Smiling is a Costly Signal of Cooperation Opportunities:
Experimental Evidence from a Trust Game*Samuele Centorrino,1 Elodie Djemai,1 Astrid Hopfensitz, 1 Manfred Milinski,2 Paul
Seabright1
This version: 11th April 2011
Abstract

We test the hypothesis that "genuine" or "convincing" smiling is a costly signal thathas evolved to induce cooperation in situations requiring mutual trust. Potential
trustees in a trust game made video clips for viewing by potential trusters before thelatter decided whether to send them money. Ratings of the genuineness of smiles varyacross clips; it is difficult to make convincing smiles to order. We argue that smilingconvincingly is costly, because smiles from trustees playing for higher stakes are
rated as significantly more convincing, so that rewards appear to induce effort. We
show that it induces cooperation: smiles rated as more convincing strongly predict
judgments about the trustworthiness of trustees, and willingness to send them money.
Finally, we show that it is a honest signal: those smiling convincingly return moremoney on average to senders. Convincing smiles are to some extent a signal of the
intrinsic character of trustees: less honest individuals find smiling convincingly moredifficult. They are also informative about the greater amounts that trustees playing forhigher stakes have available to share: it is harder to smile convincingly if you haveless to offer.

* Any correspondence should be addressed: Paul.Seabright@tse-fr.eu. The authors
are grateful to Lecio Costa-Simoes for excellent and very professional filming inToulouse; to Marie-Claire Villeval and her team at GATE at the University of Lyon,
especially Sylvain Ferriol, for their hospitality, encouragement and technical support;
and the Max Planck Institute for Evolutionary Biology in Plön for financial support.
We thank Ruxanda Berlinschi, Julia Bird, Claudia Capozza, Marie Lalanne, Maxime
Marty, Andrea Matranga, Racha Ramadan, Karine Van Der Straeten and Stéphane
Peysson for participation in pilot versions, and Jean-Louis Rullière, Alice Seabrightand James Tremewan for valuable comments on preliminary results. The usual
disclaimer applies.
1

Toulouse School of Economics, Manufacture des Tabacs, 21 allée de Brienne,
31042 Toulouse, France.
2

Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Str. 224306 Plön, Germany.

1

I. Introduction

The man who indulges us in this natural passion, who invites us into his heart, who,
as it were, sets open the gates of his breast to us, seems to exercise a species of
hospitality more delightful than any other. No man, who is in ordinary good temper,
can fail of pleasing, if he has the courage to utter his real sentiments as he feels them,and because he feels them.
Adam Smith – The Theory of Moral Sentiments1

Smiling is a form of behavior that is found in all human societies2. It appears to be
more elaborate and more central to communication in humans than in any otherspecies, and to play an important part in judgments of individuals about the characterand general trustworthiness of others. There is no scientific consensus as to why it has
evolved to be like this, nor about what it is in smiling that makes it an appropriate
basis for judgments of others. There is consensus, however, about a number of its
characteristics. First, viewers perceive smiles as varying in their degree of"genuineness" or "convincingness". Since the work of Duchenne (1862) and Darwin(1872) in the 19th century it has been known that smiles perceived as genuine (known
as enjoyment or "Duchenne" smiles) are characterized by use of the orbicularis oculi(which surround the eyes) in combination with the zygomatic major (which raises thecorners of the mouth); symmetry is also an important characteristic of Duchenne
smiles. More recent research focuses on the importance of temporal dynamics suchas smile onset, apex, and offset durations for perceived genuineness3. Second,
Duchenne smiles are not under straightforward voluntary control. Some individuals
can make them more often and more easily than others, and all individuals find themeasier to make when in certain affective states. Such states include a relaxed mood in

1

Smith (2000), p.497.
See Darwin (1872), Ekman (1982), Niedenthal et al. (2010).
3
See Krumhuber et al. (2007).
2

1

general, and feeling well disposed to a communication partner in particular. Third,
smiles induce mimicry, both in the sense that individuals viewing smiles by others
have an increased tendency to smile themselves4, and in the sense that individuals
trying to make a good impression on others (as when posing for photographs) makean effort to smile well. Although individuals can smile when alone, smiling behavior
seems to be a form of communication. But if so, what is it communicating, and why
have we evolved a form of communication behavior that is under such imperfect
conscious control?

In this paper we test the hypothesis that smiling is a form of costly
communication (costly in a sense we make precise below) that has evolved to induce
cooperation between individuals in situations requiring mutual trust. According to thisview, the necessary costliness of smiling is precisely the reason why it is under such
imperfect conscious control. This hypothesis is not original to us5, but to ourknowledge it has not previously been subjected to a comprehensive experimental test.
By a "comprehensive" test we mean one that tests separately the three component
hypotheses that smiling "genuinely" or "convincingly" is:a) costly to the smiler in terms of effort,b) causally effective in inducing the target of the smile to cooperate with the smiler,andc) a reliable signal of the likely benefits to the target of cooperating with the smiler.

45

See Niedenthal et al. (2010).
See Owren & Bacharowski (2001).
2

Component a) is important in distinguishing this hypothesis from twoalternative views: first, that smiling is a form of costless communication that solves
pure coordination problems (like "cheap talk"), and secondly, that it is notcommunication at all but merely an outward sign of an inner emotional state (likeblushing, say). Component b) is important in explaining why human beings shouldhave evolved the habit of communicating in this costly way. Component c) is
important to explain why human beings should also have evolved the tendency to be
influenced by the smiles of others. There exists some corroborating evidence forcomponents b) and c) in the literature, though in neither case have the components inquestion been rigorously tested. Shug et.al. (2010) demonstrate that individuals who
display relatively cooperative tendencies as proposers in an ultimatum game are more
emotionally expressive in the face of unfair treatment by others than those who donot, including in the tendency to emit Duchenne as opposed to non-Duchenne smiles,
which is consistent with component c). However, there is no test of any association
between their emission of Duchenne smiles and their gestures of cooperation, and thesample is small (only 20 participants). Component b) is the only one of the three to betested directly, and has received significant support (Scharlemann et al. 2001;
Johnston et al. 2010). However, the first of these studies uses still pictures, amethodology that captures only a small part of the complex interactions involved in asmile. The second study indeed uses video clips but tests cooperation in a prisoners'
dilemma (where non-cooperation is a dominant strategy, unlike in the trust game);furthermore it does so on the basis of comparison of only two clips and cannot control
for other differences between clips.

Costly signaling has been extensively studied both in economics since thework of Spence (1974), and independently in biology since the work of Zahavi3

(1975). A signal is any observable trait that imposes a cost on its bearer (a pecuniaryor non-pecuniary effort cost in economics, a fitness cost in biology) but which
reliably indicates the presence of some advantageous hidden trait because the signal ismore costly for those individuals that do not possess the trait than for those who do6.
The benefit from signaling the hidden trait is that it attracts partners in mating or insome other mutually beneficial cooperative activity, and the benefit to the signaler ofdoing so must exceed the cost of the signal. So what is the hidden trait that is signaled
by smiling? In economic exchange the hidden trait could be an intrinsic characteristicof the smiler (such as their degree of altruism or tendency to display reciprocity7), or acharacteristic of the situation in which the smiler finds herself (such as the size of thepie she is proposing to share with the smilee).

How can smiling convincingly be the result of costly effort? Emitting somekind of smile requires rather little effort. One might imagine that making the smile
appear genuine was something that people could either do or not do, depending bothon their personal characteristics and on features of the situation outside their control,
but in any case outside the reach of their conscious will and therefore requiring no
more effort than for a rudimentary smile. However, consider what happens in job
interviews. Candidates can rarely produce convincing smiles to order, but instead they
typically make a strong effort to be agreeable, to pay close attention to theirinterviewers, and interact, both conversationally and through body language in such a
way as to make smiling "come naturally"; there is also some evidence that smiling
can itself alter felt emotional states8. Robert Trivers (2000) has hypothesized that selfdeception may be a means of reducing the cognitive load required to deceive others
6

See Grafen (1990).
See Gintis et al. (2003).
8
See Strack et al. (1988).
74

successfully, a cognitive load that has been described in detail by Vrij et.al. (1996).
Our hypothesis, therefore, is that non-Duchenne smiles require negligible effort but
Duchenne smiles require significant cognitive effort, to a degree that probably varies
between individuals, unless the smiler is already in a state that makes them more
likely to be cooperative towards the target of the smile.

To test our hypotheses, and to help determine the kind of hidden trait signaled
by smiling, we observe non-verbal behavior in an economic experiment involving
trust. In a trust game9 subjects (called "senders") each decide whether to send a sumof money to a second player, called a trustee. If they do so the sum is tripled, and thetrustee may choose to keep the money, or to return some part of it to the sender. In
particular, trustees face a choice between returning the sender’s original stake, whichcorresponds to a form of reciprocating behavior, and returning an additional 50% of
the stake so as to share the total surplus equally, which is a considerably moregenerous form of behavior.

The innovation in our version of the trust game is that we asked trustees tomake short video clips to be shown to senders before the senders took their decision;
84 subjects produced a total of 168 clips. Earlier studies have observed the impact of
seeing still pictures of partners in trust games and results indicate that pictures ofsmiling partners induce more trust10. Whether trustworthy partners can be detectedfrom still pictures is controversial and might depend on the moment when the picture
was taken11. Dynamic pictures might in this respect be better12. However no earlier
study observes reactions to dynamic pictures of trustees in a situation where video
9

See Berg et al. (1995).
Scharlemann et al. (2001).
11
Yamagishi et al. (2003), Verplaetse et al. (2007).
12
Brown et al. (2003).
10

5

messages were obtained from participants knowing that this was their only means toconvince their partner to cooperate.

We said nothing to trustees about smiling, but asked them to present
themselves in a simple common format to the senders in such a way as to convince
the latter to send the money. We showed the clips to the senders and asked them totake a decision about sending the money, then to rate the clips along a number ofdimensions, one of which was the perceived genuineness of the smile. As our results
indicate, this turned out to play a crucial role in the interaction between the sender andthe trustee.

The outline of our paper is as follows. In section II we review the literature on
smiling and on costly signaling to situate our paper in the context of prior work. In
section III we set out a simple formal model of a trust game in which trustees cansend a costly signal prior to the decision taken by trusters. We use this model toderive testable empirical predictions, and in particular the three component
hypotheses described above. In section IV we describe our experimental method. In
section V we present the results. Section VI concludes.

II. Literature Review

Even though our investigation of smiles as a costly signaling device is novel, a large
number of studies in economics and psychology have in recent years investigated theimportance of emotions in games. Inspired by results from affective sciences thatemotions are not just some random noise but an essential part of the decision making

6mechanism (Damasio, 1994), theoretical and experimental work has turned toinvestigate the effect of different emotions and other visceral factors on decision
making (Elster, 1998; Loewenstein, 2000; Kahneman, 2003; Frijda et al., 2004).
While the focus has been mostly on such negative social emotions as anger and guilt(Bosman and van Winden, 2002; Sanfey et al., 2003; de Quervain et al., 2004;
Hopfensitz and Reuben, 2009), increasing attention has been given to the use of
rewards and the experience of happiness (e.g. Kahneman et al., 1999; Frey, 2008;
Frey and Neckermann, 2009). Smiles are on the one hand an expression ofexperienced happiness and might be used as a coordination device (Manzini et al.,2009), but smiling is also an important component in social exchange (Owren &Bacharowski, 2001).

To detect whether an interaction partner can be trusted we can either rely on
third party information regarding the target individual’s reputation (Sommerfeld et al.,2008) or use visual signals concerning the individual’s character (Frank, 1988).
Indeed it has been observed that players in a trust game are willing to spend money on
visual information of their partner (Eckel and Petrie, 2008). Which visual information
is used is however not clear, but honest smiles could play a crucial role in that respect(Cohn and Smith, 2004). Because activation of the orbicularis oculi (one of the mainmarkers of Duchenne smiles) is believed to be under emotional and involuntary
control (Ekman and Friesen, 1982), it might therefore be an informative signal.

Whether smiles are indeed perceived as a signal of trust has been subject of anumber of recent experimental studies. Scharlemann et al. (2001) presented
participants in a modified trust game with static pictures of sixty photographic

7

models, which were portrayed smiling and with a neutral expression. The results
show that smiling pictures are more often trusted than their non-smiling counterpart(68.3% versus 55%). Similarly Mehu et al. (2007b) assess which characteristics areassociated with honest smiles. Fifty faces (half male and half female) were rated
concerning ten different attributes: attractiveness, generosity, trustworthiness,competitiveness, health, agreeableness, conscientiousness, extroversion, neuroticism,and openness to experience. The findings show that Duchenne smiles played asignificant role in the assessment of generosity and extroversion. Further, van 't Woutand Sanfey (2008) observe that judgments of facial trustworthiness is related tosending money in a trust game. In this study, ratings of player trustworthiness (basedon showing a photograph of each player) were a significant predictor of how muchmoney these players were given in a standard one-shot trust game. In a follow-up
study, Chang et al. (2010) replicate these findings in a repeated trust game.

One drawback of such studies is the use of static pictures of smiles. Indeed
Scharlemann et al. conclude that “the use of still photograph biases the perception of
the facial expressions. [...] Dynamic footage of facial expression may be a more
appropriate mean of eliciting naturalistic viewing patterns”. Such facial dynamics
have been studied by Krumhuber et al. (2007). In their study participants played atrust game against partners that were presented with short video clips. These video
clips were manipulated so as to obtain a true smile, a fake smile and a neutral
expression for the same face. Indeed partners displaying an authentic smile were rated
higher on perceived trustworthiness, than their fake smiling or non-expressive
counterparts.

8

Another drawback of the above studies is that they can only be used to assessthat smiles elicit trust in others. Whether smiles are truthful indicator of a person's
intentions is essential for the importance of smiles as a social signal.

Altruism and cheater detection in social dilemmas has received considerable
attention in economics and biology (Cosmides and Tooby, 1992; Gintis et. al., 2001).
It is evident that signals that can be used to identify altruists might quickly be imitatedby non-altruists and would thus not be reliable (Fehr and Fischbacher, 2005). One
suggestion is that altruism as such can serve as a reliable signal of trustworthiness(Smith and Bliege Bird, 2000; Gintis et al., 2001; Lotem et al., 2003). However inmany situations behavior of the interaction partner cannot be observed. In order todetect trustworthy partners reliably in one-shot interactions, it is therefore necessary
to base decisions on verbal or non-verbal signals sent by the partner.

Brown and Moore (2002) stress that honest signals with reliable emotional
basis may be needed to guarantee positive intentions of a counterpart. This leads tothe importance of 'emotional expressivity' i.e. the ability to accurately communicate
your internal feeling state (Boone and Buck, 2003). However to be reliable, thesesignals must be costly and therefore difficult to mimic. Smiles and especially honest
smiles might be just that. Brown et al. (2003) were the first to observe that videos
from self reported altruists are rated differently by neutral observers than videos of
non-altruists. Further an analysis of video recordings from altruists and non-altruists
showed that self reported altruists showed more orbicularis oculi activity and more
symmetric smiles (see also Oda et al.; 2009).

9

To test whether smiles are indeed related to actions in a game requires thus theobservation of both behavior and facial expression. Mehu et al. (2007a) suggest thathuman smiles are more prevalent in situations which involve sharing or exploitationsof resources. By filming sixty pairs of friends during a neutral and a sharing decision
they observe that significantly more Duchenne smiles are produced during sharing
situations. Thus situations requiring sharing elicit smiles and laughter (Mehu andDunbar, 2008). Whether smiles are also predictive of a specific sharing decision has
so far not been studied and is subject of our work.

The model we develop hypothesizes that individuals may be motivated, to agreater or lesser degree, both by reciprocity and by altruism. There is a large literatureaddressing ways of incorporating social preferences in individual utility functions (seeSobel, 2005, for a survey). It is safe to say that there is no consensus as to theappropriate way of modelling such motivations, and it is emphatically not ourintention to propose a general theory here. For instance, in many models of behavior
in public goods games, individuals are considered to be motivated either byreciprocity or by altruism but not both (Fehr, Fischbacher & Gaechter, 2003); this is a
useful device for focusing on the distinction between unconditional contributors andconditional contributors. Other papers (Hwang & Bowles, 2010; Brülhart & Usunier,2004) hypothesize that individuals may have both motivations simultaneously todifferent degrees, and that is the approach we adopt here. This is a plausible andparsimonious way to capture the phenomenon, clearly present in our data, that sometrustees are willing to return the same amount that was sent to them, while others
adopt a more generous approach. We model this more generous approach as
indicating relatively high altruism, but it could equally well arise from inequality

10aversion and in our experiments the two interpretations would be observationallyequivalent; the choice between them is not what interests us in this work.

III. A model of costly signaling prior to a trust gamea. Outline

There are two players, A and B. To avoid confusion we shall refer to A as “he” and to
B as “she”, though in the experiment individuals of both sexes take each role.

Player A receives a stake of value s and must decide whether or not to send it
to player B (we consider s to be greater than or equal to 1, without loss of generality).
If it is sent it is multiplied by three, and player B may choose to send some part of the
new enlarged stake back to A.

Player A’s decision will be influenced by his beliefs about Player B along two
dimensions – how much Player B cares about strong reciprocity, and how altruistic
she is (we make these terms precise below). With respect to strong reciprocity, Player
B may be one of two types θ ∈ (L,H); for simplicity we assume there are equal
proportions of the two types in the population, though nothing of importance turns on
this. H-types have stronger preferences for reciprocity than L-types (we can call theseHigh Reciprocators and Low Reciprocators respectively). With respect to altruism,
Player B has a component of her utility that is a stochastic function of the amount she
sends back to A. Player B knows her own type at the start of the game, and notably
when she makes a video clip in order to persuade player A to send her his stake.

11

If player A sends the stake, player B must decide to send back to player A amultiple m of the original stake, where m ∈ (0,1,1.5). Since the stake has been
multiplied by 3, this means that she has a choice between keeping half the stake,keeping two-thirds of it, and keeping all of it.

The order of moves is therefore as follows: first B makes a clip which
involves sending a costly signal. Then A views the clip and forms a belief about B’s
type based on the evidence from the clip. If A chooses not to send the stake the gameends, A keeps the stake and B receives a zero monetary payoff (and a total payoff that
may include a cost of effort involved in sending the signal). If A chooses to send thestake then B finally chooses what multiple of the stake to return to A, and the gameends.

As is standard we solve the game backwards from the end.

b. Player B’s move

We model player B’s motivation for returning a multiple of A’s original stake using arandom utility function. It is separable in money and in two types of social preference.
The first social preference is for strong reciprocity, which we model as a fixed utility
derived from sending back at least the original stake to player A, but not otherwise
varying according to the amount sent. This utility, which differs between types, isgiven by  , where 1      0.5.

12The second motivation is altruism, which is increasing in the amount sent backby B to A (it can be thought of as reflecting B’s pleasure at knowing that she isincreasing A’s payoff). We model this as a utility that is a multiple β of the amountreturned, plus a random error term ε. The coefficient β is itself random and may begreater or less than one (capturing the fact that, of players who return at least somemoney, some return only the original stake while others return a larger amount).
Specifically,

0.5,1.5 with probability 1   ,  . We assume that    toreflect the fact that individuals with a greater propensity for reciprocity are also likely
to be more altruistic.

We therefore model player B’s utility function as follows:1

  3        

if m>02  3

if m=0where the error term ε has a zero mean, and is uniformly distributed between -0.5 and+0.5.

It is straightforward to see that if β=1.5, player B will always choose m=1.5,
since his utility is always strictly increasing in m. Thus either type of player will
choose m=1.5 with probability  .

13

If β=0.5 on the other hand, player B’s utility is strictly decreasing in m once m
is positive. Thus B will either choose m=0 or m=1. The probability of choosing m=1
is therefore the probability that:

3

 



2



If s=1,    is distributed uniformly on [0,1], so the probability that m=1 isjust 1    .


If s=2,   is distributed uniformly on [0.5,1.5], so the probability that m=1


is just 1     0.5.

We can write this probability as a function of s, namely as1    

 


.

We therefore summarize in Table 1 the probabilities of choosing different
values of m according to whether the player is of high or low type and whether the
stakes are high or low, as follows:[Table 1 here]14

c. Player A’s move

Player A will send the money if the expected value of doing so is greater than the surevalue of keeping it.

We also model player A’s decision using a random utility function. We ignore
altruism on the part of player A13 and consider his utility as given by his expected
payoff plus an error term η which is uniformly distributed between –e and 0 (we canconsider this as a way of allowing for risk aversion while keeping the advantages oflinear utility: η=0 corresponds to risk neutrality, while η=-e is the highest risk
aversion in the population).

Player A’s decision then depends on γ, his subjective probability of facing a
High Reciprocator type. He will send the money if the gain from receiving a net profitof half the original stake, multiplied by the probability that B chooses m=1.5, exceeds
the loss of the whole original stake, multiplied by the probability that B chooses m=0.
Formally, A sends the money iff:4

0.5"  1  "   η
1"1    2   
13





1  "1   

1
2

  

One reason for doing so is that it is plausible that A players would be less likely tofeel altruism towards those B players they believed were likely not to return them any
money, and therefore the calculation how likely the B player is to return money
precedes and predetermines the effect of altruism on player A’s decision. This is a
hard phenomenon to analyze, and we have chosen to ignore it to focus on the issues
more central to this paper.
15

Notice that the right hand side of equation (4) is strictly increasing in s. Thismeans that, for given γ, player A is less likely to send the money when the stakes arehigh than when they are low. Thus if we observe a higher probability of sending themoney when the stakes are high, this must mean that A players have higher levels ofγ.

Because of the uniform distribution of η, we can write the probability that an

A player sends the money, given the value of γ, as $% , where5 $% &0.5"  1  "   "1   1  /2     1  "1   1  /2    ()

Differentiating (5) with respect to γ yields:

6

+$% &0.5     1   1  /2     1   1  /2    (

0
+"
)

Differentiating (6) with respect to s yields

7+  $%    

0
+"+
2)

16

which shows that a given increase in γ will result in a larger increase in $% when s=2
than when s=1. So higher stakes make the probability of sending the money moresensitive to player A’s subjective probability that player B is the High Reciprocator
type.

d. The signal

Now consider the making of the video clip. Player B invests effort e, which has anincreasing convex cost - ), where - ) . - ) for all positive values of e.

This effort produces a smile whose quality is related to the effort exerted via
an increasing function /), 0, where 0 is a random variable, and the probability

distribution function 1/|) has the Monotone Likelihood Ratio Property.

We begin by assuming that this smile has a predictable positive effect on
player A’s subjective probability γ that player B is the High Reciprocator Type.
Without such an effect neither player would have any incentive to exert any effort at
all. This effect can be represented by the “smile function” "  "/, where " 3  0.
The function "/ need not be concave but if not - ) must be sufficiently convex

to yield a unique interior solution.

We next go on to show that if player B knows this, and if the quality of thesmile responds to her effort, she has reason to invest effort in smiling in such a way

17that the smile will indeed be a positive signal not just of her effort but also of theprobability that she is the High Reciprocator type. Thus A’s tendency to display
greater trust in individuals who have more convincing smiles is one that could be
expected to evolve under natural selection since it would correspond to a realempirical regularity.

To see this, write 4 for the expected utility B will receive if player A sends

6
the money and note that 4 5 4 .14 Writing )
for the optimal choice of effort by aplayer B who is playing for stake s and is of type θ, since - ) . - ) it follows
that

8

6
6
)
 )

It is also straightforward that 4  4 , and therefore that
9

6
6
)
 )

Any function /), 0 that has the Monotone Likelihood Ratio Property will
imply that the conditional probability that Player B is the High Reciprocator Type isincreasing in the value of /), 0. To see this note that Bayes’ Law with a uniform
prior implies that

14

The reason why the expected utility for B players of type H is higher than the utility
for those that are L is that they have more altruism payoff than L players do. They
could choose to return the same amount as L players do and would get at least as
much utility as L players from doing so. In fact they choose to return more (inexpected terms) than L players do, so their expected utility must be higher.
18

10

9:;<  =|/), 0 

1

6 ⁄
6 
1  1/|)
1/|)which is monotonically increasing in / by equation (8) and the Monotone Likelihood

Ratio Property. This means that an increasing smile function "/ is indeed
consistent with natural selection and therefore we can predict, substituting the smile
function into equation (6), that

11

+$%
0
+/

Finally, given that the convincingness of smiles is the result of effort in theway described in equation (10), we can calculate how the expected gain to A fromsending money is related to smile quality. We write the expected gain to A fromsending the money, conditional on smile quality as follows

12? @ |/,  A9<  =|/B C1.5.   1    

1  
D
2

A1  9<  =|/B E1.5.   1    

We can rewrite (12) as

19

 


F  13

? @ |/,  A9<  =|/B C1.5.                G  C1.5.   1    

1     2

1  
D2and therefore we can write the derivative of ? @ |/,  with respect to 9<  =|/
as

14

+? @ |/,  &  0.5                (+9<  =|/

which is strictly positive because(15)&  0.5                (   0.5      1      1    &  0.5          (and the expression on the RHS is positive for any s ≥ 0.5.

From this it follows, given (10), that16+? @ |/, 
0
+/

H/, 

which is just the statement that the expected gain to player A from sending the staketo player B is increasing in the perceived convincingness of player B’s signal.
20

e. Testable implications

Our test of the hypothesis that smiling convincingly is a costly signal, therefore,amounts to testing the following:

The costliness of the signal: inequality (9);The effectiveness of the signal in inducing cooperation: inequality (11);The informativeness of the signal: inequality (16).

IV. Experimental Methods and Data Description

We use a simplified version of the original trust game, proposing senders a binary
choice of trust or no trust and trustees three different return options15. Sessions fortrustees were conducted first, to allow them to record their video messages. Theiractions were obtained by the strategy method at the same moment. Decisions for
senders and trustees were incentivized and earnings were according to their partners'
decisions. Therefore payout for trustees did not take place until after senders had
made their respective trust decisions.

Video messages were produced by eighty-four volunteers aged between 18
and 35 years recruited from the general population in Toulouse, France. We told
trustees they would face two different but unknown partners who might be persuaded
to send them a sum that would be tripled if they did so. The difference between thetwo games was that in the first, trustees recorded their video message before being
15

See Hopfensitz & Reuben (2009).
21

informed about the precise payoffs and thus before taking their decision, while in thesecond game they recorded their message after taking their return decision16. The
trustee had to choose between returning nothing, the sender's original stake or 1.5
times the sender's original stake (thus half the total amount). Trustees were randomly
split into two payoff treatments: stakes in the Low treatment were 4 euros, and stakes
in the High treatment were 8 euros. Video clips were made on a professional TV
platform, and a practice clip helped participants to become familiar with theenvironment. A total of 168 video clips was obtained, two for each trustee. Verbal
messages during clips were standardized by giving a predetermined sentence totrustees that had to be memorized. To make the message natural for trustees they
included in this sentence their name, age and occupation and were reassured that the
precise wording did not matter. Video clips lasted around fifteen seconds on average,
with the fastest at around ten and the slowest at around twenty seconds.

Senders' behavior and evaluation of video clips were obtained in two waves ofexperiments conducted in a different experimental laboratory to minimize the risk that
senders might recognize trustees. A total of 198 student participants were recruited at
the University of Lyon; 84 senders participated in the first wave and 114 in thesecond. The difference between the two waves was that participants in the first wave
were matched with trustees and their decisions determined trustees' payoffs.
Participants in the second wave made trust decisions and were paid according to

16

These two treatments were always presented in the same order, due to theimpossibility of having participants first play a game where they are informed about
payoffs and then a game where they do not know about the different payoff options.

22trustees’ initial decision. Observations from the first wave therefore concern games
where sender and trustee faced the same stake size. In the second wave senders were
informed only that trustees might return nothing, their initial endowment or 1.5 times
their endowment. The actual stake size of their partner was varied: half of eachsender's video messages came from participants in the High stake treatment and halfcame from the Low stake treatment.

In the first and second waves each sender viewed a total of 42 (respectively28) clips in two series of 21 (resp. 14). For each clip the sender was asked to decide
whether to send money to the trustee, and then to rank the trustee on an 8-point scalealong a number of dimensions including how much they smiled, how genuine were
their smiles, their attractiveness, their trustworthiness, their intelligence and their selfconfidence. Senders were matched at random with one of the trustees from eachseries and received payoffs determined by the actual decision of this real partner. To
ensure anonymity for trustees it was not revealed which of the clips viewed had been
selected to determine senders' payoffs. From the first wave a total of 21 decisions andratings concerning each of the 168 clips was obtained. In the second wave senders
were presented with one of three different payoff treatments (Low: 4 Euro; High: 8Euro; Super High: 12 Euro) and made half of their decisions concerning partners fromthe Low and half concerning partners from the High trustee treatment. From the23second wave an average of 19 decisions and ratings for each clip were obtained17.
Figure 1 summarizes the choices made by the participants. [Figure 1 here ]All results reported use the pooled data from the two waves of the experiment.
A dummy variable distinguishing the two waves was never significant in any
specification, indicating that the two waves were conducted under indistinguishable
conditions.

[Table 2 here]

Table 2 summarizes the characteristics of our participants for each group of
players. The first column reports the means and standard deviations for the senders.
This subsample is exactly gender-balanced, the average age is 22 years old and 92%
are currently students. For a given sender, the proportion of decisions for which she
decided to send money ranges from 0 to 1. Of the 198 participants, 3 participants
decided to send money to every partner, and 20 decided never to send money. On
average, each sender decides to cooperate with 37% of their partners. Column (2)concerns the trustees, who are 25 years old on average. The sample of trustees comesfrom a less homogeneous population than the senders since only 46% are students.
The sample of trustees is fairly balanced with 55% of women. As described above,
the trustees recorded two video clips and made a decision about how to share the pie
for each clip. In the first decision (made after the first clip), 55% of the participants

17

Owing to some volunteers' not turning up for their session of the experiment there

was a slight variation in numbers of ratings per clip: the clips in our dataset have an
average of 40 ratings each, with a minimum of 38 and a maximum of 45.

24

decided to share equally the amount received multiplied by 3, 31% decided to sendback the original stake to the sender and to keep 2/3 of the total pie, and the remaining
14% decided to return nothing. In the second decision (made before the second clip),the distribution suggests a slight shift from equal sharing to sending nothing.

V. Results

Figure 2 shows a comparison of High and Low treatments of trustees in terms of theaverage ratings by senders of the genuineness of their smiles, their averagetrustworthiness rating, the proportion of senders who decided to send money, and the
proportion of trustees who chose to return at least some of the money they received.
The latter is a measure of their being motivated by social preferences, since trustees
had nothing financially to gain from returning the money to senders.

[Figure 2 here]

Figure 2 indicates that trustees under the High treatment (playing for twice thestakes of those under the Low treatment) are perceived as having more genuine smiles
and as being more trustworthy, and are associated with a higher percentage of senders
sending money, although a smaller percentage of trustees under the High treatment
actually return any money to the senders. It might be thought that the positive
correlation of the High treatment with smile genuineness and with selfish behavior
would imply that genuine smiles are positively correlated with selfish behavior.
However, Figure 3 indicates that this is not so. The explanation is that those in the25

High group who succeeded in making genuine smiles were not a random subset of
those in the High treatment; they were a more unselfish group than those who did not
succeed.

In Figure 3 clips are divided into those whose smiles were given averageratings above 5 (46% of the clips) and the rest. Clips with smiles perceived as genuine
were given higher ratings for trustworthiness, attractiveness and intelligence, andwere associated with a higher willingness to send money, but were also associatedwith a higher willingness to return some money to senders. So overall it appears thatthe High treatment created both a higher incentive to smile in a way perceived as
genuine, and a higher incentive to be selfish instead of returning money to the sender,
but that those who succeeded in smiling genuinely were those who were most likely
to return the money. As Figures 2 and 3 indicate, all of these comparisons weresignificant at 5% levels, and all but two were significant at well under 1%. We report
one-tailed p-values as the theory yields unambiguous predictions as to the sign of thedifference between the groups.

[Figure 3 here ]These comparisons by treatment cannot tell us whether there is a genuinecausal effect, for two reasons. First, because of the experimental design and the needto match senders with trustees in the same treatment in the first wave, there was somecorrelation in the overall data between the treatment of trustees and the treatment ofsenders: these two treatments need to be separately controlled. Secondly, it isimportant to control for a number of other dimensions along which clips differed,such as age, gender and so forth. For these reasons multivariate regression analysis isrequired. We consider our three component hypotheses in turn. In all cases, in order to26

avoid possible "justification effects" in which users' ratings are influenced by thedecisions they have already taken whether to send money to the trustees, we use asmeasures of smile quality, trustworthiness and attractiveness the average rating ofeach clip across all viewers, rather than the rating given by the individuals
themselves; this requires, however, that standard errors be calculated clustering by
clip.

Table 3 reports our tests of these three hypotheses. Equation A tests the
hypothesis that smiling convincingly is costly, and therefore is more likely to happen
under the High treatment when the returns to smiling convincingly are higher. The
treatment effect is significant at under 2%: 0.12 points, which is about 36% of one
standard deviation of the distribution of mean ratings by clip18.

[Table 3 here ]Other notable features of Equation A are that more convincing smiles areassociated with trustees who are rated as more intelligent, and also with older trustees.
Trustees with beards are rated as having less convincing smiles, and women with asignificant décolleté are rated as having significantly more convincing smiles (it is not

18

Though this is not a large effect, our treatment was itself not very large. Although

the difference between a 24 Euro maximum gain and a 48 Euro maximum gain may
seem important for an experimental session that lasted only around half an hour, themean gain to trustees in the High treatment (which was of course reduced if senders
did not send money, and if trustees returned part of the money) was just over 12
Euros, compared to a little over 7 Euros for those in the Low treatment.

27

clear whether the causal mechanism is via the psychology of the smiler or of theviewer). There is no significant effect of gender of either the sender or the trustee, norof perceived attractiveness of the trustee, and no effect of whether the clip is filmed
before or after the decision to return the money has been sent. These coefficients (likethose of other controls) are not reported, though the full specification is available
from the authors.

Equations B and C test the hypothesis that smiling convincingly induces
cooperation, the first by looking at what subjects say and the second by looking at
what subjects do. Equation B considers whether convincing smiles are associated with
judgments of greater trustworthiness. There is a massively significant correlation (tratio of over 8); a one-point deviation increase in smile quality is associated withslightly more than a half point increase in perceived trustworthiness. Perceived
intelligence is also positively and very significantly correlated with perceived
trustworthiness, and there is a significant effect of the High treatment independentlyof smile quality, suggesting that trustees are putting effort into other dimensions of
non-verbal communication as well. Equation C examines whether convincing smiles
lead to an increased probability of sending money to the trustees. Once again there isa massively significant association: a one point increase in smile quality leads to a
21% increase in the probability of sending the money, which is equivalent to a 7%
increase per standard deviation of smile quality. Perceived intelligence is again a very
important factor in the decision.

Equation D tests the hypothesis that convincing smiles are an informative
signal, that is, whether they are associated with higher gains to the sender fromcooperating with the trustee. We therefore regress gains from sending money on

28average smile quality, without other controls. The effect is small but positive (0.9Euros per one point increase, or 0.3 Euros per standard deviation) and significant atunder 1%19.
Finally, we investigate whether convincing smiles are associated more closelywith the amount of money the trustee has available to offer the sender or with the
intrinsic character of the trustee. We therefore regress a dummy variable for the Hightreatment on the mean smile quality, and in a separate equation we regress on thesame measure of smile quality a dummy variable indicating that the trustee takes anunselfish decision. The purpose is to see whether the smile quality is a reliable
informative of the amount available to share, and of the character of the trustee. As
reported in Table 4, the smile quality is positively related to both the size of the pie tobe shared and the unselfish behavior by the trustee. Two caveats are in order,
however. First, the coefficient on unselfish behavior by the trustee has a large
standard error so we cannot be confident in its measurement, which is not statisticallysignificantly different from zero at conventional levels (unlike the coefficient on theHigh treatment). Secondly, as we saw in Figure 2, unselfish behavior itself appears to
be influenced by the treatment, so we cannot be confident in treating it as a measureof the intrinsic character of the trustee. So we should conclude that smile quality is

19

In the decision equation (though not in the others) the treatment effect for senders islarge and highly significant, and follows an inverted-U shape: a High treatment makes
senders more likely to send money, but a Superhigh treatment makes them much lesslikely to do so.

29definitely informative about high cooperation opportunities, and may also signal the
intrinsic character of the smiler.

VI. Conclusions

We have tested three component hypotheses of the theory that smiling convincingly isa costly signal that has evolved to induce cooperation in situations requiring mutual
trust. All three components are supported by the evidence. First, smiling convincingly
is costly, because smiles from trustees playing for higher stakes are rated as
significantly more convincing, by over a third of one standard deviation; this strongly
suggests that they are produced when there are rewards to the additional effort
required. Secondly, we show that smiling convincingly induces cooperation: smiles
rated as more convincing are strong predictors of judgments about the trustworthinessof trustees, and of the revealed willingness to send them money. Finally, we show thatsmiling convincingly is an informative signal: those smiling convincingly return moremoney on average to senders. It is clearly informative of the amount the trustee hasavailable to share with the truster; there is weaker evidence that it may also be asignal of the intrinsic trustworthiness of the trustee independently of the amount at
stake.

30

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Table 1: Probabilities that player B chooses various values of m

m=0High Reciprocator
type (θ=H)
Low Reciprocator type (θ=L)

m=1
1    
2

1    

1    
2

1    

1   
1   

m=1.5
1  

2

1  

2








Table 2: Summary statistics
(1)

(2)

A Players (trusters) B players (trustees)
Proportion Male

0.50 (0.50)

0.45 (0.50)

Mean Age21.58 (4.37)

24.86 (4.73)

Proportion Student

0.92 (0.27)

0.46(0.50)

Proportion Trusting

0.37 (0.23)

First decision:
Equally share the triple stake

0.55

Send back the original stake

0.31

Send back nothing

0.14

Second decision:
Equally share the triple stake

0.49

Send back the original stake

0.32

Send back nothing

0.19

Number of observations

198

Note: standard deviations in parenthesis.

38

84

Table 3: Tests of components of costly signaling hypothesis
Equation A

Equation B

Equation C

Equation D

Dependent

Smile Quality

Trustworthiness

Variable:(scale 1-8)

(scale 1-8)

Decision
to
send
money
(send=1)

Gain (Euros)from sendingmoney

0.124**

0.079**-0.011(0.017)(0.026)(0.400)0.54***

0.219***

0.911***(0.000)(0.000)(0.005)0.213**

0.310***

0.154**(0.030)(0.000)(0.012)0.0149**

0.007

0.005

(0.017)(0.139)(0.142)-0.262***-0.006-0.050(0.003)(0.867)(0.404)0.229**-0.0080.067(0.011)(0.821)(0.188)Ind.
variable(characteristicsof trustee):Hightreatment

Smile quality

IntelligenceAge of trustee

Beard

DécolletéNote: p-values in parentheses, one-tailed values reported for High treatment andSmile quality, two-tailed values for other variables. Standard errors clustered by clip,**=significant at 5%; ***=significant at 1%. Equations A, B and D are estimated byordinary least squares, Equation C is a probit estimated by maximum likelihood.
Other controls include gender of truster and trustee, perceived attractiveness, video
sequence, truster’s treatment, dummy variables for the trustee being black, having
visible piercing and wearing glasses in equations A, in addition to perceived self39

confidence, and smile frequency in Equation B. Equation C adds to the previous set ofcontrols a dummy variable for A players’ self-reported unselfish behavior from theGeneral Social Survey, income, age of truster and score on a simple intelligence test.
The estimated coefficients for the other controls not reported, available from authors
on request. Number of observations= 6,720. Variables Smile Quality, Intelligence andTrustworthiness are means by clip.

Table 4: Character or Opportunity? Determinants of smile quality

Dependent Variable:

Trustee is in High treatment

Unselfish behavior by trustee(dummy variable)(dummy variable)

0.516

0.403

(0.038)**(0.126)

Independent Variable:
Mean smile quality rating

Note: one-tailed p-values in parentheses, standard errors clustered by clip,**=significant at 5%. Probit equations estimated by maximum likelihood. Number ofobservations=6,720.

40

Decision game 1

Clip 1

Decision game 2

Clip 24 weekslater

payoutquestionnaire

1 out of 21 [14] selected for payout

Series 2:

1 out of 21 [14 in second wave]
selected for payout

Series 2:

New set of 21 [14] different partners Same 21 [14] different partners– trust decision for each partner– rating of clips
Mix of clip1 and clip2

Series 1:

21 [14] different partners – Same 21 [14] different partners
trust decision for each partner– rating of clips
Mix of clip1 and clip2

Series 1:

First mover:Note: faces are blurred in the Figure to preserve subject anonymity in publication; actual clips were not blurred

questionnaire

Test recording

Second mover:Figure 1: Order of choices for Second and First Movers in the Experiment

(b)

(a)

mean
(1 not at all - 8 very much so)

4,90p = 0,0265

5,00

4,43

4,56

p = 0,0023

39,9%High (8 euro)Low (4 euro)

positive returns by second
movers80,1%

p = 0,0000

87,2%High (8 euro)

trust decision of 1st movers

36,1%

p = 0,0008

Low (4 euro)

mean of ratings: genuineness of mean of ratings: trustworthinesssmile

100,0%
90,0%
80,0%
70,0%
60,0%
50,0%
40,0%
30,0%
20,0%
10,0%
0,0%

4,00

4,50

5,00

5,50

6,00

Figure 2: Differences in (a) smile quality and (b) trust and trustworthiness by treatment

percent

(b)

(a)

4,33

Mean of ratings:
Trustworthiness

4,7

p = 0,0000

trust

4,78

Mean of ratings:
Intelligence

4,92

p = 0,0001

82,90%

non genuine smile (score ≤ 5)

returning positive amount84,60%

p = 0,0341

non genuine smile (score ≤ 5)

Mean of ratings:
Attractiveness

4,16

p = 0,0000

4,35

35,60%

genuine smile (score > 5)40,80%

p = 0,0000

genuine smile (score > 5)
100,0%
90,0%
80,0%
70,0%
60,0%
50,0%
40,0%
30,0%
20,0%
10,0%
0,0%

4

4,5

5

5,5

6

Figure 3: Differences in (a) ratings of trustees and (b) trust and trustworthiness by smile quality
mean(1 not at all - 8 very much so)
percent