Dilemmas and bargains: Autism, theory-of-mind, cooperation and fairness. Elisabeth Hill 1* and David Sally 2 1 Institute of Cognitive Neuroscience, University College London, UK. 2 Cornell University, USA. * Corresponding author. Institute of Cognitive Neuroscience University College London 17 Queen Square London WC1N 3AR. UK. Tel: +44 (0)20 7679 1177 Fax: +44 (0)20 7813 2835 Email: [email protected]KEYWORDS: autism, bargaining, cooperation, dilemmas, theory-of-mind
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Dilemmas and bargains: Autism, theory-of-mind, cooperation and fairness.
Elisabeth Hill1* and David Sally2
1 Institute of Cognitive Neuroscience, University College London, UK.
The percentage of each group cooperating on each round of each Prisoner's dilemma game
is shown in Figure 4. A repeated measures ANOVA with one between factor (group) and two
within factors (Prisoner’s dilemma game; round) was applied to the data for the number of
cooperative moves, first for the normal groups (adults versus all children together). There were
significant effects of group [F (1,62) = 4.08, p < .05], game [F (1,62) = 99.64, p < .001], and
significant interactions of group by game [F (1,62) = 16.19, p < .001] and game by round [F
(1,62) = 4.58, p < .05]. The first three significant effects have been described previously. The
game by round interaction reflected a more similar profile of cooperation in the encouraged
cooperation and computer opponent games than in the human opponent game. In the latter game,
normal children competed progressively more over the course of the sixteen rounds while normal
adults sustained a more even rate of cooperation.
[Figure 4 about here]
The trial-by-trial decisions of the individuals with autism were compared to those of their
normally developing peers for the adult and child groups separately. For the children, there was a
significant effect of game [F (1,65) = 30.01, p < .001], described previously. The normally
developing children appeared to distinguish more between playing the human opponent than the
computer opponent or encouraged cooperation games, highlighted by the less cooperative
strategy that they adopted. This performance profile was not evident in the children with autism.
There was a significant interaction between game and round [F (1,65) = 11.5, p < .001]. Once
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again, this interaction reflected a more similar profile of cooperation in the encouraged
cooperation and computer opponent games than in the human opponent game.
For the adults, there was a significant effect of game only [F (1,28) = 54.15, p < .001],
described previously and indicating that there were no significant differences between the adults
with autism and the normal adults in terms of cooperative choices across the 16 rounds of each
Prisoner’s dilemma game. Figure 4 shows, however, that the adults with autism were consistently
less cooperative on the encouraged cooperation game and generally less competitive when
playing the other two games, particularly against the human opponent. Thus they were less
influenced by the task demands than their normal peers and this neutrality may reflect the
application of a particular, pre-set decision rule or pattern across all the games.
Furthermore, the responses of the adults with autism in the semi-structured interview
reflected the special status of the human opponent PD, indicating that where the adults with
autism appeared to produce similar patterns of cooperation as the normal adults, this arose out of
their knowledge that they needed to predict the workings of their opponent’s mind, were
generally unable to do this spontaneously and thus needed to rely on rule-based methods. This
was indicated by many of the adults with autism, for example, "I've gotta put a mental state in
Sarah [the confederate], think what she was thinking" (a 32-year-old woman with autism). This
was the nature of the response for many of the adults with autism for the PD tasks, the Happé
stories as well as in their daily lives. The normal adults did not make such statements during their
interviews.
Taken together these results show that although there was no significant difference between
the degree of cooperation elicited in the individuals with autism and controls when all rounds of
each game were taken together, more subtle differences were evident, specifically in the degree
of cooperation between the last round of the human or computer version of the game (whichever
was played second) and the first round of the encouraged cooperation PD, where a lack of
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switching between a competitive to a cooperative strategy was evident in the individuals with
autism, especially the children. With respect to the human and computer opponents, older
children cooperated initially more than did younger children and normal adults, while neither
group of children nor adults with autism fully reproduced the level and pattern of competition
manifested by normal adults. We can now turn to an explicit analysis of the role of mentalising in
fostering or retarding cooperation in these games.
In order to establish whether there was a relationship between mentalising ability and
choice of strategy when playing each version of the prisoner's dilemma, a comparison was made
between performance on the second-order false belief test and the degree of cooperation
evidenced in each game for the child participant groups. All members of the normal adult group
passed this task, and thus such a comparison was not warranted between the adult groups. An
alternative comparison based on performance on the Happé stories was used to investigate any
relationship between mentalising and degree of cooperation in the adult groups, and is reported
below.
To ascertain whether a relationship between mentalising ability and strategy choice
existed in the children, a repeated measures ANOVA with two between factors (group; second-
order false belief performance) and one within factor (PD game) was applied to the data for
number of cooperative moves (children with autism versus all normally developing children
together). There was a significant effect of game [F (1,62) = 19.72, p < .001], as described
previously. The effect of false belief approached significance [F (1,62) = 3.72, p = .058],
suggesting that second-order false belief passers had a tendency to be more cooperative than
second-order false belief failers, irrespective of whether or not an individual was diagnosed with
autism. A child who failed this false belief test presumably also had a tough time understanding
what the counterpart’s beliefs about the child’s own intentions were in the PD. Generally, a
player wants to be cooperative only if she forsakes narrow self-interest and if she can anticipate
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that the other will cooperate (Kiyonari, Tanida & Yamagishi, 2000). The target of this latter
anticipation is, of course, a similarly conditional, cooperative expectation, and hence, the
importance of a theory-of-mind.
None of the normal children failed the first-order false belief task, while a third of the
children with autism did so. To determine the relationship between this fundamental mentalising
capacity and cooperation, the performance of the children with autism was analysed with a one
between factor (first-order false belief performance) and one within factor (PD game) repeated
measures ANOVA. There was a significant effect of the game [F (1,16) = 2.13, p < .05], as
described previously. Passing the false belief task significantly decreased cooperation across the
games, mean number of cooperative responses, 4.72 and 7.27 for false belief passers and failers,
respectively [F (1,16) = 4.46, p < .05]. There was no interaction between game and task
performance [F (2,16) = 2.01, p > .1].
This result is the opposite of the one reported for second order false belief: an acutely
malfunctioning theory-of-mind enhanced cooperation. The children who could not decipher the
first-order (Sally-Anne) false belief task cooperated, on average, in approximately half the trials
of each of the PD game versions. One of the ways a player could generate a cooperation rate of
50% is to simply choose randomly on each round without any regard for the decisions of the
counterpart. If this form of decision-making was employed, the player would be equally likely to
choose the circle or the triangle in a round regardless of which shape the opponent chose on the
previous round, in other words, random reciprocation. (The tit-for-tat strategy, by contrast,
assures that circle follows the other’s circle and triangle, triangle with certainty.) For each of the
children with autism, the conditional response rates to the opponent’s cooperating or defecting in
the previous round were calculated. The hypotheses that these conditional response rates were
equal to 50% were tested for those children who had passed or failed the Sally-Anne task. For the
children with first-order false belief troubles the hypothesis of random reciprocation could not be
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rejected in three of four instances (computer opponent: cooperation after cooperation t (5) = .0, p
> .1, defection after defection t (5) = 1.42, p > .1; human opponent: cooperation after cooperation
t (5) = .44, p > .1, defection after defection t (5) = 4.07, p < .01). In this last case, defection was
reciprocated a little more than 70% of the time. By contrast, those who passed the first-order false
belief test did not respond randomly in any setting (computer opponent: cooperation after
cooperation t (12) = -3.19, p < .01, defection after defection t (12) = 4.83, p < .001; human
opponent: cooperation after cooperation t (12) = -3.71, p < .005, defection after defection t (12) =
6.23, p < .001). This sub-group of test passers was more likely to reciprocate defection and to
exploit cooperation. The evidence, then, strongly suggests that a first-order theory-of-mind or a
rule-based, effective substitute is necessary to reciprocate in a strategic fashion in the prisoner’s
dilemma.
To investigate the relationship between mentalising ability and cooperation in social
dilemmas in the adult groups, each adult participant was allocated a categorical score for their
performance on the Happé stories. Each story had been scored between 0 and 2. A participant's
mean accuracy score was converted into a categorical score of 0, 1 or 2. The data for the adult
groups were then analysed using a repeated measures ANOVA with two between factors (group;
theory-of-mind categorical score) and one within factor (PD game) on the number of cooperative
moves. There was a significant effect of game [F (1,26) = 30.72, p < .001], described previously,
and a significant interaction between game and theory-of-mind category [F (2,26) = 3.85, p <
.05]. This interaction indicated that those participants with superior theory-of-mind performance
adhered to the expected performance profile of more overall competitive play in the human and
computer opponent versions of the game and more overall cooperative play in the encouraged
cooperation version of the game, irrespective of whether or not an individual was diagnosed with
autism. The greater adherence to the expected task performance - as inherent in the rules of each
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game - suggests that mentalising ability is involved in conditionally responding to the
counterpart.
One possible explanation of this result is that it is driven simply by a disparate recognition
of the changed rules in the initial round of the enforced cooperation game and does not involve an
ongoing divergence in strategy. However, the theory-of-mind category score did not correlate
with the likelihood of switching from a competitive response on the 32nd round of the game
(either playing the human or computer opponent) to a cooperative response on the first round of
the encouraged cooperation PD in either adult group [normal adults, r2 (13) = -.12, p > .1; autism
adults, r2 (13) = -.33, p > .1]. Thus, mentalising did not appear to be involved in responding to
changes in the setting and rules of these PD games, but rather to the maintenance of a consistent
strategy across sixteen rounds.
This flexibility across games and consistency across rounds of the same game may be
attributed to 'real' mentalising skill in the normal adult group, and to a compensatory mechanism
in the adults with autism. The small number of the latter individuals who performed relatively
successfully on the Happé stories reported doing so in a rule-based way ("It's politeness, that's
what my mother taught me. I've never really understood why", a 46-year-old woman with
Asperger syndrome; "I should say the opposite of what I think", a 32-year-old woman with
autism), and many of the adults with autism reported approaching the PD tasks similarly ("The
problem I've got with autism … other people who don't have it, they have slightly different
strategies", a 24-year-old man with Asperger syndrome). Taken together, these comments suggest
that the individuals with autism may be performing rationally by drawing on their logical
reasoning skills. Overall this speculation is supported not only by participant self-report, but also
by their slowed responses to the Happé questions.
Did players distinguish between the human and computer opponent? The inclusion of the
human versus computer opponent version of the Prisoner's dilemma task was a manipulation
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designed to allow investigation of this issue, in particular relating to a section of the semi-
structured interview where questions were asked concerning any difference in the feeling or
playing of the participants in these two games. On the whole the normal adults felt a difference in
these two games and ascribed this difference to the nature of their opponent, using mental state
terms and/or a sense of empathy to describe this: "There's no way to judge the computer's actions
but I could obviously do so with Sarah [the confederate]." (a 30-year-old normally developing
man); "I felt she could be intuitive to what I was doing whereas I don't perceive a computer as
being intuitive. Its just mechanical." (a 33-year-old normally developing man). While a
proportion of the adults with autism described feeling different in these two tasks, and identified
the locus of this difference as lying in the nature of the opponent, responses included fewer
mental state terms, no empathic sense and had a sense of learned difference rather than the
intuitive human sense seen in the normal adults: "It was more complicated to play with Sarah …
Because it [sic] was a person." (a 37-year-old man with Asperger syndrome). "Playing the
machine was easier because the machine is predictable … and I felt more comfortable ... It’s
easier to read a machine or anticipate a machine … it’s far easier. A person is unpredictable … a
machine is easier because you're not up against emotion. It’s safer playing a machine. I don't fear
playing a machine but I fear the woman." (a 41-year-old man with Asperger syndrome). A final
example that particularly highlights the contrast between the two groups is illustrated by the
opposing sense of prediction seen in the following representative comments of an adult with and
one without autism: "I actually felt there was something about the way the computer was
programmed that I might eventually be able to work out where as I didn't feel that way about
Sarah." (a 46-year-old woman with Asperger syndrome); "I felt I could predict Sarah's responses
more than I could predict the computer's" (a 21-year-old normally developing woman). Although
asked to identify the strategy of their opponent, very few players in either group felt that they
could do so concretely (see Hill, Sally & Frith, in preparation).
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Given the many comparable results of the individuals with and without autism in these PD
tasks, there was no prominent quantitative manifestation of internal discomfort with the human
opponent. Overall the decisions of the individuals with autism, whether derived through the
generation of a relevant rule or the application of a weakened theory-of-mind, largely reproduced
those of the matched normal participants. It may be that the discomfort of the autistic individuals
matched the distrust of the normal participants, who played the real PDs in a very competitive
manner.
There was one sub-group, however, who might be more prone to react to the perceived
“unpredictability” of the human opponent or take comfort in the assumed “dependability” of the
computer opponent, namely, those individuals who failed the coin flip task. These participants
made a mistake in the face of the uncertain coin, and their decisions might be similarly affected
by an opponent with equal or greater levels of capriciousness. Much evidence suggests that
children in general reflect the thoughts voiced by our participants with autism in that they are
more reluctant than adults to predict stability in the behaviour of other people (Miller & Aloise,
1989), but are no more likely to find machines or physical objects befuddling (Kalish, 2002).
Accordingly, the relationship between levels of cooperation with the human and the
computer opponents and the coin flip decision was investigated. A two between factor ANOVA
(diagnostic group - normal, autism; shape choice on coin flip task - circle, triangle) was applied
to the number of cooperative responses when playing the human and computer opponents
separately. The result of interest in these analyses is that of any influence of coin flip choice on
cooperation in the PD. There was no significant difference in the cooperation rates of coin flip
“passers” and “failers” when playing the human opponent [F (1,94) = 1.58, p > .1]. A significant
difference emerged on this measure when comparing performance on the computer opponent PD
[F (1,94) = 7.03, p < .01]. In this case those making the nondominant choice on the coin flip were
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more likely to cooperate on the PD (mean cooperation on PD computer opponent for
nondominant versus dominant coin flip choice, 6.21 versus 3.61 respectively).
One potential hypothesis concerning these coin flip results is that these individuals have an
overwhelming preference for triangles over circles. The fact that coin flip “failers” did not pick
triangles (thereby cooperating) more frequently in the human opponent game eliminates this
hypothesis. Rather, it seems that the predictability of the computer made these participants feel
more secure and hence, much more willing to cooperate.
Summary
The performance of normally developing children was found to be less strategic than that of the
normal adults in the current study, supporting the picture of a developmental trajectory in levels
of spontaneous cooperation beginning with competition and ending with competition or
cooperation, as appropriate to task demands in adulthood. It is clear that this pathway is not fully
matured by the age of ten years. In relation to autism, differences existed in comparison to the
normal groups, particularly in terms of less strategic responses to the first round of each game
and across the individual rounds. In terms of mentalising and its influence on levels of
cooperation, mentalising ability aided strategic behaviour irrespective of the presence or absence
of autism. The skills used by those individuals with autism who appeared to have mentalising
abilities, and which could be considered to reflect quasi-mentalising ability, may have allowed
such individuals to 'get-by' in the Prisoner's dilemma task by using strong reasoning skill. These
individuals appreciated that the task required an understanding of another's mind, they had clear
insight into their difficulties in this regard and that they must draw on other resources to work out
what was expected of them. If this is the case, more subtle experimental manipulations of the set-
up used in the current study should elicit the oft-reported autism difficulties in this domain, and
would be particularly striking in real-life situations.
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In the Prisoner’s dilemma, the issues of cooperation, generosity, and retribution are
interwoven with uncertainty about the counterpart’s intentions and actions and with a multiplicity
of rationales for a given action in each round. In a second study, an alternative form of strategic
interaction that may clarify these—bargaining—was investigated.
Experiment Two – Bargaining
Nature, inaccurate accounting, gravity, an overstocked shelf, chance, a misplaced wallet,
an academic researcher, or some other dea ex machina might endow an individual not only with a
prize or a lump of value but also with a companion and with a decision about division. In the
dictator game, the choice is how much of the prize to grant to the other party who is bound to
accept the grant. In the ultimatum game, the choice is how much of the value to offer to the other
party who then may accept the offer or refuse it. Acceptance achieves the suggested division;
refusal results in the whole prize being withdrawn and both parties receiving nothing. For
example, an experimenter might confer upon a participant ten candies (Murnighan & Saxon,
1998), ten marks or some other unit of currency (Güth & Tietz, 1990), or ten points or tokens
(Harbaugh, Krause & Liday, 2000). This endowed person would, as a dictator, decide how many
of the ten units, if any, to give to another person, and as the proposer in the ultimatum game, how
many to offer the other party knowing that a rebuff would wipe out the grant entirely.
The ultimatum game represents, among other social situations, the possibility in a
negotiation of one bargainer making a final offer to the counterpart and walking away from the
table leaving the other to sign the deal or not. Experience and introspection tell us that in this
setting such a dramatic proposal has a good chance of failing. However, in orthodox economics,
such an ultimatum should work: the equilibrium, corresponding to the prediction based on
rational self-interest, is that the responder should accept any offer greater than zero, and
therefore, the proposer should offer the smallest possible positive amount. In fact, this
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equilibrium is rarely realized in any of the numerous assays that have been conducted in
laboratories and field sites around the world during the last twenty years. The regular findings,
rather, are the following: (i) the modal offer is between 40% and 50% of the whole prize, (ii) tiny
offers are almost always rejected, and (iii) a majority of responders will refuse offers below a
third of the total (see Güth & Tietz, 1990; Camerer & Thaler, 1995; Oosterbeek, Sloof & van de
Kuilen, 2001 for reviews).
The literature has focused on understanding why offers are so robust, and why responders
are so rancorous. One possible explanation for the generosity of the proposers is that they have a
certain taste for fairness and a preference for sharing some part, or even half, of their dowry.
Forsythe, Horowitz, Savin & Sefton (1994) asked participants to play an ultimatum game and a
dictator game to test this hypothesis, since fairness considerations would dictate that proposers
give the same amount in both games. However, these authors found that the proportion of equal
split offers declined from 75% in a $10 ultimatum game to 21% in a $10 dictator game. The
mean offer in a standard 10 unit dictator game is between 20% and 25% (Rigdon, 2002), and in
the ultimatum game, 40% and 45%. Roughly, then, half of the typical proposer’s generosity is
driven by a taste for fairness and half by strategic considerations of the possible spite of the
responder.
Subsequent dictator experiments have shown that the taste for fairness can be heightened
or slaked by the context of the game. The degree of selfishness among dictators is raised by
allowing them complete anonymity, even from the experimenter (Hoffman, McCabe & Smith,
1996) and by placing them in a business setting of buying and selling (Hoffman, McCabe, Shacat
& Smith, 1994); the frequency of altruistic grants is raised if the recipient is a charity (Eckel &
Grossman, 1996) and if more personal characteristics of the recipient are identified (Bohnet &
Frey, 1999; Charness & Gneezy, 2000). Subsequent ultimatum experiments have shown that the
strategic and fairness concerns of both parties move in predictable directions: when the proposed
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split of $10 is generated by a roulette wheel as opposed to another person, the mean minimal
offer acceptable to responders is much lower—$1.20 rather than $2.91 (Blount, 1995); when a
written note saying “I know you’d like more, but that’s the way it goes” is attached to a small
offer, a rebuff from the responders is more likely (Kravitz & Gunto, 1992); when the endowment
is worth more to one side than the other (e.g., 50¢ versus 10¢ per chip) and the other side is
ignorant of this fact, advantaged proposers are more likely to suggest an even split of the
counting units rather than total value, and advantaged responders are more likely to reject fair
splits of the underlying units to induce a more equitable split of surplus value (Croson, 1996;
Kagel, Kim & Moser, 1996).
The variants just described could be reflective of mentalising ability or social rule-
following. For instance, a person might reject a small offer because she imagines that the
proposer thinks she is unworthy, gullible, or dim-witted, or because she recognizes this game as a
sharing situation which demands that greedy people be punished. Similarly, a munificent dictator
might utilize her theory-of-mind to anticipate the disappointment of an unfunded recipient, or she
might recognize the applicability of a sharing norm. A norm may substitute for mentalising: as
the other driver in a narrow lane approaches, you need not read his eyes, thoughts, or intentions,
you need only remember the locale and move to the left in the UK and to the right in the US.
Mentalising may become necessary only if the interaction does not proceed as expected: when
the other driver fails to move to the proper side, then you need to notice the direction of his gaze,
the tenseness of his hands, and the expression on his face.
The evidence on the relative utilization of mentalising versus norm-following in the
standard, anonymous ultimatum game is mixed. On the one hand, Henrich et al. (2001) found
that much of the variance in mean offers among fifteen small-scale societies (ranging from 26%
among the Machiguenga in Peru to 58% among the Lamelara in Indonesia) could be explained by
two factors—the importance of cooperation in the society’s economic production and the reliance
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on market exchange in daily life. These factors would seem to develop and mould norm
formation rather than mentalising abilities. The authors themselves suggest that their participants
applied the analogous (and varying) norms found in their societies:
[W]hen faced with a novel situation (the experiment), they looked for analogues in their daily experience, asking “What familiar situation is this game like?” and then acted in a way appropriate for the analogous situation. For instance, the hyper-fair…offers (greater than 50 percent) and the frequent rejections of these offers among the Au and Gnau reflect the culture of gift-giving…, accepting gifts, even unsolicited ones, commits one to reciprocate at some future time to be determined by the giver (Henrich et al., 2001, p. 76). A second experiment that both documented the under-utilization of mentalising and its
potential impact is that of Hoffman, McCabe and Smith (2000). Here, in a $10 ultimatum game
with a business context, an additional line was added to the instructions encouraging the proposer
(i.e., seller) to strategize and read the mind of the opponent: “Before making your choice,
consider what choice you expect the buyer to make. Also consider what you think the buyer
expects you to choose.” This encouragement caused the mean offer to rise to $4.17 from $3.71 in
a control condition where no explicit mindreading prompt was given, and this increase suggests
that proposers in the control condition were solving the game without fully employing their
theory-of-mind.
On the other hand, studies in which an asymmetry in information between the offerer and
responder is strategically exploited support the relative prominence of mentalising. Respondents
in one experiment received a set sequence of twelve offers for either $1 or $2 out of a total
surplus of $20 (Pillutla & Murnighan, 1996). There was a complicated information structure
overlaid on the set of games: (i) during the first half of the sequence, none of the responders knew
that the total prize was $20, making it difficult to deem an offer unfair; (ii) half of the responders
knew that the (fictitious) offerers knew that the low offers were unfair and therefore could more
easily attribute greedy intentions to them. (Note that this second manipulation depends upon a
theory-if-mind both to understand the different contents of the other’s mind and to respond
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emotionally.) After making each decision, participants reported how they reacted to the offer and
how they felt. These verbal responses were coded for the degrees of unfairness and anger
expressed. In relation to the current study there were two important findings: first, the
manipulation relying on theory-of-mind was successful—participants who knew both that an
offer was low and that the other knew it was low were far angrier. Second, this anger resulted in a
greater frequency of rejection, and was more predictive of the likelihood of rejection than was the
expressed degree of unfairness alone.
As any overtaxed parent can testify, children reject various ultimatums all day long and
readily employ multiple notions of “fairness.” There is a vast literature on prosocial behaviour
among children, some of it emphasizing social rules and some, perspective taking. Numerous
donation studies (similar to the dictator game) have found that children are more generous when
they have seen a model being generous (e.g., Harris, 1970; Wilson, Piazza & Nagle, 1990).
Within social learning theory (Bandura, 1986), a model affects the observer by directly
representing the presence or application of a rule rather than by triggering a mediating internal
process, suggesting that mentalising is less important in giving. On the other hand, a child’s
abilities to take the perspective of another person visually, emotionally, and cognitively are
positively related to prosocial behaviour in most studies (Underwood & Moore, 1982), and in one
specific study, two factors relying on a child’s theory-of-mind, affective reasoning and sympathy,
caused a large increase in donations to a needy person (Knight, Johnson, Carlo & Eisenberg,
1994). Both sources of prosociality should become stronger as children grow up, and indeed, a
meta-analysis by Eisenberg and Fabes (1998) found that sharing and donating became more
prevalent from preschool through adolescence.
Two specific ultimatum studies, however, showed a less clear developmental trend.
Harbaugh, Krause and Liday (2000) found that fourth and fifth graders made larger grants as
dictators than did second graders or ninth graders. While these authors found that ultimatum
38
proposals on average increased with grade level, Murnighan and Saxon (1998) found a non-
monotonic pattern with kindergarteners offering more candies than third graders, who, in a game
with a dollar at stake, offered fewer cents than did sixth graders, who were more generous than
ninth graders. Finally, younger children in both studies were more likely to accept small offers.
This mixture of results demonstrates that the offering and responding behaviour of children may
be affected by the specific details of game presentation, and may reflect a general inconsistency
in inference about social interaction. Kalish (2002) has shown that while children and adults will
equally predict consistency in repeated physical events such as pumice floating in water, children
will much more often predict that a person would behave differently in the future than he or she
did in the past, for instance, preferring Bert tomorrow despite preferring Ernie today. If the
reaction of the other party is inconsistent or unreliable, then it makes sense to accept whatever the
current offer is, and to not be too strategic in formulating an offer.
By investigating the giving and receiving behaviour of children and adults with and
without autism, the importance of mentalising for both generosity and consistency can be
determined.
METHOD
The participants were the same as those included in the first experiment (social dilemmas), with
the addition of one eight-year-old.
Materials and Methods. The testing set-up remained the same as that reported for the first
experiment with participants being assessed in a quiet room, sitting at a laptop to the right of the
confederate. Responses were recorded on-line for later analysis. Task instructions were presented
on the computer and the experimenter verbalised them to ensure that participants understood each
task. Players were told that they must try to win as many points as possible and that the total
points won on the games would be exchanged at the end of the testing session for stickers
39
(children) or chocolates (adults). The greater the number of points won, the greater the reward at
the end of the test session. Two versions of a bargaining task - dictator game and ultimatum game
- were completed by participants, with the dictator game always played first
Dictator game. The dictator (participant) was given ten points and asked how much s/he
wanted to give to the opponent, knowing that s/he would keep the remainder. Eleven cards were
presented on the computer screen, outlining all possible permutations by which the points could
be split, ranging from the dictator keeping all ten points for her/himself to giving all ten points to
the opponent. The dictator made his or her choice and indicated this by selecting the relevant card
on the computer screen. The choice that the dictator had made and the points allocated to both
players were displayed. This process was repeated 16 times throughout the course of the game,
with the participant acting as the dictator for rounds 1-4 and 9-12, and the confederate taking the
part of the dictator for the remaining rounds. The participant was unaware that there would be
more than one round of the dictator game and that the confederate would also take a turn as the
dictator. In the latter case the confederate allocated approximately the same amount of points to
the participant as the participant had to her.
Ultimatum game. This game was essentially the same as the dictator game but the opponent
had the choice to accept or reject the offer made to them by the proposer in each round of the
game. The game started as the dictator game. Once the proposer had made an offer, the opponent
indicated whether s/he accepted or rejected that offer. If the opponent accepted the proposer's
offer, the points were divided as proposed (exactly as in the dictator game). If the opponent
rejected the proposer's offer, neither player received any points. The choices made by each
player, as well as the points won were displayed after each round of the game. The set-up of the
ultimatum game was identical to that of the dictator game, with the participant acting as the
proposer and the confederate as the opponent for rounds 1-4 and 9-12, and with the roles reversed
for the remaining rounds. The participant was not told explicitly that there would be more than
40
one round of the game and that the confederate would also take a turn as the proposer. In the
latter case the confederate allocated approximately the same amount of points to the participant
as the participant had to her and always rejected offers of less than an equal split (i.e. four or
fewer points being allocated to the confederate).
RESULTS & DISCUSSION
Once again, there is a lack of studies which track the strategy of normal children and adults on
our version of the dictator and ultimatum games. This comparison will be presented first,
followed by the performance of the individuals with autism. Comparisons of the full dataset will
then be reported.
Offers made.
The offers made by the participant to the confederate were expected to be lower in the dictator
game than in the ultimatum game. The mean points offered to the confederate by the participant
across the first four rounds of each game, and on the first round only, are shown for each group in
Figures 5a and 5b respectively. A repeated measures ANOVA with one between factor (group)
and one within factor (game) was applied to the data for mean points offered. For performance
across the first four rounds of each game, there was a significant effect of group [F (3,62) = 3.17,
p < .05]. A series of Tukey tests revealed this difference to arise from higher offers being made
by the six- in comparison to the eight-year-old children [p < .05]. There was a significant effect
of game [F (1,62) = 77.87, p < .001], reflecting higher offers being made to the confederate in the
ultimatum game, and a significant interaction between group and game [F (3,62) = 3.5, p < .05].
The interaction reflected a greater difference between the offers made across the two games by
the adult group. Thus, while both adults and children responded in the predicted manner, the
adults did so more strikingly, making a greater distinction between the size of their offers in the
41
two games, with a greater number of points being kept for self in the dictator game versus the
ultimatum game. This pattern of performance was also seen in the analysis of the mean offers
made to the confederate on the first round of each game, with the exception of the difference
between the groups [group, F (3,62) = .62, p > .1; game, F (1,62) = 59.03, p < .001; group by
game, F (3,62) = 3.07, p < .05]. These results correspond to the equivocal results of previous
ultimatum studies in that there was no clear trend in offer amounts across age groups. More work
is needed to explain this finding within the findings of the prosocial literature which shows that
sharing and donating become more prevalent as children grow up (Eisenberg & Fabes, 1989). A
tentative explanation for the differences may be that this task evoked exchange norms which are
already fairly firmly implanted by the age of six.
[Figure 5 about here]
Having established the pattern of performance across the two bargaining tasks used in the
current study, the autism samples were added to the analysis and comparisons made between the
two adult and child groups separately for the mean number of points offered by the participants to
the confederate across the first four rounds of each game as well as on the first round only (see
Figure 5). In all cases (adults; children; four rounds; first round) there was a significant effect of
game [adults, F (1,28) = 34.19, p < .001; children, F (1,67) = 27.75, p < .001], with more points
being offered to the confederate in the ultimatum game, but no effect of group and a mildly
significant interaction between group and game [adults: group, F (1,28) = .02, p > .1; group by
game, F (1,28) = 3.27, p > .05; children: group, F (1,67) = .7, p > .1; group by game, F (1,67) =
2.95, p > .05. On average, it appears that the individuals with autism approached the bargaining
tasks in a way that was comparable to their normally developing peers, suggesting that some
individuals with autism may have an intact mechanism that deals with fairness. There is, also,
some indication that individuals with autism did not react as vigorously to the strategic
dimensions of the ultimatum game.
42
More evidence for the relative effects of autism on fairness and tactical giving appear
when looking at the underlying distributions of offers. In particular, Figure 6 displays the
dispersal of first round ultimatum offers by adults and children with and without autism.
Visually, there appears to be a strong divergence. The powerful Epps and Singleton (1986) test
was used to determine if these two samples of discrete data were likely to be from identical
populations. This CF statistic, based on the empirical characteristic function, is asymptotically
distributed as chi-square with four degrees of freedom and can be corrected for small samples.
For the first round ultimatum of autistic and normal adults displayed in Figure 6a, the null
hypothesis of similar distributions is strongly rejected [CF = 11.83, p < .02]. One interpretation of
this result is that adults with autism applied one of two rules: split the amount fairly and squarely,
or take everything that you can. A far greater proportion of the normal adults tried to strategically
shade their offers by taking a point or two extra for themselves.
[Figure 6 about here]
We can contrast the distributions of first round ultimatum offers of children with and
without autistic spectrum disorder in Figure 6b. Here, again, there was evidence of distinct
patterns of first offers [CF = 9.96, p < .05]. There were no significant differences in offer
distributions between the adults and the children who shared the same condition [normal, CF =
6.59, p > .1; autism, CF = 2.54, p > .1]. Moreover, when comparing first round dictator offers
there were no significant differences in the underlying distributions across any groups. Since the
initial dictator grants were the same, it can be concluded that core generosity did not vary by age
or with autism. However, once an element of strategic anticipation was added by empowering the
responder in the ultimatum game, those with autism seemed to employ one of two salient rules:
cut the total in half, or keep it all. In contrast, the mentalising abilities of the normal participants
were utilized to generate mildly unequal, slightly shaded offers.
43
The direct effects of mentalising on first round offers among the children can be seen in
Figure 7. The striking visual difference in the distribution of offers is strongly confirmed by an
Epps-Singleton test (CF = 9.64, p < .05). Here, the majority of those who failed the second-order
false belief test offered the responder nothing or only one point, while the majority of those who
passed the test offered an even split. (These distributions of initial offers have means whose
distinctiveness approaches significance [F (1,63) = 3.73, p = .058].) A theory-of-mind that was
effective due to intuition or synthetic construction was very helpful to the child making a
reasonable offer in this game.
[Figure 7 about here]
The extent of learning across rounds of the ultimatum game was investigated, in light of
the apparently different strategies of the individuals with and without autism. The confederate
consistently rejected offers of four points or fewer, so participants had the chance to learn, adjust
and converge on the optimal offer of an even split. A comparison of the groups on a round by
round basis was made on the dictator and ultimatum games for all eight rounds (see Figure 8). A
repeated measures ANOVA with one between factor (group) and two within factors (bargaining
game, round) was applied to the data for the mean offer made by each group on all eight rounds
of each game. For the comparison of the normal adults and children, there was a significant effect
of game [F (1,64) = 118.66, p < .001], and a significant interaction between group and game [F
(1,64) = 7.93, p < .01]. These significant effects have been described previously. When
comparing the mean offers of adults with and without autism, there was a significant effect of
game only [F (1,28) = 38.19, p < .001]. Unlike the first round, however, this similarity in the
means across the groups for rounds two through four and nine through twelve is also reflected in
comparable underlying distributions of individual offers (all CFs < 7.0, all p’s > .1). Moreover,
mentalising, as measured by performance on the Happé stories, was insignificant in an ANOVA
of the average offer over multiple rounds. Once autistic adults had a single experience with the
44
ultimatum game, their offers were largely indistinguishable from those of the control group.
Hence, the combination of a scaffolded theory-of-mind, choice of a relevant norm and one
reaction from another person allowed the adults with autism to mirror the behavior of their
normal counterparts.
With respect to the average offers of the children there was a significant effect of game [F
(1,67) = 62.38, p < .001], described previously and a significant interaction between group,
bargaining game and round [F (1,67) = 4.21, p < .01]. This interaction highlighted divergence
between the amounts offered to the confederate in the two games on round one in the normally
developing children only. Most of the children seem to learn the game as quickly as the adults: by
the second round the offers of autistic and normal children as a group are dispersed in statistically
similar ways. This concurrence is confirmed by the insignificance of second-order theory-of-
mind in an ANOVA of average offer over all eight rounds. The one group that remains distinct
are the six-year olds: even after eleven rounds of the game, in their final turns as proposers, their
offers are scattered over all the possibilities and are distributed differently from those of the
eight- and ten-year olds [CF = 11.62, p < .02] and those of the autistic children [CF = 8.29, p <
.1].
[Figure 8 about here]
Offers rejected.
The mean points rejected over the eight rounds of the ultimatum game by each participant group
are shown in Figure 9. A one factor ANOVA was used to compare the mean points rejected by
each participant group. There was a significant difference between offers rejected by the normal
groups [F (1,65) = 5.09, p < .05], reflecting a developmental trend from childhood to adulthood,
with lower offers being acceptable to the children [mean (SD) points rejected: adults, 3.23 (2.71);
children, 2.34 (1.22)]. No significant differences existed between acceptable offers to either
45
adults with or without autism [F (1,29) = .44, p > .1], children with or without autism [F (1,68) =
.08, > .1], or autistic adults or children [F (1,32) = .62, p > .1],. Thus in terms of offers made by
the confederate that were deemed acceptable by the participant, a developmental progression
emerged: Both those with and without autism were tolerant of another's gain, accepting offers of
less than 50% for themselves. There was, however, a limit in all groups with adults rejecting
offers to self of less than 32% and children being more tolerant, rejecting offers of less than 23%
of the share for self. This conclusion is in accord with the most robust finding in the literature on
children and bargaining: children, younger children in particular, are less likely to reject smaller
offers.
[Figure 9 about here]
Lastly, mentalising appeared to play no role in the rejection of offers. Performance on the
relevant theory-of-mind task did not explain any of the variance in average offer rejected by
normal adults and children or by autistic adults and children. Hence, for our participants the
ability to decipher the confederate’s intentions and envisage her disdain did not affect the
likelihood of a small offer being rejected. It is as though the offence generated internally within
the recipient of an undersized offer is sufficiently motivating.
Summary.
The youngest normally developing children (aged 6 years) were found to be more prone to
sharing than the 8-year-olds in this sample, and the normally developing children as a whole
more tolerant of their opponent's gain (as measured by the offers rejected by participants).
Normal children demonstrated more pure generosity in the dictator game and less strategic
munificence in the ultimatum game than did adults. There were hints of a similar pattern among
our autistic participants. Lastly, for each group with the exception of the 6-year-olds, repeating
the ultimatum game caused differences to dissipate. The older children learned and adapted so
46
that by the second round their offers were indistinct from those of the adults; meanwhile, even by
the twelfth round, the youngest children were still somewhat at a loss. Although the evidence is
not overwhelming, there is a suggestion of a developmental trajectory in levels of bargaining.
Autistic children and adults were distinguished from their peers in the initial round. The
adults with autism spectrum disorder were more likely to choose either an even split or a tender
of zero. Autistic children showed a similar predilection for proposals of nil or five in contrast to
normal children who were most likely to just divide the prize in half. An ineffective theory-of-
mind was apt to result in an initial offer of no more than one point, while deciphering the second-
order false belief story correctly tended to lead to an equitable offer. Autistic adults proposed a
little less than four points on average, and normal adults a little more, but this resemblance masks
bimodal roots of the former and the deliberately strategic nature of the latter. The development of
theory-of-mind skills may help the child first to recognize and act upon relevant norms of
behaviour such as fairness, and later, to stretch those norms and improvise away from them when
the situation calls for it.
A single experience as proposer was sufficient to counteract any deficits in mentalising in
the succeeding rounds of the this ultimatum game. Without question, the static nature of the
payoffs and counterpart in this bargaining game is essential to the observed decay in the effects
of mentalising. A more dynamic and realistic negotiation would probably continue to demand the
application of an active theory-of-mind.
In contrast, rejection of offers did not vary with the efficacy of the participant’s
mentalising capability. The ability to sense another’s unfairness or contempt was not necessary to
reject offers of a third or less. So, the generation of an initial appropriate offer depends on theory-
of-mind, but the denial of an inapt or inequitable offer does not.
47
GENERAL DISCUSSION
In the experiments reported here the approach to two-way, reciprocal social interaction was
investigated using three mixed-motive games. The study had two broad aims, first to track the
development of decision-making on these games, and second to investigate the relationship
between mentalising and strategy choice.
Normally developing children did not, on the whole, perform in the same way as the
normal adults in situations involving a social dilemma (the prisoner's dilemma). This was the
case both for the games that encouraged competition between players and for the game that
encouraged cooperation. While normal adults showed a clear pattern of competition and
cooperation according to the task requirements, normally developing children aged 6-10 years
mixed both behaviours with their opponent in all situations, irrespective of whether such an
approach was overtly beneficial to them. There was some evidence of a developmental trend as
10-year-olds were more likely to cooperate in the initial round of the game playing against a
human opponent and pursued a level of cooperation that was more responsive to the identity of
the counterpart and the rules of the game than did the younger children. Normal children as a
group were more cooperative with the computer opponent than were normal adults, and they
became relatively more competitive with their human opponent over the course of the sixteen
rounds.
In contrast, many differences in the bargaining games were resolved after one or two
repetitions. As with the prisoner’s dilemma, adults were more sensitive to the strategic
possibilities offered by the structure of the games, in this case, the dictator versus the ultimatum
game. Adults, on average, changed their offers more in the latter game, an acknowledgement of
the responder’s potential veto power. There were no clear age trends with respect to the average
generosity of the offers of the young participants, but the very youngest were significantly more
likely to accept a share of the endowment that was less than 30%. In addition, many of these 6-
48
year-olds seemed to remain baffled by the ultimatum game after repeated plays, as their offers in
the twelfth round were scattered relative to the adults and other children. This excess dispersion
may be in keeping with the finding that younger children are less likely to predict consistency in
the actions of other people, in this case, the responder (Kalish, 2002).
The adult players with autism appeared, on the surface, to perform similarly to their
normal adult counterparts on both kinds of game. However, strategy differences were identified
on both the prisoner's dilemma and ultimatum game, although on the former to a greater extent
than the latter. Specifically the adults with autism showed less extreme behavioural choices of
competition and cooperation on the one hand (prisoner's dilemma) and different distributions of
opening offers on the other (ultimatum game). Contra our hypotheses, autistic adults were not
less (more) likely to cooperate with the human (computer) opponent, and they failed to adjust
fully for the dominant choice in the encouraged cooperation version. Moreover, by the second
round of the ultimatum game the discrepancy in offer distributions had disappeared. The overall
pattern was similar when comparing the two groups of children. The autistic children did not
adapt in any noticeable way to the encouraged cooperation PD, a strategic failure that may reflect
the perseverative continuation of earlier choice patterns. Normal and autistic children gave the
same unilateral gifts in the dictator game. Finally, with the just noted exception of the 6-year-
olds, the large difference in initial ultimatum offer distributions among the children was erased by
the second round.
We also investigated mentalising performance directly. A child’s ability to pass the
second-order false belief test, arising from either a functional theory-of-mind or rational, rule-
based deduction, was found to be positively related to the likelihood of cooperation in the three
PD games and to perfectly fair ultimatum offers rather than very small proposals. Those autistic
children who failed the simplest theory-of-mind test cooperated more than did those who passed
the test, but this difference seemed to result largely from the much more random responses of the
49
test failers to the moves of the counterpart. Adults with more effective mentalising abilities
employed them both to compete against the human and computer opponents and to cooperate in
the encouraged cooperation game. However, with this group, performance in the mentalising test
(interpretation of Happé stories) did not explain the variance in individual ultimatum offers.
All told there are numerous differences in the decisions and underlying strategies of the
participant groups. Roughly speaking, the development of theory-of-mind does seem to be
correlated with increasing generosity through childhood and then more strategic behaviour in
adulthood. However, when compared to the dramatic distinctions anticipated by our hypotheses
or the markedly varying introspections of the adults on strategy and choices, these findings are
weaker than expected. Arguably, the rather more surprising findings are those of the initial
similarity in performance profile, in particular in terms of the mean number of cooperative moves
across all rounds of the PD games and the offers made/rejected in the bargaining games. Such
similarity does not mirror the behavioural differences observed in autistic and nonautistic
individuals in similar real-life situations. How could this similarity on the experimental tasks be
explained in light of the differences in strategy-choice adopted by all players, the striking
mentalising deficits evidenced by the autistic participants and their relevant difficulties in daily
life?
A relationship between strong mentalising ability and increased social cooperation in
mixed-motive games has intuitive, and some experimental support. On the basis of the findings
of the current study it might seem that mentalising is differentially involved in the prisoner's
dilemma versus the bargaining games, being more critical in the former and less in the latter,
especially when supplemented by direct experience. However, the underlying differences in
strategy identified through statistical analysis, and corroborated in introspective reports as well as
in the comments of autistic adults about their interactions in daily life suggest, rather, that some
form of compensatory mechanism is driving the choices of the autistic individuals. One candidate
50
for compensation would be the substitute of intuitive understanding with a laboured, rule-based
approach in autism whereby the 'rules' of social interaction are gradually learned. These rules
must then be applied in on-line situations. This would likely be a laborious process. By such an
account it would not be surprising that behaviour could appear odd since social interaction does
not, in reality, operate on the strict application of rules alone. If a rule-based mechanism was
acting as a substitute for intuitive, easy interactions in the mixed-motive games reported here, it
is conceivable that the greater group differences highlighted in choices on the prisoner's dilemma
suggest that these social games were compensated for differentially in high-functioning
individuals with autistic spectrum disorders. This could arise because the 'rules' recruited for
bargaining can be more easily learned and/or applied than those for dealing with a dilemma. If
this were the case one might predict that an offer of exactly half would be made to the opponent
in the ultimatum game, a logical rule which cannot fail to be acceptable. In the first round, this
was exactly the profile identified in 60% of the autistic participants but in less than a third of the
normal participants. Moreover, more than a quarter of the autistic adults and children wished to
keep all ten points for themselves in the initial trial. Perhaps these participants had not developed
a rule for fairness, or identified the ultimatum game as a “finders keepers” game, i.e., if you’re
given something, it is yours alone. In contrast the 'rules' of the prisoner's dilemma are more
opaque and therefore harder to identify and use as successfully. Though relatively simple, a rule
such as ‘tit-for-tat’ may not suggest itself as easily in the PD as the fairness rules do in the
dictator and ultimatum games and so, the need to mentalise remains prominent throughout the
PD.
While it is not within the scope of the current study to pursue the issue of neural
activation when performing mixed-motive social games, published findings might shed some
light on the compensatory mechanism potentially adopted by the autistic individuals. Neuro-
imaging studies of mentalising in normal individuals have identified a network of brain regions
51
that is consistently active during mentalising over and above the other task demands. This
network involves the medial prefrontal cortex (especially anterior paracingulate cortex), the
temporal-parietal junction and the temporal poles (Fletcher et al., 1995; Brunet, Sarfate, Hardy-
Bayle & Decety, 2000; Castelli, Happé., Frith & Frith, 2000; Gallagher et al., 2000; Vogeley et
al., 2001). These areas appear to be activated less in the brains of autistic adults when performing
mentalising tasks (Happé et al., 1996; Baron-Cohen et al., 1999; Castelli, Frith, Happé., & Frith,
2002).
With respect to mixed-motive games, a recent functional magnetic resonance imaging
(fMRI) study in which playing a two-way reciprocal trust game against both a human and
computer opponent was contrasted showed increased activation in non-specified areas of the
prefrontal cortex in those players who consistently attempted cooperation with a human
opponent, than when the same players played against a computer following a fixed, known
probabilistic strategy. Those players who did not cooperate consistently did not show this pattern
of increased prefrontal cortex activation (McCabe, Houser, Ryan, Smith & Trouard., 2001). This
finding may accord with the notion of a social brain network described above, in which the
medial prefrontal cortex plays an important role in verbal and non-verbal mentalising tasks, as
well as in monitoring your own inner states. In a second fMRI study, Rilling et al. (2002)
required normal individuals to play an iterated prisoner's dilemma against both a human and a
computer opponent. In this study, mutual cooperation was associated with consistent activation in
brain areas that have been linked with reward processing, in particular the nucleus accumbens,
caudate nucleus, ventromedial frontal/orbitofrontal cortex and rostral anterior cingulate cortex.
Taken together these two studies suggest the potential involvement of mentalising and/or
reward/punishment systems in the brain. While the current study can not draw specific
comparisons to brain imaging data, it would be of interest to establish whether the brain
activations of autistic individuals would reflect those of normal individuals when making
52
behavioural choices that are - in outcome - identical across the two groups. Given the differing
levels and patterns of neural activation of this population for mentalising tasks, and the differing
strategies adopted by the two groups in the current study, it would seem most likely that the
neural activations of autistic and non-autistic individuals would differ. Information as to the
nature of the approach taken by the individuals with autism could be revealed by such imaging
studies.
The tests reported in this paper identified an unexpected profile of similarities as well as
differences in the performance of individuals with and without autism. Mentalising per se may
not be necessary for basic strategic rationality, but a quasi-mentalising compensatory mechanism
may be needed. Better mentalising (or greater success of a compensatory strategy) increased
levels of cooperation in some settings and of strategic behaviour in others. Thus on the surface a
putative compensatory mechanism in the autistic participants yielded similar behaviour to that
seen in the normal individuals. This contrasts with the striking difficulties in social interaction
experienced by individuals with autism in social interactions in the real-world. Perhaps it is the
on-line aspects of mentalising and mental flexibility which cause the greatest difficulty for high-
functioning autistic individuals in dilemma and bargaining situations in the real-world where far
more distractions and far fewer cues to guide behavioural choices exist than do in the almost
sterile laboratory where tasks can be seen to be abstract. We are currently investigating this
possibility.
53
ACKNOWLEDGEMENTS
This research was supported by funding from the UK's Medical Research Council (grant number
G9716841). We gratefully acknowledge the willing participation of all individuals in this study.
We are indebted to Sarah Griffiths, Zoë Fortune and Sakina Adam-Saib for substantial help with
data collection and especially to Professor Uta Frith for invaluable support for, and discussion of
the project.
54
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FIGURE LEGENDS
Figure 1: A generic prisoner's dilemma
Figure 2: Mean number of cooperative responses across all 16 rounds of each Prisoner's
dilemma game (Figures 2a and 2c) and percentage of each participant group
cooperating on the first round of each Prisoner's dilemma game (Figures 2b and 2d)
Figure 3: Percentage of each group (6-10 year olds combined) being 'reliably cooperative',
'reliably competitive' and 'variable' when playing the human opponent (Figure 3a),
computer opponent (Figure 3b) and encouraged cooperation (Figure 2c) versions of
the Prisoner's dilemma game
Figure 4: Percentage of each group (6-10 year olds combined) cooperating on each of the
sixteen rounds of each Prisoner's dilemma game
Figure 5: Mean points offered (max=10) by the participant groups to the confederate across
four rounds of the dictator and ultimatum games (Figures 5a and 5c) and on first
round only (Figures 5b and 5d). Error bars show standard deviation
Figure 6: Dispersal of first round ultimatum offers by adults and children with and without
autism (Figures 6a and 6b, respectively)
Figure 7: First round ultimatum offers based on second order false belief test result
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Figure 8: Mean points offered (max=10) by the participant to the confederate for each
participant group (6-10 year olds combined) on the eight rounds of the dictator and
ultimatum games
Figure 9: Mean number of points (max=10) rejected by participants (6-10-year-olds