see, e.g., Strack, Schwarz, and Gschneidinger [1985]; Myers
and Tingely [2011]). After subjects are primed with these emotions, they engage in a
decision task and the behavior of those primed with different emotions is compared.
Our design differs from these previous studies in several important ways. First,
we do not induce emotions per se but rather ask our subjects to watch a sporting event in
a natural setting and allow the events of the game to alter their emotional state. Second,
and perhaps more importantly, our design is dynamic in the sense that we do not induce
an emotion at one point in time and then measure the impact of that primed emotion on
behavior. Rather, we allow our subjects to take an emotional journey over a three-hour
8
Formally, the key assumption is that the cross partial of utility with respect to wealth and
happiness is negative, that is the marginal utility of money is lower when someone is happier.
This is equivalent to happiness making individuals feel richer. Some results additionally require
an additional assumption on the form of the marginal utility with respect to mood.
timespan — of the kind they might experience during many naturally occurring events of
their life — and track how changing emotions affect their decision behavior. 9 Since
during the game the fundamentals of a subject’s wellbeing are not changing, we can
impute the changes in their decisions to the impact of the game on their happiness.10
This paper proceeds as follows. In Section II we present our experimental design.
In Section III we present our results. Since our results indicate that emotions have a
predictable impact on decision-making, in Section IV we offer a model of decision
making under the influence of emotions that puts mood into the utility function and can
rationalize our results. In Section V we offer some conclusions.
II. Experimental Design
The experiment involved two experimental sessions at two sports bars in the
Upper East Side neighborhood of New York City. Subjects were recruited from an NBC
Sports subject pool consisting of people who had volunteered in the past to take part in
focus groups.11 Recruitment information informed potential subjects that in the study they
would watch an NFL game in a sports bar, be given $15 to subsidize their food
consumption, be guaranteed $30 for showing up, and have the chance of earning more
money during the experiment depending on the decisions they made.
9
Put another way, our experiment generates a time series of self-reported happiness and
associated decisions rather than a response to an emotion at a signal point in time.
10
We are not the only researchers to recognize that sports can be a useful way to vary emotions of
sports fans. A paper by Lambsdorff, Giamattei, Werner, and Schubert (2015) uses soccer as an
emotional prime. However, their set up is quite different from ours on a number of
dimensions, the most prominent difference is that subjects only make one decision and do so
before the game begins.
11
The project was funded by NBC Sports as part of a larger program investigating the impact of
sports viewing on decision-making.
Since subjects were invited to a sports bar they had to be at least 21 years old to
participate in the study. Consequently, our subjects are demographically distinct from the
university undergraduates traditionally used in laboratory experiments. In addition to
being older, our sample is almost all working rather than in school (49 out of 64 subjects
reported having full-time employment while only 1 out of 64 was a student) and our
sample has relatively high earnings (48 out of 64 subjects reported earning $50,000 or
more). The average age of subjects was 41 years old and 51 of 64 had completed at least
a Bachelor’s degree with 30% having an advanced degree. Table 1 reports the
demographics of our subject population.
Table 1: Subject Demographics
Demographics
Mean (SD)
Number of Subjects
64
Female
38%
Age
41.0(12.1)
Education
PhD
2%
Masters Degree
28%
Bachelors Degree
50%
Some College
19%
High School
2%
Employment
Full time employed
77%
Part time employed
17%
Student
2%
Unemployed
5%
Income
Income over $100,000
33%
Income $50,000 to $99,999
42%
Income $25,000 to $49,999
19%
Income less than $25,000
6%
Notes: Table 1 reports the percentage of the subjects
who reported being in each demographic category.
Means (with standard deviations in parentheses) are
reported for continuous variables.
Subjects arrived one hour before the game started and were instructed about the
content of the experiment. It was explained that they would engage in four incentivized
decision-making tasks and answer four un-incentivized questions at the start of the game
and at a number of commercial breaks during the broadcast. On average, subjects entered
data (i.e., made decisions and answered questions) 15 times over the course of the study.
Subjects were told that at the end of the experiment, the computer would randomly pick
one of the decision tasks and one of the entry times and their decision in that task and
entry time would determine payoffs.
II.A. Demographic Questionnaire
Before the game, we recorded demographic information about our subjects by
asking them their work status, education, gender, age, and income, the results of which
are reported in Table 1. In addition, they were asked their feelings about watching sports,
football, and the particular game they were about to watch (see the full list of questions in
Appendix A). The subjects were also asked to choose among a set of charities to which
they might donate and a set of consumer goods that they might buy during the experiment
(as will be described in the following subsections).
II.B. Four Decision Tasks and Emotion Question
In the following subsections we describe the four decision tasks that subjects
faced as well as the un-incentivized questions we had them answer. Each time subjects
provided data in the experiment, these tasks and questions were displayed in the order
described below.
II.B.1 Charitable Giving
In the charitable giving task, subjects were told they had the opportunity to donate
money to a charity. At the start of the experiment, they were asked to choose a favorite
charity from a set of three: (a) United Way, (b) American Cancer Society, and (c) World
Wildlife Fund. Each time subjects entered data, they were asked how much of a $40
endowment they wanted to donate to the charity they had chosen at the start of the
experiment (see Instructions in Appendix B). If this task was chosen for payment at the
end of the experiment, any money not donated was given to the subject. Subjects were
explicitly told that any money donated would actually be given to the charity they
selected.12
II.B.2 Willingness to Pay for Consumer Good
In the willingness to pay task, subjects had a $40 endowment that they could use
to buy a consumer good. At the start of the experiment, subjects had the option to choose
a good from a set of three options: (a) a wool hat (they could choose between a men’s or
women’s hat), (b) Sony headphones, or (c) a “Chromecast”, Google hardware for
streaming video. Each of these goods had a retail price of $30 to $40. Each time subjects
entered data, they were asked how much out of their $40 endowment for this task they
were willing to pay for the good they had selected. We used the Becker-DeGrootSubjects were told verbally: “You can be 100% confident that the money will be donated.”
Donations were made after both sessions of the study were run.
12
Marschak mechanism (BDM) to elicit their willingness to pay. The mechanism was
explained to subjects and they were explicitly told it was in their best interest to report the
highest amount of money they would be willing to pay for the good but not more (see
Instructions in Appendix B). If this task was chosen to be payoff-relevant for a subject,
the BDM mechanism was employed. A price was randomly selected and the subject
either kept the $40 endowment (if the randomly determined price was above the stated
willingness to pay) or bought the good at the randomly selected price (if the price was
below the stated willingness to pay).
II.B.3 Willingness to Pay for a Risky Gamble
This decision task was nearly identical to the consumer good task except that
subjects were asked about willingness to pay for a lottery ticket that offered a 50%
chance of receiving $40 and a 50% chance of receiving $0. Again, each time subjects
entered data, they were asked how much out of their $40 endowment for this task they
were willing to pay for the good using the BDM mechanism (see Instructions in
Appendix B). If the subject ended up buying the lottery ticked at the BDM determined
price, that price was subtracted from their $40 endowment and the risky lottery was
realized (they either received an extra $40 or $0). If they did not buy the lottery ticket,
they kept their $40 endowment.
II.B.4 Trust Game
The final task was a discretized trust game. In this game, each subject interacted
anonymously with another subject in the session. Subjects were randomly assigned to be
either a sender (“Player A” in the instructions) or a receiver (“Player B” in the
instructions). Subjects were told that the sender started with $32 and the receiver started
with $0. The sender could choose to send $0, $8, $16, $24, or $32 of his $32 to the
receiver. The receiver would get three times the amount of money transferred by the
sender and have the opportunity to transfer money back — from $0 up to the total amount
received from the sender’s transfer. This money was returned one-for-one to the sender
without being multiplied.
Each sender was asked to choose one amount ($0, $8, $16, $24, or $32) to send to
the receiver. Each receiver was asked to choose one amount to return for each of the
possible amounts they might get from the sender using the strategy method. In particular,
all receivers were asked how much they wanted to return to the sender if they got $24, if
they got $48, if they got $72, and if they got $96 (see Instructions in Appendix B). No
feedback was given during the experiment, but subjects were told that if this decision
problem was chosen for cash payment, the game would be played out and payoffs
determined accordingly.
II.B.5 Questionnaire
After subjects engaged in each of the four decision tasks, they made self-reports
about their current emotional state and their reaction to the recent events in the game.
Subjects were asked to report (on a scale from 1 to 7) answers to the following four
questions, in the following order:
1. How surprised are you about the recent events in the game, i.e. events since the
last commercial break entry? (7-point Likert scale where 1 is “not at all,” 3 is
“somewhat,” 5 is “a lot,” and 7 is “incredibly.”).
2. How exciting do you find the game you are watching? (7-point Likert scale
where 1 is “not at all,” 3 is “somewhat,” 5 is “a lot,” and 7 is “incredibly.”).
3. How do you feel right now? (7-point Likert scale where 1 is “very unhappy,” 2
is “unhappy,” 3 is “somewhat unhappy,” 4 is “neither happy nor unhappy,” 5 is
“somewhat happy,” 6 is “happy,” and 7 is “very happy.”).
4. What do you think the chances are that the team you said you were rooting for
will win? (Scale from 0 to 100 where 0 is “definitely won’t win” and 100 is “definitely
will win.”)
We were primarily interested in how being in a good mood would affect the
decision tasks noted above and so we were most concerned with the answer to question 3
about happiness. However, we wanted to make sure we could control for other features of
the game that might affect choices in the decision tasks — and might be correlated with
self-reported happiness — but not work through an effect on mood. To address this issue,
we asked about excitement and surprise, which we thought might be affected by events in
the game and could potentially serve as controls for other things about the game that
might influence decisions without working through an effect on happiness.
II.C. Comments on our experimental design
A few things about our experimental design are worth noting. First, doing
experiments in sports bars is not common. In a field setting like a sports bar, you may not
be able to maintain the same control over the environment that you typically have in the
lab.13 One particularly important element of the lack of control in a sports bar is alcohol.
Subjects in our experiment were each given a voucher worth $15 for food but had to buy
their own drinks if they wished. While some subjects did drink, our observation was that
alcohol consumption was relatively light (e.g. no one became obviously intoxicated
during the study). While alcohol consumption has been known to influence choice (see
Burghart, Glimcher, and Lazzaro [2013] on how alcohol affects the ability to satisfy
GARP), we had no indication that it was a major factor in the behavior of subjects and, as
will be discussed below, in all our results we control for how many entries the subject has
made, suggesting that an increase in alcohol consumption over the course of the evening
is not driving results.
Second, since subjects were recruited from a pool maintained by NBC Sports, the
experiment did not select a random sample of the population but was skewed toward
sports fans. This feature of the design serves our purpose well as we are interested in
using the random variation of events in the games to generate swings in mood, and this is
more likely to be successful with sports fans. This also heightens the realism of our
paradigm since people who dislike sports are unlikely to watch sports on a regular basis.
13
In Session 1, we ran our experiment on a floor of the sports bar designated for our study. In
Session 2, conducted in a different sports bar, we had the entire back end of the bar, which was
isolated from the rest of the bar. While in both sessions we ensured that all screens subjects could
see were showing our game, other patrons cheering for other games in other parts of the bars
could have theoretically distracted subjects. In addition, subjects completed the experiment on
web-based software (written specifically for this experiment) that was accessible on tablets that
could be used from anywhere in the bar. This had the advantage of allowing subjects to sit
wherever they wanted in our designated sections and watch the football game as they would have
otherwise; however, we did not force subjects to stay seated, so they could leave the bar to smoke
or to go to the bathroom and thus miss an opportunity to enter data.
Third, while subjects were incentivized in the decision tasks they performed, they
were not incentivized for their responses to our questionnaire about emotions or beliefs.
We know of no scheme that truthfully elicits people’s emotions, and self-reports of
emotions have been successfully used in Economics (see, e.g., van Winden [2007]) and
in Psychology (e.g. the many papers cited above).14
Fourth, as stated above, our design uses a naturally occurring event, an NFL
football game, to induce a dynamic path of emotions rather than inducing one static
emotion at one point in time. This introduces realism into the experiment insofar as it
generates the kind of common swings in emotions people experience on a day-to-day
basis and it allows us to view the same person as the mood fluctuates reported as it is
likely to do outside the lab.
III. Results
On average, subjects enter data — that is, complete the four decision tasks and
report their mood — 14.77 times during the study.15 Importantly for our study, the vast
majority of subjects display variation in their emotional state over the course of the game.
Table 2 reports the percentage of subjects who change their emotional state and change
their decision task choices at least once during the course of the game.
14
Of course, one could try to measure subjects' emotional states using some type of physical
measurement like fMRI or skin conductance, but it is not clear to us that those measures are
reliable enough and such tests are obviously hard to administer in a sports bar.
15
The minimum number of entries was 10 and the maximum was 18. Not every subject
completed entered data every time it was requested. Subjects may have been otherwise occupied
(e.g. eating or in the restroom) when asked to enter data. In addition, subjects were technically
able to enter data at times other than when we asked them to do so. Nevertheless 55% of subjects
submitted exactly 15 reports, and 89% of subjects submitted either 14, 15, or 16 reports.
A total of 52 of the 64 subjects (81%) changed their answer to the happiness
question: “How do you feel right now?” at least once in the study. It is reassuring to see
this variation in reported mood, since such variation is necessary for us to evaluate how
emotional changes affect economic decision-making. In addition, as we will show below,
this variation in emotions is not random. Instead, it predictably responds to the events of
the game. Events that constitute good news for a subject’s preferred team on average
make that subject happier. Consequently, when we investigate how changes in reported
emotions correlate with changes in economic decisions, we can be confident that we are
leveraging variations in emotions induced by exogenous events in the game.
We also observe variation in the economic decisions subjects made over the
course of the game. In particular, 30 of the 64 subjects (47%) change the amount they
choose to donate; 36 of the 64 subjects (56%) change the maximum amount they are
willing to pay for a good they selected at the start of the experiment, and the same
number, 36 of the 64 subjects (56%), change the maximum amount they are willing to
pay for a lottery ticket that pays out $40 with 50% probability. In total, 89% of subjects
display variation in at least one decision task. That there is variation in these economic
decisions allows us to investigate the cause of this variation and whether changes in
happiness correlate with these changes in behavior.
Table 2: Variation in Questions and Decisions
% of subjects who
Question or Decision
show variation
Happiness
81%
Surprise
95%
Excitation
95%
Donation to charity
47%
Willingness to pay for good
56%
Willingness to pay for gamble
56%
Transfer to trustee (out of 32 subjects)
50%
Return/transfer by trustee to any (out of 32 subjects)
78%
Return/transfer by trustee to 24 (out of 32 subjects)
44%
Return/transfer by trustee to 48 (out of 32 subjects)
44%
Return/transfer by trustee to 72 (out of 32 subjects)
63%
Return/transfer by trustee to 96 (out of 32 subjects)
72%
Variation in at least one decision task
89%
III.A. What determines mood?
In this subsection, we investigate the mood that subjects report and show that it
responds predictably to events in the game. At the start of each session, we asked subjects
which of the two teams playing in the game they favored. 29 out of the 30 subjects
watching the December 29, 2013 game between the Philadelphia Eagles and the Dallas
Cowboys reported that they favored either the Eagles or the Cowboys, and 32 out of the
34 subjects watching the January 4, 2014 game between the Philadelphia Eagles and the
New Orleans Saints reported that they favored either the Eagles or the Saints.16
For these 61 subjects, we can code scores in the game — i.e. touchdowns and
field goals — as either being a touchdown for their favored team, a touchdown for their
disfavored team, a field goal for their favored team, or a field goal for their disfavored
16
Subjects could refuse to answer the question by selecting a team that was not playing that day
to be their favored team for that game. In the December 29, 2013 game between the Philadelphia
Eagles and the Dallas Cowboys, 17 subjects favored the Eagles and 12 subjects favored the
Cowboys. In the January 4, 2014 game between the Philadelphia Eagles and the New Orleans
Saints, 13 subjects favored the Eagles and 19 favored the Saints.
team.17 We asked subjects to report their emotions in the commercial break that followed
each score, so we can compare how responses to the emotions questions change over the
course of game, comparing how emotions respond when no score occurs to when subjects
experience one of the four outcomes listed above. Note that when a score occurs, it will
be coded as a score for the favored team for some subjects and a score for the disfavored
team for other subjects, depending on which team they prefer. In the results that follow,
we restrict the effect of the score for a favored team to be the same, regardless of the
team the subject favors.
Table 3 reports regression results displaying how happiness changes as a result of
scores in the game. Looking at regression (1), we see that subjects asked how they feel
immediately following a favored team scoring a touchdown report being happier than
they are on average throughout the game. The same pattern arises for a favored team field
goal, although the coefficients are smaller in magnitude, suggesting a directionally
smaller effect of a field goal on mood. The effect of a disfavored team touchdown leads
to a decrease in happiness and there is no significant effect associated with a disfavored
team field goal.
Regression (2) additionally controls for a subject’s self-reported probability that
their favored team will win the game, elicited at the same time as the happiness measure.
Comparing regressions (1) and (2) we see that controlling for the probability that the
favored team wins the game shrinks the magnitude of the coefficients associated with the
scores, suggesting that at least some of the effect on happiness associated with the scores
is driven by scores leading to a change in their subjective probability that the favored
17
No safeties were scored in either of the games in our experiment. In addition, in this analysis
we ignore points scored post touchdown. Since fumbles and interceptions were very rare events
in the games our subjects watched, our results on them are inconclusive.
team will win the game which also affects happiness. Nevertheless, an effect of the scores
on happiness persists even excluding the effect that works through the change in belief
that the favored team will win.18
Table 3: How Mood Responds to Events in the Game
Self-Reported Happiness (0-6)
(1)
(2)
Favored Team TD
0.34
0.25
(0.081)***
(0.074)***
Favored Team FG
0.26
0.14
(0.081)***
(0.077)*
Disfavored Team TD
-0.33
-0.24
(0.12)**
(0.11)**
Disfavored Team FG
-0.027
0.067
(0.10)
(0.091)
Prob. favored wins (0-100)
0.017
(0.0035)***
Constant
3.92
2.79
(0.027)***
(0.22)***
Subjects
61
61
Obs.
912
912
R-Squared
0.667
0.698
Notes: Table 3 shows the effect of scores in the game on selfreported happiness elicited in a Likert-scale measured on a 0 to
6 scale. The regressions control for average happiness of each
subject and cluster the coefficients by subject. Significance
denoted as * p < 0.1, ** p < 0.05, *** p < 0.01.
The same scores that generate fluctuations in subject happiness also increase selfreported excitement and surprise (see Table A1 in the Appendix).19 This suggests that to
isolate the effect of happiness on economic decisions may require controlling for surprise
and excitement that are correlated with happiness (see Table A2 in the Appendix).
18
As might be expected, subjects with an above median interest in sports in general and in
football in particular had directionally bigger swings in emotion resulting from scores.
19
As might be expected, the relationship between scores and excitement and surprise do not
appear to be mitigated by controlling for the probability the favored team will win the game.
In total, the pattern of results suggests that happiness responds predictably to
events in the game, suggesting that the observed emotional swings are not random but
rather result from subjects’ experiences watching the game. We now turn to investigating
how such swings in happiness affect decision-making.
III.B. How mood affects decision making
Subjects’ self-reported happiness strongly predicts observed variation in subjects’
choices in the experiment. Tables 4 and 5 show results for the economic decisions for all
subjects during the experiment. Regressions include subject fixed effects and control for
the number of times the subject had previously entered data. The even numbered
regressions additionally control for self-reported excitement and self-reported surprise,
which are correlated with happiness and might have independent effects on the economic
decisions. Including these additional controls does not affect the relationship between
happiness and the decisions.
Table 4 reports on each of the decision tasks independently. Charitable giving,
willingness to pay for the consumer good, willingness to pay for the lottery (a measure of
risk aversion), and transfer in the trust game all statistically significantly increase (at
p<0.1 or p<0.05) with happiness. The charitable donation, willingness to pay for the
good, and willingness to pay for the lottery each increase by between $0.46 and $0.56 per
point of happiness on the 7-point scale, with only slight variation across task and
specification. The amount transferred by senders in the trust game increases by about $1
out of a potential $32 for each point of happiness on the 7-point scale. Percent of transfer
returned is the percentage of the amount that a receiver gets from the sender that is
returned. This amount also directionally increases with happiness, but the relationship is
not statistically significant.
Since all the response in Table 4 are in the “same direction”, Table 5 collapses
data across all economic decisions. Regressions (1) and (2) combine the three decision
tasks in which subjects choose a gift or willingness to pay out of a $40 endowment. On
average, a one-point increase on the happiness scale increases the amount given or the
willingness to pay by just over $0.50. Regressions (3) and (4) combine all choices in the
experiment — including the trust game choices — by representing each decision as a
percentage of the action space the subject is willing to give, pay, transfer, or return (i.e.
the percentage of the $40 endowment in the first three games, the percentage of the $32
for the senders, and the percentage of the amount the receiver gets for the receivers). This
percent of action space increases by 1.31 to 1.39 percentage points per point on the
happiness Likert-scale.
Table 4: How Each Choice Responds to Emotional State
Happiness (0-6)
Constant
Charity
WTP for Good
WTP for Lottery
Transfer
Percent of Transfer
($ out of 40)
($ out of 40)
($ out of 40)
(0, 8, 16, 24, or 32)
Returned
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
0.55
0.46
0.48
0.56
0.53
0.51
1.12
0.81
1.24
1.06
(0.28)*
(0.27)*
(0.21)** (0.21)*** (0.29)*
(0.27)*
(0.50)** (0.35)**
(0.94)
(0.87)
15.7
15.3
18.1
18.5
15.6
15.4
15.7
14.8
29.9
25.8
(1.08)*** (1.65)*** (0.78)*** (1.21)*** (1.71)*** (2.19)*** (2.43)*** (2.54)*** (5.22)*** (7.12)***
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Time Controls
Additional
Controls
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Subjects
64
64
64
64
64
64
32
32
32
32
Observations
949
949
949
949
949
949
463
463
1,872
1,872
R-squared
0.938
0.940
0.945
0.946
0.873
0.878
0.886
0.893
0.749
0.755
Notes: Table 4 shows regressions of the incentive-compatible economic decisions of how much to donate to a charity (chosen by the
subject at the start of the experiment, either: the United Way, the American Cancer Society, or the World Wildlife Fund); willingness
to pay (WTP) for a good (chosen by the subject at the start of the experiment, either: a wool hat, a pair of headphones, or a video
streaming device); willingness to pay (WTP) for a lottery that is a 50% chance of winning $40; how much to transfer in a trust game;
and how much to transfer back out of what was sent on self-reported happiness. Time Controls include non-parametric controls for
how many commercial break entries the subject has made interacted with session. Additional Controls are non-parametric controls for
self-reported measures of excitement and surprise interacted with session. Happiness, excitement and surprise were each elicited with
a Likert-scale on a 0 to 6 scale. The regressions control for the average of the dependent variable of each subject and cluster the
coefficients by subject. Significance denoted as * p < 0.1, ** p < 0.05, *** p < 0.01.
Table 5: How Choices Respond to Emotional State
All excluding trust game
All choices
($ out of 40)
(% of action space)
(1)
(2)
(3)
(4)
Happiness (0-6)
0.52
0.51
1.39
1.31
(0.19)***
(0.17)***
(0.59)**
(0.55)**
Constant
16.5
16.4
38.6
36.2
(0.85)***
(1.23)***
(2.98)***
(4.27)***
Time Controls
Yes
Yes
Yes
Yes
Additional Controls
No
Yes
No
Yes
Subjects
64
64
64
64
Observations
2,847
2,847
5,182
5,182
R-squared
0.489
0.490
0.413
0.415
Notes: Table 5 shows regressions of the incentive-compatible economic decisions in the
experiment. Time Controls include non-parametric controls for how many commercial
break entries the subject has made interacted with session. Additional Controls are nonparametric controls for self-reported measures of excitement and surprise interacted with
session. Happiness, excitement and surprise were each elicited with a Likert-scale on a 0
to 6 scale. The regressions control for the average of the dependent variable of each
subject and cluster the coefficients by subject. Significance denoted as * p < 0.1, ** p <
0.05, *** p < 0.01.
Our results are surprising. It is curious that people’s moods are so malleable that
they can change repeatedly over a period of a few hours merely by watching a football
game. What’s more puzzling, however, is that such changes in mood brought upon by
objectively frivolous events are capable of altering the economic decisions that
individuals make. These results have a variety of important implications.
First, our results offer insights into the $518 billion a year advertising market
(Zenith Optimedia [2014]). Advertisers who pay for television airtime should be aware of
the relationship between events in a broadcast and their impact on mood and decisions,
since the relationship might suggest a more sophisticated advertising policy that
conditions advertisements based on the expected mood of viewers. For example, in the
context of football games, if a touchdown makes fans rooting for the scoring team
happier, and thus, for example, temporarily more risk seeking, advertisements for the
state lottery or a Las Vegas vacation may be relatively more effective. On the other hand,
the fans of the scored-upon team who are temporarily more risk averse might be more
responsive to an advertisement for car insurance. Given that most sporting events feature
teams from different cities — and thus different media markets — our results might
suggest advertising different goods in these different cities depending in the events of the
game. Even more targeted opportunities exist in new media where advertisers can
potentially target advertisements to specific content — that they believe to induce good
or bad moods — to take advantage of the relationship between mood and generosity,
trust, risk, and willingness to pay.
Our results similarly open the door for advertisers to manipulate mood themselves
in an effort to sell products. Advertisements the emphasize happiness (like those for
Coca-Cola or McDonald’s) may be aimed at — among other things — manipulating
mood in an effort to sell goods that some consumers might otherwise not buy. In other
words, advertisers need not wait for external content (e.g. the events of a sporting event,
news article, or television show) to alter mood in order to leverage this relationship
between mood and decision-making; they might instead induce the mood themselves.
Finally, our results speak to economic theory in general and discrete choice theory
in particular. In the next section, we propose a specific way for utility theory to
incorporate mood, but our results suggest that mood may already play a roll in the error
terms of existing models. In the theory of discrete choice, it is assumed that when a
decision maker chooses between several discrete objects, her utility for any object is
affected by a random utility shock drawn from a particular distribution (e.g. an Extreme
Value Type I distribution). However, the source of these shocks is rarely discussed. Our
results suggest that one source for these shocks is the mood that the decision maker
happens to be in at the precise time the decision needs to be made. Since in our daily
lives we are bombarded by exogenous events that constantly change our mood, it may not
be surprising if these utility shocks were in some way related to these shocks to our
happiness.
IV. A Model of Mood and Decision Making
In this section, we develop a simple utility model of mood and decision-making
that can rationalize the results described in the previous section and can serve as a
framework for thinking about how mood might affect economic behavior more
generally.20
In standard economic theory, utility is typically a function of material payoff.
However, in recent years scholars have extended this construct to include such factors as
the payoff of others (see, e.g., Fehr and Schmidt [1999]; Bolton and Ockenfels [2000]),
beliefs (see, e.g., Geanakopolos, Pearce and Stacchetti [1989]; Rabin [1993];
Brunnermeier and Parker [2005]), and other factors. But utility may also be a function of
the mood one is in when making a decision. Such a link has been described by
20
There is an interesting relationship between what we present here and the model of Kimball
and Willis (206) where it is assumed that happiness and utility are included in a model of lifecycle utility maximization. Happiness, in that framework, is considered as a shock to lifetime or
long-run utility. What is interesting in our paper is that we see an effect of short-term happiness
on decisions and the short-term happiness is induced by events that have absolutely no effect on
lifetime satisfaction. Hence, we find that happiness can affect behavior even when it is well
known that it has no impact of long-term outcomes.
Loewenstein (2000), which posits that one can model such dependency in a statedependent framework.
Here we propose a model of mood-dependent decision-making that allows us to
give some theoretical insights into the decisions made by our subjects. The model we
propose is flexible enough to explain our data yet structured enough to provide an
explanation of how mood can influence a decision maker’s choice in a variety of settings.
To start, we need to distinguish two types of situations where mood may be
relevant: one-person decisions and multi-person interactions. In both situations, we model
mood as an exogenous parameter that, in the case of our experiment, is affected by the
events in the game being watched and not by their choices in the decision tasks. In other
words, the act of stating that they will give money to a charity or pay a certain amount for
a good does not change subjects’ mood during the experiment over and above the
exogenous mood induced by watching the game.21
In the case of a one-person decision task, we propose a simple utility function
where utility is a function of exogenous mood and material payoff as follows:
𝑢𝑖 (𝜎𝑖 , 𝜋𝑖 )
(1)
where 𝜎𝑖 , is the exogenous mood (determined by the events of the game) and 𝜋𝑖 is the
material payoff of person 𝑖.
In the case of a two-person interaction between 𝑖 and 𝑗, we posit the following
utility function:
21
Note that the assumption that mood does not depend on choices in the experiment does not
mean that a subject is not made happier by a purchase or that a subject does not receive a “warm
glow” utility from helping others. It simply means that helping others does not alter his mood. We
think this is realistic given that the decisions subjects are making will not be implemented until
the end of the experiment and so are unlikely to affect happiness during the experiment. Put
succinctly, we look at decision making conditional on mood where the mood is determined
exogenously.
𝑈𝑖 (𝜎, 𝜋𝑖 , 𝜋𝑗 ) = 𝛽𝑖 𝑢𝑗 (𝜎𝑗 , 𝜋𝑗 ) + 𝑢𝑖 (𝜎𝑖 , 𝜋𝑖 )
(2)
where 𝜎𝑖 is again the decision maker’s exogenous mood and 𝜎𝑗 is the exogenous mood of
person 𝑗, with whom person 𝑖 is interacting, 𝛽𝑖 is the weight given by person 𝑖 to 𝑗's
utility. 𝜋𝑗 is the material payoff of person 𝑗.
While a decision maker 𝑖 can be assumed to know his own mood at any time, he
may only know the distribution from which the mood of 𝑗 is drawn, so we can write the
utility function as:
𝑈𝑖 (𝜎, 𝜋𝑖 , 𝜋𝑗 ) = ∫ [𝛽𝑖 𝑢𝑗 (𝜎𝑗 , 𝜋𝑗 ) + 𝑢𝑖 (𝜎𝑖 , 𝜋𝑖 )]𝑑𝜇(𝜎𝑗 )
𝑗
In order to simplify the notation, we define 𝑢1 =
𝜕𝑢𝑖 (𝜎𝑖 ,𝜋𝑖 )
𝜕𝑢𝑖 (𝜎𝑖 ,𝜋𝑖 )
𝜕𝜎𝑖
𝜕𝜋𝑖
, 𝑢2 =
, and 𝑢12 =
𝜕2 𝑢𝑖 (𝜎𝑖 ,𝜋𝑖 )
𝜕𝜎𝑖 𝜕𝜋𝑖
.
IV.A. Charitable Giving
In our experiment, the charitable giving task is framed as a Dictator game in
which subjects transfer money to a charity they select at the start of the session. In the
data, we observe that an increase in happiness leads to an increase in charitable giving. In
order to model this, we consider a model with some “warm glow” utility from giving
money to charity. In the experiment, a subject was given an endowment of 𝑤 ($40 in the
experiment) from which he could donate 𝑐 ≤ 𝑤 to charity and keep 𝑤 − 𝑐 for himself.
Since the subject’s choice has an externality on the charity we use (3) to represent the
subject’s utility function.
𝑈𝑖 (𝜎, 𝜋𝑖 , 𝜋𝑗 ) = ∫ [𝛽𝑖 𝑢𝑗 (𝜎𝑗 , 𝑐) + 𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑐)]𝑑𝜇(𝜎𝑗 )
𝑗
Note that we are modeling the recipient of money, person 𝑗 , with the utility
function 𝑢𝑗 (𝜎𝑗 , 𝑐). Since the recipient of the transfer in this case is a charity, however,
this implies that the charity has a mood. We prefer, instead to think of the recipient as the
person to whom the charity makes a transfer. Hence, the charity is merely a conduit for
giving to others. (As will be shown below, as long as 𝛽𝑖 𝑢𝑗 (𝜎𝑗 , 𝑐) does not change with the
mood of subject 𝑖, the results are independent of any assumption about its structure.)
The dictator’s utility is a linear combination of his own “direct” utility, 𝑢𝑖 (𝜎𝑖 , 𝑤 −
𝑐) , and the recipient’s utility, 𝑢𝑗 (𝜎𝑗 , 𝑐) . We want to look at how giving changes
systematically with mood. To start, we assume 𝑢12 < 0, meaning that as the subject has a
more positive mood, his own marginal utility of consumption decreases. Let 𝑐 ∗ be the
current equilibrium amount given to charity and suppose that mood increases. Giving one
more dollar to charity entails a smaller marginal decrease in 𝑢𝑖 . However, the marginal
utility to the Dictator of giving an extra dollar (over the current equilibrium amount) is
𝛽𝑖 𝑢𝑗 (𝜎𝑗 , 𝑐 ∗ ) and has not changed. Hence, if the Dictator was in equilibrium with respect
to charitable giving before a change in mood then as his mood increases his giving will
increase since, due to his increased mood, the marginal cost of giving has decreased
while the marginal benefit has remained constant. This will lead to an increase in
charitable giving as mood increases. If we instead assume that 𝑢12 > 0, we get the
opposite result. We can summarize this in the following proposition (note: all proofs are
in Appendix C)
Proposition 1:
If 𝑢12 <0, then charitable giving is increasing in mood.
If 𝑢12 >0, then charitable giving is decreasing in mood.
IV.B. Willingness to Pay for a Good
Since this decision contains no externality, we use (1) to represent the subject's
utility. Under the BDM mechanism, once a subject states a price for a good, they either
receive it or not depending on the realization of the random variable of the mechanism.
Let 𝑐 ∈{0,1} be a variable which indicates whether subject 𝑖 received the good and
expand the utility function to 𝑢𝑖 (𝜎𝑖 , 𝜋𝑖 , 𝑐𝑖 ). His utility function is 𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑝, 1) when
he wins the good at price 𝑝 and 𝑢𝑖 (𝜎𝑖 , 𝑤, 0) when he does not. Then subject 𝑖 is asked to
choose a 𝑝∗ such that
𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑝∗ , 1) = 𝑢𝑖 (𝜎𝑖 , 𝑤, 0)
Assume that the utility of good consumption and money is separable and that the utility
of receiving the good does not depend on mood and denote 𝑣𝑖 (1) as the utility
component of the good so that the utility when the subject wins the good is
𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑝, 1) = 𝑣𝑖 (1) + 𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑝)
(4)
With this form, we again get a clean characterization of how the optimal choice of
𝑝 changes with mood. As with the previous tasks, whether 𝑝 is increasing or decreasing
in mood depends on whether the marginal utility of money is increasing or decreasing in
mood (i.e., whether 𝑢12 is greater or less than 0). For example, if 𝑢12 < 0, then the
marginal value of money is decreasing in mood while the marginal increase in the
probability of winning the good remains constant. Hence, it is less costly to increase the
probability of wining the good so if the decision maker was in equilibrium before the
mood change, he would be willing to increase 𝑝 as his mood increased. This leads to an
increase in the willingness to pay and the following proposition:
Proposition 2:
Let utility be additive in the good. If 𝑢12 < 0, then willingness to pay is increasing in
mood. If 𝑢12 > 0, then willingness to pay is decreasing in mood.
IV.C. Gamble
We again use utility function (1) since there is no externality in the subject's
choice about the gamble. In the experiment, we asked the subjects to choose 𝑥 where 𝑥 is
the amount they are willing to pay for a gamble offering $40 or $0 with equal probability.
The subjects started off with $40. Using a BDM mechanism, a number 𝑦 ∈ [0,40] is
drawn and a subject receives the gamble if 𝑦 < 𝑥 and would have final wealth levels
80 − 𝑦 if he won the gamble and 40 − 𝑦 if he lost. Subjects therefore choose the 𝑥 that
solves:
𝐸[𝑢|𝑔𝑎𝑚𝑏𝑙𝑒 𝑎𝑡 𝑝𝑟𝑖𝑐𝑒 𝑥] = 𝐸[𝑢|𝑛𝑜 𝑔𝑎𝑚𝑏𝑙𝑒]
1
(𝑢 (𝜎 , 𝑤 − 𝑥) + 𝑢𝑖 (𝜎𝑖 , 2𝑤 − 𝑥)) = 𝑢𝑖 (𝜎𝑖 , 𝑤)
2 𝑖 𝑖
To look at how the willingness to pay for the gamble changes with mood, we need
to look at how risk aversion changes with mood. To do this, we consider how the
coefficient of absolute risk aversion changes with mood and make an additional
assumption concerning the form of 𝑢1 . This leads us to the following proposition:
Proposition 3:
If 𝑢1 is a convex transformation of 𝑢𝑖 , then the willingness to pay for the gamble will be
increasing in mood. If 𝑢1 is a concave transformation of 𝑢𝑖 , then the willingness to pay
for the gamble is decreasing in mood.
The condition that 𝑢1 is a convex transformation of 𝑢𝑖 has a sensible interpretation
in the case when 𝑢12 < 0. We can show that convexity condition implies that
−
𝑢22
𝑢122
≤−
𝑢2
𝑢12
which is equivalent to the coefficient of absolute risk aversion 𝐴(𝑤, 𝜎𝑖 ) =
−𝑢22 (𝜎𝑖 ,𝑤)
𝑢2 (𝜎𝑖 ,𝑤)
decreasing in 𝜎𝑖 . If we interpret mood as acting as an increase in wealth, then this
condition is similar to the usual condition for decreasing absolute risk aversion. Consider
a utility function of the form 𝑢𝑖 (𝑓(𝜎𝑖 ) + 𝑤). Then
𝑢122
𝑢12
=
𝑢𝑖 ′′′(𝑓(𝜎𝑖 )+𝑤)
𝑢𝑖 ′′(𝑓(𝜎𝑖 )+𝑤)
and
𝑢22
𝑢2
=
𝑢𝑖 ′′(𝑓(𝜎𝑖 )+𝑤)
𝑢𝑖 ′(𝑓(𝜎𝑖 )+𝑤)
,
so the convexity condition implies that
−
𝑢𝑖 ′′(𝑓(𝜎𝑖 ) + 𝑤)
𝑢𝑖 ′(𝑓(𝜎𝑖 ) + 𝑤)
≤−
𝑢𝑖 ′′′(𝑓(𝜎𝑖 ) + 𝑤)
𝑢𝑖 ′′(𝑓(𝜎𝑖 ) + 𝑤)
which is the standard assumption for decreasing absolute risk aversion. Hence, the
convexity assumption translates well into standard assumptions on the utility function
when 𝑢12 < 0.
IV.D. Trust Game
Unlike the previous three decision tasks, this task actively involves two players in
a game and is therefore a bit more involved. In the Trust Game, the sender starts off with
𝑤 and can choose an amount 𝑡 ≤ 𝑤 to send to the receiver. The amount the receiver gets
is 3𝑡, from which he can choose and amount 𝑐 ≤ 3𝑡 to return to the sender. Thus, the
monetary outcomes for the sender and receiver are 𝑤 − 𝑡 + 𝑐 and 3𝑡 − 𝑐, respectively.
Using our utility functions, we have that the utility of the sender, when he sends 𝑡 and
receives 𝑐 in return is:
∫ [𝛽𝑖 𝑢𝑗 (𝜎𝑗 , 3𝑡 − 𝑐) + 𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑡 + 𝑐)]𝑑𝜇(𝜎𝑗 |𝑐).
𝑗
The receiver’s utility when he gets 3𝑡 and returns 𝑐 is:
∫ [𝛽𝑖 𝑢𝑗 (𝜎𝑗 , 𝑤 − 𝑡 + 𝑐) + 𝑢𝑖 (𝜎𝑖 , 3𝑡 − 𝑐)]𝑑𝜇(𝜎𝑗 |𝑡)
𝑗
Since this is an extensive form game, we can analyze it by working backwards.
Let us think of the problem of a receiver 𝑗 who gets 3𝑡 when 𝑢12 < 0. Let us fix the
transfer at 3𝑡 and equilibrium amount returned to be 𝑐 ∗ . We will look at what happens as
the receiver’s exogenous mood increases. Since 𝑢12 < 0, his own marginal utility of
money will be decreasing. Thus, we should expect him to give more money back to the
sender as his mood increases since the extra money for the sender will have a positive
marginal utility of 𝛽𝑗 𝑢𝑖 (𝜎𝑖 , 3𝑡 − 𝑐 ∗ ), which has remained constant, but will cost the
receiver less in terms of his egoistic utility 𝑢𝑗 than it did before the increase in mood.
When 𝑢12 > 0, a similar logic leads to the conclusion that the amount sent back by the
receiver is decreasing in mood.22
Moving back to the sender 𝑖, he can infer what the receiver will return given the
receiver’s mood. However, since players are anonymously matched, the sender doesn’t
know what the receiver’s mood will be. In this way, sending money to the receiver is
22
This part of the analysis is very similar to our discussion of charitable giving in subsection
IV.A.
similar to a gamble, where the amount the receiver returns is equivalent to winning or
losing the gamble.
First, suppose that 𝑢12 < 0 and that the sender is at an interior equilibrium in the
sense that the amount sent, 𝑡, is less than the sender’s endowment of 𝑤. Now assume that
for any given amount a sender transfer 𝑡, we can split the receivers into two types: those
who transfer back 𝑐 > 𝑡 and those who transfer back 𝑐 < 𝑡 . When facing those who
return 𝑐 > 𝑡, the sender would always prefer to send more endowment (since they will
both have higher wealth). Therefore, in order to have an interior solution in the amount
sent, it must be that there are enough people who will return at a rate less than one. Now,
consider an increase in the emotional state of the sender. Since 𝑢12 < 0, the sender now
has a lower marginal utility of wealth for himself. However, given that he was willing to
transfer an interior amount before the mood increase, he is willing to transfer even more
now for reasons related to the decision in the charitable giving task.
Now suppose that 𝑢12 > 0. The analysis here is not as straightforward. If, for any
amount sent, the sender was facing only receivers who return 𝑐 < 𝑡, then the sender
would like to reduce the amount of money sent since, by 𝑢12 > 0, an increase in mood
causes him to place more relative weight on his own egotistic utility. However, there
might also be types that return 𝑐 > 𝑡. When facing these types, the sender would prefer to
transfer more. However, we can use the fact that from the sender’s perspective,
transferring money to the receiver is like a gamble. Supposing that a change in own mood
is independent of the receiver’s mood, then how much the sender sends will depend on
how risk aversion changes with mood. As we showed in the gamble task, this behavior
requires an assumption on 𝑢1 being a concave transformation of 𝑢𝑖 . If this condition
holds, then the coefficient of risk aversion increases with mood and the sender would
prefer to send less money. Combining all these results, we get our final proposition:
Proposition 4: If 𝑢12 < 0, then the transfer by sender and amount returned by the
receiver are both increasing in mood. If 𝑢12 > 0, then the amount returned by the
receiver is decreasing in mood. If 𝑢1 is a concave transformation of 𝑢𝑖 and 𝑢12 > 0,
then the transfer by the sender is decreasing in mood.
Our utility model that incorporates mood generates sharp predictions about
behavior in each of our four decision tasks in the experiment as a function of the sign of
𝑢12 (and in some cases the form of 𝑢1 ). These predictions are summarized in Table 6
alongside the empirical results. As can be seen from the table, our empirical results can
be rationalized in this model with the simple assumption that 𝑢12 < 0.23
23
While our model is agnostic to the specific utility function that generates the negative crosspartial of 𝑢12 < 0, our empirical results would be rationalized by a utility function of the form
𝑢𝑖 (𝑓(𝜎𝑖 ) + 𝑔(𝜋𝑖 )) where 𝑢12 < 0 is guaranteed by 𝑓’>0, 𝑔 ‘>0 and the concavity of 𝑢𝑖 . This
formulation suggests that mood and money are substitutes, that a positive mood shock increases
utility, and makes it easy to interpret our results as suggesting being in a better mood makes
subjects feel richer.
Table 6: Empirical Results and Predictions of Model in Decision Tasks
as Mood Increases
Task
Empirical
Results
+
+
+
+
+3
𝒖𝟏𝟐 <0
𝒖𝟏𝟐 =0
Charitable Giving
+
0
Gamble
+1
0
WTP
+
0
Trust Game: Sender
+
0
Trust Game:
+
0
Receiver
1
requires additional assumption that 𝑢𝑖,1 is a convex transformation of 𝑢𝑖,1
2
requires additional assumption that 𝑢𝑖,1 is a concave transformation of 𝑢𝑖,1
3
not significant at conventional levels.
𝒖𝟏𝟐 >0
−
−2
−
−2
−
V. Conclusion
This paper investigates the impact of short-term changes in mood on decisionmaking. Surely, many life events can have long lasting influences on emotions (e.g. the
death of a parent or child, divorce, career setbacks, etc.) and choices made under the
cloak of these events may be distorted in ways that are understandable. However, we
focus on short-term fluctuations in mood because they are regularly affected by a variety
of factors and it is perhaps less understandable why economic decisions would be
distorted by such emotional swings that are known to be orthogonal to the fundamentals
of our wellbeing. Standard economic theory has no role (or tolerance) for mood to effect
behavior and yet we find that subjects have systematic changes in behavior when they are
temporarily made happier or less happy by the events of an NFL football game.
In particular, we find that watching the game affects viewers’ mood, as measured
by self-reported happiness, and that these changes in mood are predictably related to the
events of the game. More importantly, this self-reported happiness is highly correlated
with behavior in the four decision tasks subjects engage in during our experiment. When
the mood of subjects’ increases — that is, when they report being happier — they give
more to charity, pay more for a good, are less risk averse, and are more trusting of others.
Our results have a number of interesting consequences. First, economic theory
and its emphasis on revealed preference rely heavily on the assumption that people
behave consistently when making decisions. Such consistency has been documented by
Fisman, Kariv, and Markovits (2007), which finds that subject behavior is consistent with
GARP. Nevertheless, there is always a seemingly irreducible amount of inconsistency in
human decision making, and our papers suggests that some of this inconsistency might be
attributable to variations in mood that decision makers can experience over even short
periods of time. Such emotional swings may lead to the appearance that people choose
stochastically when, in fact, their choice may be state-dependent with mood being a main
mover of states.
From a methods point of view, our paper is unique in that we present a paradigm
in which mood is varied by naturally occurring events over the course of an NFL football
game. Watching the game alters the emotional states of viewers over the course of a few
hours. Hence the data generated by our experiment allows us to observe not only the
impact of mood on decisions but also the impact of changing mood on changes in
decision making, a type of data not generated by other investigators in this area.
Finally, in this paper we present a simple theory that incorporates mood directly
into a decision maker’s utility function that allows us to succinctly explain the data
generated by our experiment. The result has a natural interpretation that being in a good
mood makes individuals feel richer. We see this as providing a foundation for future
researchers on the relationship between mood and decision-making. If other emotions can
be as parsimoniously included into models of decision making, we may be able to
generate some traction in getting economic theory to consider the role of emotions more
generally.
VI. References
Aderman, David, “Elation, depression, and helping behavior,” Journal of Personality and
Social Psychology, 24 (1972), 91-101.
Andrade, Eduardo and Dan Ariely, “The Enduring Impact of Transient Emotions on
Decision Making,” Organizational Behavior and Human Decision Processes, 109
(2009), 1-8.
Andreoni, James “Impure Altruism and Donations to Public Goods - A Theory of Warm
Glow Giving,” Economic Journal, 100 (1990), 464-477.
Andreoni, James and John Miller, “Giving According to GARP: An Experimental Test of
the Consistency of Preferences for Altruism,” Econometrica, 70 (2002), 737-753.
Anik, Lalin, Lara B. Aknin, Michael I. Norton, and Elizabeth W. Dunn “Feeling Good
about Giving: The Benefits (and Costs) of Self-Interested Charitable Behavior,”
Harvard Business School Working Paper 10-012, 2009.
Ariely, Dan and George Loewenstein, “The Effect of Sexual Arousal on Sexual Decision
Making,” Journal of Behavioral Decision Making, 19 (2006), 87-98.
Battigalli, Pierpaolo and Martin Dufwenberg, “Guilt in Games,” American Economic
Review Papers and Proceedings, 97 (2007), 170-176.
Bechara, Antione, Hanna Damasio, Daniel Tranel, and Antonio Damasio, “Deciding
Advantageously Before Knowing the Advantageous Strategy,” Science, 275 (1997),
1293-1295.
Benjamin, Daniel, Ori Heffetz, Miles S. Kimball, and Nichole Szembrot, “Beyond
Happiness and Satisfaction: Toward Well-Being Indices Based on Stated
Preferences,” American Economic Review, 104 (2015), 2698-2735.
Benjamin, Daniel, Ori Heffetz, Miles Kimball, and Alex Rees-Jones, “What Do You
Think Would Make You Happier? What Do You Think You Would Choose?” American
Economic Review, 102 (2012), 2083-2110.
---------- “Can Marginal Rates of Substitution Be Inferred from Happiness Data?
Evidence from Residency Choices,” American Economic Review, 104 (2014), 34983528.
Bentham, Jeremy, An Introduction to the Principles of Morals and Legislation, 1789.
Brunnermeier, Markus, and Jonathan Parker, “Optimal Expectations,” American
Economic Review, 95 (2005), 1092-1118.
Bolton, Gary and Axel Ockenfels, “ERC: A Theory of Equity, Reciprocity, and
Cooperation,” American Economic Review, 90 (2000), 166-193.
Bosman, Ronald, Matthias Sutter and Frans van Winden, “The Impact of Real Effort and
Emotions in the Power-to-Take Game,” Journal of Economic Psychology, 26, (2005),
407-429.
Boyce, Chrisopher, Mikołaj Czajkowski, Nick Hanley, Charles Noussair, Michael
Townsend, and Steve Tucker, “The Effects of Emotions on Preferences and Choices for
Public Goods,” University of St. Andrews Discussion Papers in Environmental
Economics, 2015.
Burghart, Daniel, Paul Glimcher, and Stephanie Lazzaro, “An Expected Utility
Maximizer Walks Into A Bar…,” Journal of Risk Uncertainty, 46 (2013), 215-246.
Capra, C. Monica, “Mood-Driven Behavior in Strategic Interactions,” American
Economic Review Papers and Proceedings, 94 (2004), 367-372.
Caplin, Andrew and John Leahy, “Psychological Expected Utility Theory and
Anticipatory Feelings,” Quarterly Journal of Economics, 116 (2001), 55-79.
Card, David and Gordon Dahl, “Family Violence and Football: The Effect of Unexpected
Emotional Cues on Violent Behavior,” Quarterly Journal of Economics, 126 (2011), 103143.
Charness, Gary and Martin Dufwengerg, “Promises and Partnerships,” Econometrica, 74
(2006), 1579-1601.
Choi, Syngjoo, Ray Fisman, and Douglas Gale, “Revealing Preferences Graphically: An
Old Method Gets a New Tool Kit,” American Economic Review Papers and Proceedings,
97 (2007), 153-158.
Dunn, Jennifer and Maurice Schweitzer “Feeling and believing: The influence of emotion
on trust,” Journal of Personality and Social Psychology, 88 (2005), 736–748.
Earely, Joseph and James Konow “The Hedonistic Paradox: Is Homo Economicus
Happier?” Journal of Public Economics, 92 (2008), 1-33.
Edmans, Alex, Diego Garcia, and Øyvind Norli, “Sports Sentiment and Stock Returns,”
The Journal of Finance, 62 (2007), 1965-1998.
Elster, Jon “Emotions and Economic theory,” Journal of Economic Literature, 36 (1998),
pp. 47-74.
Fehr, Ernst and Klaus Schmidt, “A Theory of Fairness, Competition, and Cooperation,”
Quarterly Journal of Economics, 114 (1999), 817-868.
Fisman, Raymond, Shachar Kariv, and Daniel Markovits, “Individual Preferences for
Giving,” American Economic Review, 97 (2007), 1858-1876.
Frey, Bruno , Simon Luechinger, and Alois Stutzer, “The Life Satisfaction Approach to
Valuing Public Goods: The Case of Terrorism,” Public Choice, 138 (2008), 317-345.
Geanakopolos, John, David Pearce, and Ennio Stacchetti “Psychological Games and
Sequential Rationality,” Games and Economic Behavior, 1 (1989), 60-79.
Gilbert, Daniel, Stumbling on Happiness (New York, NY: Random House).
Ifcher, John and Homa Zarghamee, “Happiness and Time Preference: The Effect of
Positive Affect in a Random-Assignment Experiment,” American Economic Review, 101
(2011), 3109-3129.
Isen, A.M., and Levin, P.F., “The effect of feeling good on helping: Cookies and
Kindness,” Journal of Personality and Social Psychology, 21 (1972), 384-388.
Johnson, Eric and Amos Tversky, “Affect, Generalization and the Perception of Risk,”
Journal of Personality and Social Psychology, 45 (1983), 20-31.
Kahneman, Daniel, Alan Krueger, David Schkade, Nobert Schwarz, and Arthur Stone,
“A survey method for characterizing daily life experience: The Day Reconstruction
Method,” Science, 306 (2004), 1776-1780.
Kimball, Miles and Rober Willis, “Utility and Happiness,” University of Michigan,
Mimeo, 2006.
Kirchsteiger, George , Luca Rigotti, and Aldo Rustichini, “Your morals might be your
moods,” Journal of Economic Behavior & Organization, 59 (2006), 155-172.
Lambsdorffl, Joseph, Marcus Giamatei, Katharina Werner, and Manuel Schubert “The
Origin of Cooperation – Experimental Evidence from the 2014 Soccer World Cup,”
Working Paper, 2015.
LeDoux , Joseph E, “The Emotional Brain”, (New York, NY: Simon and Schuster)
Lempert, Karolina and Elizabeth Phelps, “Neuroeconomics of Emotion and Decision
Making,” In P.W. Glimcher and E. Fehr (eds). Neuroeconomics: Decision Making and
the Brain, 2nd ed. (Waltham, MA: Academic Press).
Lerner, Jennifer and Dacher Keltner, “Beyond Valence: Toward a Model of Emotion
Specific Influences on Judgement and Choice,” Cognition and Emotion, 14 (2000), 473493.
----------, “Fear, Anger, and Risk,” Journal of Personality and Social Psychology, 81
(2001), 146-159.
Lerner, Jennifer, Deborah Small, and George Loewenstein, “Heart Strings and Purse
Strings- Carryover Effects of Emotions on Economic Decisions,” Psychological Science,
15 (2004), 337-341.
Loewenstein, George, “Emotions and Economic Behavior,” American Economic Review
Papers and Proceedings, 90 (2000), 426-432.
Loewenstein, George and Jennifer S. Lerner, “The Role of Affect In Decision Making,”
in Handbook of Affective Science, Richard Davidson, Hill Goldsmith, and Klaus Scherer,
ed., (Oxford: Oxford University Press).
Loewenstein, George and Scott Rick, “The Role of Emotions in Economic Behavior,” in
Handbook of Emotions, 3rd ed. (New York, NY: Guilford Press).
Loewenstein, George, Elke Weber, Christopher Hsee, and Ned Welch, “Risk and
feeling,” Psychological Bulletin, 127 (2001), 267-286.
Myers, Dan and Dustin Tingley, “The Influence of Emotions on Trust,” Mimeo, PLESS,
Princeton University, 2011.
Nygren, Thomas, Alice Isen, Pamela Taylor, and Jessica Dulin, “The Influence of
Positive Affect on the Decision Rule in Risk Situations: Focus on Outcome (and
Especially Avoidance of Loss) Rather Than Probability,” Organization Behavior and
Human Decision Making, 66 (1996), 59-72.
Rabin, Matthew, “Incorporating Fairness into Game Theory and Economics,” American
Economic Review, 83 (1993), 1281–1302.
Reuben, Ernesto and Frans van Winden, “Fairness Perceptions and Prosocial Emotions in
the Power to Take,” Journal of Economic Psychology, 31 (2010), 908-922.
Rosenhan, D. L., Underwood, B., and Moore, B. “Affect moderates self-gratification and
altruism,” Journal of Personality and Social Psychology, 30 (1974), 546-52.
Sacks, Daniel, Betsey Stevenson, and Justin Wolfers, “The New Stylized Facts About
Income and Subjective Well-Being,” American Economic Review Papers and
Proceedings, 12 (2012), 1181-1187.
---------- ,“Growth in income and subjective well-being over time,” NBER Working
Paper No. 16441, 2012.
Simons, Eric, The Secret Lives of Sports Fans: The Science of Sports Obsession, (New
York, NY: The Overlook Press).
Stevenson, Betsey, and Justin Wolfers, “Economic growth and subjective well-being:
reassessing the Easterling paradox,” Brookings Papers on Economic Activity, 1 (2008),
1– 84.
Strack, Fritz, Norbert Schwarz, and Elisabeth Gschneidinger, “Happiness and
Reminiscing: The Role of Time Perspective, Affect, and Mode of Thinking,” Journal of
Personality and Social Psychology, 49 (1985), 1460-1469.
van Winden, Frans “Affect and Fairness in Economics,” Social Justice Research, 20
(2007), 35-52.
Zenith Optimedia,“Executive summary: Advertising Expenditure Forecasts December
2014”, (http://zenithoptimedia.com, Zenith Optimedia)
Online Appendix
Appendix A: Demographic Questionnaire and Additional Tables
Demographic Questionnaire
Question
1. Name
Entry
Users entered on text interface.
2. Work Status
Full time employed, Part time employed, Student,
Unemployed.
3. Gender
Male, Female.
4. Highest Education
Achieved
PhD, Masters Degree, Bachelors Degree, Some
College, High School.
5. Do You Like Watching
Sports in general?
Likert scale where 1 is “Not very much” and 7 is
“More than all other types of entertainment.”
6. Do you like watching
football in particular?
Likert scale where 1 is “Not very much” and 7 is
“Football is my favorite sport to watch.”
7. What is your favorite
team?
Any of the 32 NFL teams.
8. Which team are you
rooting for in the game
today?
One of the two teams playing in the game.
9. How strongly do you care
for the team you are
Likert scale where 1is “Not at all”, 3 is “Somewhat”,
rooting for in the game
5 is “A lot”, and 7 is “Passionately.”
today?
10. How strongly do you
dislike the team you are
not rooting for in the
game today?
Likert scale where 1 is “I hate them with a passion”,
3 is “I dislike them somewhat”, 5 is “I like them”,
and 7 is “I like them almost as much as the other
team.”
11. Why do you want the
team you are rooting for
today to win?
“They are my favorite team,” “Several players on
that team are on my fantasy football team,” “I need
that team to win in order for my truly favorite team
to make the playoffs,” and “I bet on that team.”
Table A1: How Excitement and Surprise respond to events in the game
Excitement (0-6)
Surprise (0-6)
(1)
(2)
(3)
(4)
Favored Team TD
0.46
0.45
0.51
0.47
(0.13)*** (0.13)*** (0.10)***
(0.10)***
Favored Team FG
0.35
0.34
0.37
0.31
(0.14)**
(0.13)*** (0.11)***
(0.11)***
Disfavored Team TD
0.46
0.47
0.39
0.43
(0.11)*** (0.12)*** (0.12)***
(0.12)***
Disfavored Team FG
-0.11
-0.10
0.012
0.057
(0.12)
(0.13)
(0.11)
(0.11)
Prob. favored wins (0-100)
0.0017
0.0083
(0.0047)
(0.0033)**
Constant
2.50
2.39
3.19
2.66
(0.053)*** (0.32)*** (0.046)*** (0.23)***
Subjects
61
61
61
61
Obs.
912
912
912
912
R-Squared
0.594
0.594
0.628
0.633
Notes: Table A1 shows the effect of scores in the game on self-reported excitement and
surprise. The dependent variables were elicited in a Likert-scale measured on a 0 to 6
scale. The regressions control for the average of the dependent variable of each subject
and cluster the coefficients by subject. Significance denoted as * p < 0.1, ** p < 0.05, ***
p < 0.01.
Table A2: Correlation in Emotions Measures
Change in
Happiness
Change in
Surprise
Change in
Happiness
1
Change in
Surprise
0.1600***
1
Change in
Excitement
0.2177***
0.3927***
Change in
Excitement
1
Notes: Table A2 reports correlations between the changes in the emotions measured as
the difference between the current measurement and the previous measurement. The
correlation matrix suggests that changes in happiness are positively correlated with
changes in excitement and changes in surprise, which are also positively correlated with
each other. Significance denoted as * p < 0.1, ** p < 0.05, *** p < 0.01.
Appendix B: Experimental Instructions
Instructions
Thank you for participating in this study. This study is about decision-making and
entertainment. Over the course of the study, you will answer questions and make
decisions. We will record your answers on the tablet in front of you. Please make sure
that you are always using the tablet assigned to you. If you have difficulty with the tablet,
just raise your hand and someone will come over to help you. However, please do not use
the tablet for any purpose other than this study. If you want to surf the Web please use
your own cell phone or tablet. We will now describe the study and the ways in which
you may earn money in the study.
Over the course of the study you will watch an NFL football game. Before the game and
at certain commercial breaks during the game, we will ask you to answer a set of
questions and to choose a decision for each of four decision problems. The questions and
decision problems will be the same at the beginning of the game and at each commercial
break. You can enter the same answer or different answers each time you are asked. At
the end of the study, we will randomly select one of the four decision problems you
engaged in and randomly select your choice made before the game or during one of the
commercial breaks and pay you cash based on your choice for that decision problem. In
addition to the money you make in the decision problem you will receive $30 just for
showing up.
Only one of your decisions will be randomly chosen for payment, so each time you are
asked to make a decision you should answer as if this is the only decision you are making
today. In other words, each time you make a decision you should answer it as if that
answer is your best answer ignoring everything else you have done today, since that
answer may be the only one that counts.
The decision problems are described below.
Decision Problem 1:
During this game you may have the opportunity to donate money to a charity.
There are three possible charities to which you can donate as part of this study. The three
charities are: CHARITY A (The United Way), CHARITY B (The American Cancer
Society), and CHARITY C (The World Wildlife Fund). On your tablet you will be asked
to select one when the time arrives.
If this decision is randomly selected for payment, you will receive $40 dollars and you
will have the opportunity to donate some of this money to the charity you selected.
In particular, you will keep $40 minus the amount you choose to donate to the charity and
the charity will receive the amount you chose to donate to the charity. If this decision
problem is chosen for payment, you will receive your $30 show-up fee plus whatever
amount of the $40 you decided to keep.
We will collect all the money donated to charity by all people in the room and write
checks to those charities when the study is over. You can be 100% confident that the
money will be donated.
Only one of the decisions you made either before the game or during a commercial break
will be randomly chosen for payment, so each time you are asked this question you
should answer as if this is the only decision you are making today.
Please raise your hand if you have any questions.
Decision Problem 2:
For this decision problem, we will give you $40 out of which you might spend to buy one
of three goods of your choosing, which will be shown to you now.
During this game you may have the opportunity to buy your chosen good. When the time
comes, you will select the good you would like to be offered for purchase by entering it
in your tablet.
Once before the game and at each commercial break, we will ask you how much you are
willing to pay out of your $40 for the good that you have selected. Whether you actually
are able to buy the good, and at what price, will be described below, but it is in your best
interest to write down exactly the most you would be willing to pay for the good (and not
more or less than the most you would be willing to pay) each time you are asked.
The way that we determine whether you buy your good is that we will randomly select a
price between $0 and $40. If the price is below the amount you report you are willing to
pay, you pay that randomly selected price and get the good. If the price is above the
amount you report that you are willing to pay, you will not receive the good but will be
able to keep the entire $40. For example, if you report $25 as what you are willing to pay,
then if the price is randomly selected to be $10 you will pay $10 to get the good. In this
case you will pay $10 for the good out of your $40 and also get the good. If you report
$25 as what you are willing to pay, then if the price is randomly selected to be $30, you
will not pay for the good and you will not receive the good but will keep the entire $40.
So here you will leave the experiment with $40. Given that the price is randomly selected
and not determined by what you report, it is in your best interest to write down exactly
the most you would be willing to pay for the good (and not more or less than the most
you would be willing to pay). Remember, whatever your payment is in this decision
problem you will be paid your $30 show-up fee in addition.
Only one of the decisions you made either before the game or during a commercial break
will be randomly chosen for payment, so each time you are asked this question you
should answer as if this is the only decision you are making today.
Please raise your hand if you have any questions.
Decision Problem 3:
For this decision problem, we will give you $40 out of which you might spend money to
buy a risky gamble that gives you a 50% chance of receiving $0 and a 50% chance of
receiving $40.
Once before the game and at each commercial break, we will ask you how much you are
willing to pay for this risky gamble. Whether you actually are able to buy the risky
gamble, and at what price, will be described below, but it is in your best interest to write
down exactly the most you would be willing to pay for the risky gamble (and not more or
less than the most you would be willing to pay).
The way that we determine whether you get the gamble is that we will randomly select a
price between $0 and $40. If the price is below the amount you report you are willing to
pay, you pay that randomly selected price and get the risky gamble. If the price is above
the amount you report that you are willing to pay, you will not get the risky gamble.
Instead, you will get to keep the $40 we gave you. For example, if you report $25 as what
you are willing to pay, then if the price is randomly selected to be $10 you will pay $10
to get the risky gamble. In this case you will pay $10 for the gamble out of your $40 and
also get to engage in the gamble. If the gamble ends up paying you $40, then your payoff
will be $70 = $40 - $10 +$40. However, if the gamble ends up paying you $0, then your
payoff will be $30 = $40 - $10 + $0. If you report $25 as what you are willing to pay,
then if the price is randomly selected to be $30, you will not get the gamble. You will be
able to keep your initial $40 so your payoff will be $40. Remember, whatever your
payment is in this decision problem you will be paid your $30 show-up fee in addition.
Given that the price is randomly selected and not determined by what you report, it is in
your best interest to write down exactly the most you would be willing to pay for the
risky gamble (and not more or less than the most you would be willing to pay). If you
buy the risky gamble, we will have the computer flip a coin and you will either get $0
with 50% probability or $40 additional dollars with 50% probability.
Only one of the decisions you made either before the game or during a commercial break
will be randomly chosen for payment, so each time you are asked this question you
should answer as if this is the only decision you are making today.
Please raise your hand if you have any questions.
Decision Problem 4:
During this game you will interact anonymously with another person in this study. In the
interaction, you will be randomly assigned to be Player A or Player B. At the start of the
interaction, Player A has $32and Player B has $0. Player A can choose to send $0, $8,
$16, $24, or $32to Player B. Player B will receive three times (i.e. 3x) the amount of
money transferred by Player A. For example, if Player A transfers $32, Player B will
receive $96, if Player A transfers $16, Player B will receive $48, if Player A transfers $0,
Player B will receive $0.
Player B then has the opportunity to transfer money back to Player A, from $0 up to the
total amount Player B received from Player A’s transfer. This money is transferred onefor-one without being multiplied. For example, if Player B transfers $32 back to Player
A, Player A receives $32; if Player B transfers $16 back to Player A, Player A receives
$16; if Player B transfers $0 back to Player A, Player A receives $0.
If you are randomly chosen to be Player A, you will choose how much money to send to
Player B. If you are randomly selected to be Player B, you will choose how much money
to send back to Player A for each amount of money he or she might send to you.
If this decision problem is chosen for cash payment, we will look at the decisions you
made either before the game or at one randomly chosen commercial break. If you are
Player A your payoff will be equal to the $32 you started out with minus what you sent to
Player B plus what Player B sent back to you. If you are Player B, your payoff will be
equal to the amount Player A sent to you minus what you sent back to Player A.
Remember, whatever your payment is in this decision problem you will be paid your $30
show-up fee in addition.
You will not receive any feedback from this decision problem and will be asked for
choices at the start of the game and at each of the commercial breaks.
Only one of the decisions you made either before the game or during a commercial break
will be randomly chosen for payment, so each time you are asked this question you
should answer as if this is the only decision you are making today.
Please raise your hand if you have any questions.
Appendix C: Proofs
We will now go over the proofs of the propositions in Section IV. As a quick reminder on
notation, we will use 𝑢1 =
𝜕𝑢𝑖 (𝜎𝑖 ,𝜋𝑖 )
𝜕𝑢𝑖 (𝜎𝑖 ,𝜋𝑖 )
𝜕𝜎𝑖
𝜕𝜋𝑖
, 𝑢2 =
and 𝑢12 =
𝜕2 𝑢𝑖 (𝜎𝑖 ,𝜋𝑖 )
𝜕𝜎𝑖 𝜕𝜋𝑖
.
Proposition 1: In the charitable giving game, if 𝑢12 < 0, then charitable giving is
increasing in mood. If 𝑢12 > 0, then charitable giving is decreasing in mood.
Proof of Proposition 1:
The utility function of the dictator who is endowed with wealth w and chooses to give c
is given by
𝑈𝑖 (𝜎𝑖 , 𝑤, 𝑐) = ∫ [𝛽𝑢𝑗 (𝜎𝑗 , 𝑐) + 𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑐)]𝑑𝜇(𝜎𝑗 )
𝑗
If we take the derivative of this utility function with respect to 𝜎𝑖 and c, we get
𝜕 2 𝑈𝑖 (𝜎𝑖 , 𝑤, 𝑐)
= ∫ [−𝑢𝑖,12 (𝜎𝑖 , 𝑤 − 𝑐)]𝑑𝜇(𝜎𝑗 )
𝜕𝜎𝑖 𝜕𝑐
𝑗
Our assumption that 𝑢12 ≥ 0 implies that the above expression is submodular. Hence, by
Topkis’s Theorem, we get that c is decreasing in 𝜎𝑖 . The proof for when 𝑢12 ≤ 0 is
analogous.
Proposition 2: In the willingness to pay task, if utility be additive in the good and 𝑢12 <
0, then willingness to pay is increasing in mood. If utility be additive in the good and
𝑢12 > 0, then willingness to pay is decreasing in mood.
Proof of Proposition 2:
When considering the willingness to pay for a good by subject i, the utility function of
other players doesn’t enter into i’s utility function. Our assumption on the utility form
ensures that utility of a i when he receives the good and pays a price p is
𝑈𝑖 (𝜎𝑖 , 𝑤 − 𝑝, 𝑔) = 𝑣(𝑔) + 𝑢(𝜎𝑖 , 𝑤 − 𝑝)
Again, we will show use Topkis’s Theorem. Note that the cross-partial derivative of
𝑈𝑖 (𝜎𝑖 , 𝑤 − 𝑝, 𝑔) is
𝜕 2 𝑈𝑖 (𝜎𝑖 , 𝑤 − 𝑝, 𝑔)
= −𝑢12 (𝜎𝑖 , 𝑤 − 𝑝)
𝜕𝜎𝑖 𝜕𝑝
Hence, our assumption that 𝑢12 ≥ 0 implies that the above expression is submodular, and
we conclude that p is decreasing in mood. The proof for when 𝑢12 ≤ 0 is analogous.
Proposition 3: If
𝜕𝑢𝑖 (𝜎𝑖 ,𝜋 )
𝜕𝜎𝑖
= 𝑢1 (𝜎𝑖 , 𝜋 ) is a convex transformation of 𝑢𝑖 (𝜎𝑖 , 𝜋 ), then the
willingness to pay for the gamble will be increasing in mood. If
𝜕𝑢𝑖 (𝜎𝑖 ,𝜋 )
𝜕𝜎𝑖
= 𝑢1 (𝜎𝑖 , 𝜋 ) is a
concave transformation of 𝑢𝑖 (𝜎𝑖 , 𝜋 ), then the willingness to pay for the gamble is
decreasing in mood.
Proof of Proposition 3:
Subjects were asked to choose and 𝑥 which solved the following equation
1
(𝑢 (𝜎 , 𝑤 − 𝑥) + 𝑢𝑖 (𝜎𝑖 , 2𝑤 − 𝑥)) = 𝑢𝑖 (𝜎𝑖 , 𝑤)
2 𝑖 𝑖
Let 𝑥(𝜎𝑖 ) be the function which gives the 𝑥 which solves this equation for different
moods 𝜎𝑖 . If we plug this into the above equation and take the derivative with respect to
𝜎𝑖 , we get
1
𝜕𝑥(𝜎𝑖 )
(𝑢1 (𝜎𝑖 , 𝑤 − 𝑥(𝜎𝑖 ) ) + 𝑢1 (𝜎𝑖 , 2𝑤 − 𝑥(𝜎𝑖 ) ) −
(𝑢2 (𝜎𝑖 , 2𝑤 − 𝑥(𝜎𝑖 ) )
2
𝜕𝜎𝑖
+ 𝑢2 (𝜎𝑖 , 𝑤 − 𝑥(𝜎𝑖 ) )) ) = 𝑢1 (𝜎𝑖 , 𝑤)
Rearranging this equation to solve for
𝜕𝑥(𝜎𝑖 )
𝜕𝜎𝑖
, we get that
1
𝜕𝑥(𝜎𝑖 ) 2 (𝑢1 (𝜎𝑖 , 𝑤 − 𝑥(𝜎𝑖 ) ) + 𝑢1 (𝜎𝑖 , 2𝑤 − 𝑥(𝜎𝑖 ) )) − 𝑢,1 (𝜎𝑖 , 𝑤)
=
𝜕𝜎𝑖
𝑢2 (𝜎𝑖 , 2𝑤 − 𝑥(𝜎𝑖 ) ) + 𝑢2 (𝜎𝑖 , 𝑤 − 𝑥(𝜎𝑖 ) )
Hence,
𝜕𝑥(𝜎𝑖 )
𝜕𝜎𝑖
> 0 is positive if and only if
1
2
(𝑢1 (𝜎𝑖 , 𝑤 − 𝑥(𝜎𝑖 ) ) + 𝑢1 (𝜎𝑖 , 2𝑤 −
𝑥(𝜎𝑖 ) )) > 𝑢1 (𝜎𝑖 , 𝑤).
Suppose that 𝑢𝑖1 (𝜎𝑖 , 𝜋 ) is a convex transformation of 𝑢𝑖 (𝜎𝑖 , 𝜋 ) (i.e., there is a convex
function 𝜑 such that 𝑢1 (𝜎𝑖 , 𝜋 ) = 𝜑(𝑢𝑖 (𝜎𝑖 , 𝜋 )) . By an application of Jensen’s
Inequality, we get
1
𝑢1 (𝜎𝑖 , 𝜋 ) = 𝜑(𝑢𝑖 (𝜎𝑖 , 𝜋 )) = 𝜑 ( (𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑥) + 𝑢𝑖 (𝜎𝑖 , 2𝑤 − 𝑥)))
2
≤
1
(𝜑(𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑥)) + 𝜑(𝑢𝑖 (𝜎𝑖 , 2𝑤 − 𝑥)))
2
=
Thus,
𝜕𝑥(𝜎𝑖 )
𝜕𝜎𝑖
1
(𝑢 (𝜎 , 𝑤 − 𝑥(𝜎𝑖 ) ) + 𝑢1 (𝜎𝑖 , 2𝑤 − 𝑥(𝜎𝑖 ) ))
2 1 𝑖
> 0 and the willingness to pay for the gamble is increasing in mood.
Suppose that 𝑢1 (𝜎𝑖 , 𝜋 ) is a concave transformation of 𝑢𝑖 (𝜎𝑖 , 𝜋 ) (i.e., there is a concave
function 𝜓 such that 𝑢1 (𝜎𝑖 , 𝜋 ) = 𝜓(𝑢𝑖 (𝜎𝑖 , 𝜋 )). Again, by using Jensen’s inequality, we
have
1
𝑢1 (𝜎𝑖 , 𝜋 ) = 𝜓(𝑢𝑖 (𝜎𝑖 , 𝜋 )) = 𝜓 ( (𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑥) + 𝑢𝑖 (𝜎𝑖 , 2𝑤 − 𝑥)))
2
≥
=
Thus,
𝜕𝑥(𝜎𝑖 )
𝜕𝜎𝑖
1
(𝜓(𝑢𝑖 (𝜎𝑖 , 𝑤 − 𝑥)) + 𝜓(𝑢𝑖 (𝜎𝑖 , 2𝑤 − 𝑥)))
2
1
(𝑢 (𝜎 , 𝑤 − 𝑥(𝜎𝑖 ) ) + 𝑢1 (𝜎𝑖 , 2𝑤 − 𝑥(𝜎𝑖 ) ))
2 1 𝑖
< 0 and the willingness to pay for the gamble is decreasing in mood.
Proposition 4: If 𝑢12 < 0, then the transfer by sender and amount returned by the
receiver are both increasing in mood. If 𝑢12 > 0, then the amount returned by the
receiver is decreasing in mood. If 𝑢1 is a concave transformation of 𝑢𝑖 and 𝑢12 > 0,
then the transfer by the sender is decreasing in mood.
Proof of Proposition 4:
Let us first focus on the case of the receiver. Suppose that the receiver j has received 3t
and must choose c (i.e., how much to send back). His utility function is given by
𝑈𝑗 (𝜎𝑗 , 3𝑡, 𝑐) = ∫ [𝛽𝑢(𝜎𝑗 , 3𝑡 − 𝑐) + 𝑢(𝜎𝑖 , 𝑤 − 𝑡 + 𝑐)]𝑑𝜇(𝜎𝑖 |𝑡).
𝑖
We note that this problem is very similar to that of the dictator game. The receiver gets to
choose how much to share, just as the dictator did.
If we take the cross-partial derivatives, we note that
𝜕 2 𝑈𝑗 (𝜎𝑗 , 3𝑡, 𝑐)
= ∫ [−𝑢𝑗,12 (𝜎𝑗 , 3𝑡 − 𝑐)]𝑑𝜇(𝜎𝑖 |𝑡)
𝜕𝜎𝑗 𝜕𝑐
𝑖
As in the dictator game, Topkis’s Theorem gives us our desired results for the receiver.
Now we move back a step to the sender’s problem. Since our sender is rational,
he can predict what the receiver would return in a given mood. Let 𝑐(𝜎𝑗 , 𝑡) be the amount
returned by a receiver in mood 𝜎𝑗 when he is sent an amount 𝑡. Since receivers and
senders are randomly matched, the sender is not aware of the receiver’s mood and must
take an expectation over the receiver’s possible moods. Hence, the sender’s utility when
he is in mood 𝜎𝑖 and sends 𝑡 is given by
𝑈𝑖 (𝜎𝑖 , 3𝑡, 𝑐) = ∫ [𝛽𝑢 (𝜎𝑗 , 3𝑡 − 𝑐(𝜎𝑗 , 𝑡)) + 𝑢 (𝜎𝑖 , 𝑤 − 𝑡 + 𝑐(𝜎𝑗 , 𝑡))] 𝑑𝜇(𝜎𝑗 ).
𝑗
The problem of the sender is thus a bit more involved than our previous problems. The
sender must consider how much the receiver will return for a given amount 𝑡. First, let us
think about the problem when we assume that 𝑢12 ≤ 0 and suppose that we have an
interior solution (i.e., 𝑡 < 𝑤). Then there must be some receivers who are returning at a
rate less than one, by which we mean 𝑐(𝜎𝑗 , 𝑡) < 𝑡. If this were not so, than the sender
could increase 𝑡 slightly and be better off. Consider a slight increase in 𝜎𝑖 . Now the
marginal utility of money is decreasing for the sender’s egoistic utility function 𝑢.
Sending more to those receivers who return at a rate less than one increases the receiver’s
egoistic utility function 𝑢 at the same rate as before while the loss to the sender is
smaller. For those receivers who return at a rate higher than one, the sender would still
prefer to give more. Hence, increasing 𝑡 is beneficial and the sender’s 𝑡 is increasing in
mood 𝜎𝑖 .
For the opposing case, 𝑢𝑖,12 ≥ 0, the same kind of logic doesn’t imply. When
mood increases, the sender’s egoistic marginal utility of money is increasing. If the
sender knew he were facing a receiver who returns at a rate less than one, then he would
like to keep more for himself by decreasing 𝑡. If the sender knew that he were facing a
receiver who returns at a rate higher than one, then he would like to increase giving.
Thus, the two types of receivers are creating different incentives for the sender and we
will need additional assumptions in order to know which dominates.
Fortunately, we can do this by noting the similarity between the sender’s problem
and that of a gamble. The sender is gambling on what kind of receiver he will face (we
can think of 𝑐(𝜎𝑗 , 𝑡) as the outcome of the gamble). Thus, our assumptions that ensure
risk aversion is increasing will ensure that increasing 𝑡 is less attractive. The amount sent
by the sender will be decreasing in mood 𝜎𝑖 .