Social Cognition in Silica

A ‘Theory of Mind’ for Socially Aware Artiﬁcial Minds

Michael Harr

Complex Systems Research Group, Faculty of Engineering and IT, The University of Sydney, Sydney, 2006, NSW, Australia

Keywords:

Theory of Mind, Artiﬁcial Intelligence, Social Networks, Game Theory.

Abstract:

Each of us has an incredibly large repertoire of behaviours from which to select from at any given time,

and as our behavioural complexity grows so too does the possibility that we will misunderstand each other’s

actions. However, we have evolved a cognitive mechanism that allows us to understand another person’s

psychological space: their motivations, constraints, plans, goals and emotional state and it is called our ‘Theory

of Mind’. This capability allows us to understand the choices another person might make on the basis that the

other person has their own ‘internal world’ that inﬂuences their choices in the same way as our own internal

world inﬂuences our choices. Arguably, this is one of the most signiﬁcant cognitive developments in human

evolutionary history, along with our ability for long term adaptation to familiar situations and our ability to

reason dynamically in completely novel situations. So the question arises: Can we implement the rudimentary

foundations of a human-like Theory of Mind in an artiﬁcial mind such that it can dynamically adapt to the

likely decisions of another mind (artiﬁcial or biological) by holding an internal representation of that other

mind? This article argues that this is possible and that we already have much of the necessary theoretical

foundations in order to begin the development process.

1 INTRODUCTION

One of the key drivers of work on the development

of artiﬁcial human-like reasoning has focused on how

we come to understand the inanimate world. For ex-

ample, it is not uncommon to discuss cognitive devel-

opment almost solely in terms of the cognitive struc-

tures relating to inanimate objects (see (Tenenbaum

et al., 2011) for an example, where work on Theory

of Mind is mentioned in Open Questions). While the

learning of inanimate relationships is an important di-

rection to explore, it is only one piece of the puzzle

of cognition. In contrast, the focus of this work is

on our ability to understand interpersonal animate re-

lationships, an ability that appears to be equally old

and important in evolutionary terms as other forms of

comprehending the world.

Earlier work in anthropology has revealed some

striking facts about our neuro-cognitive architecture

and the role it plays in our social development as a

species. In 1992 Robin Dunbar put forward the hy-

pothesis that our neocortex grew in size in order to ac-

commodate the cognitive pressures imposed upon us

by our growing social group size. One of the notable

predictions to come out of this work is that humans

should have a social group size of approximately 150

individuals (Dunbar, 1992), this has been called Dun-

bar’s Number. The relationship between the neo-

cortex size and social group size is called the So-

cial Brain Hypothesis (Dunbar and Shultz, 2007) and

over the last 20 years considerable evidence across

many primate and non-primate species has been col-

lected supporting the hypothesis (Kudo and Dunbar,

2001; Shultz and Dunbar, 2007; Lehmann and Dun-

bar, 2009). Perhaps most signiﬁcantly, recent studies

have shown that this hypothesis is true at the individ-

ual as well as at the species level. In a study pub-

lished last year (Powell et al., 2012) by Dunbar and

colleagues it was shown that in individual humans,

the size of their social network was linearly related to

the neural volume of the orbital prefrontal cortex. A

secondary but critical ﬁnding of the same study is that

neural capacity is necessary but not sufﬁcient for large

social networks, the subjects also needed to have de-

veloped the psychological skills necessary for under-

standing another persons point of view. This cogni-

tive skill, called Theory of Mind (ToM (Baron-Cohen

et al., 2000)), enables us to understand that other peo-

ple have mental states and that these states might be

different from our own. This enables us to better

manage our social relationships and maintain a larger,

more complex and more diverse set of social relation-

657

Harré M..

Social Cognition in Silica - A ‘Theory of Mind’ for Socially Aware Artiﬁcial Minds.

DOI: 10.5220/0004917606570662

In Proceedings of the 6th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2014), pages 657-662

ISBN: 978-989-758-015-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

ships than any of our primate relatives.

Following on from these studies, the aim of this

article is to introduce a simple model of social inter-

actions between artiﬁcial agents that imply a view of

the agent as ﬁltered through the strategic perspective

of another agent, this is called a strategic Theory of

Mind (Harr

e, 2013). This is then extended to interac-

tions of multiple agents in a social network such that a

single agent’s decision-making process is inﬂuenced

by those in closest proximity in their social network,

but these closest relationships are in turn inﬂuenced

by second order relationships that are not directly re-

lated to the ﬁrst agent. The result is an extension of

strategic ToM to a socio-strategic ToM and social net-

works in general.

2 SPECIFIC FUNCTIONAL

ROLES OF THEORY OF MIND

Theory of Mind research looks at how we are able

to reason based on an internal representation of how

an individual believes other people’s minds operate in

general and then to use this representation to under-

stand how speciﬁc contexts inﬂuence another individ-

ual’s actions. In strategic interactions, such as eco-

nomic game theory, understanding another person’s

state of mind has the direct and obvious advantage

of beneﬁting in terms of increased payoffs (Bhatt and

Camerer, 2005), but these beneﬁts extend to every as-

pect of our lives, to how we teach children, collab-

orate in scientiﬁc research, empathise with the less

fortunate and how the economic division of labour al-

lows us to divide tasks according to the speciﬁc skills

and abilities of each individual.

In order to understand the neural foundations of

our ToM, recent progress has been made in the neuro-

imaging of human subjects carrying out ToM related

tasks. A complex network of brain regions have

been revealed that are activated during any cogni-

tive task that involves thinking of another person’s

state of mind or even social interactions with animate

rather than inanimate agents. Focusing speciﬁcally

on understanding and internally representing the men-

tal states of others, two of the most important func-

tional properties of these brain networks are the abil-

ity to recognise that people, unlike other things in the

world, have mental states that include thoughts, feel-

ings, constraints, goals and perceptions and the de-

velopment of an internal model of how these men-

tal states inﬂuence the decisions they make within a

speciﬁc environmental context (Lieberman, 2007). In

this article, the focus will be on person A thinking of

the environmental context in which person B is mak-

ing decisions, and B’s environment will be a social en-

vironment (that may include A). Note that this is only

a subset of the possible contexts in which B could be

making a decision and A might still ﬁnd it useful to

have a ToM for B in such contexts, but this is not the

focus of this article.

A special case worth highlighting is perspective

taking, which most commonly refers to understand-

ing the sensory perception of another person, for ex-

ample that another person sees something different

to what you can see. Humans can solve perceptual

perspective-taking tasks using visuo-spatial reasoning

without the need of a ToM mechanism (Zacks and

Michelon, 2005). However there is a broader mean-

ing to perspective taking that includes adopting or

considering another person’s psychological perspec-

tive, and this is sometimes understood as being syn-

onymous with empathy (Lieberman, 2007) (and so

sometimes is called cognitive empathy (Lamm et al.,

2007)). From this point of view adopting another per-

son’s perspective is equivalent to a person trying to

place themselves in the same psychological space as

the other person, including emotions, constraints etc.

and this is called the simulation theory of ToM (Gold-

man, 2005) (contrast with theory-theory ToM). This

article proposes a simpliﬁed form of the simulation

theory of ToM: an artiﬁcial mind can potentially con-

tain a model of another agent’s psychological per-

spective (either artiﬁcial or human), and can use this

perspective to improve their decision-making in so-

cial contexts.

2.1 A ‘Game Theory of Mind’

Arguably one of the most signiﬁcant insights to come

from economics is to ask the central question: How

do people make decisions in the context of other peo-

ple’s decisions? This strikes close to issues central

to our ToM, if one person understands that another

person’s actions will change the reward they will re-

ceive, then understanding the way in which that other

person chooses their actions would be an invaluable

tool. From this point of view, without comprehend-

ing another person’s inner cognitive workings when

the value of a reward depends upon the other’s de-

cisions a vast world of cooperative and competitive

advantage is lost to us. Such reasoning requires in-

dividuals to account for how other’s view each of the

likely decision’s everyone else will make, and in do-

ing so they collectively change the decision-making

patterns of the collective.

In a similar vein, decision-making has been mod-

elled across large populations using stochastic differ-

ential equations in order to explain their choices in

ICAART2014-InternationalConferenceonAgentsandArtificialIntelligence

658

economic games. In a notable study, at an economic

conference on game theory, the participants were

asked to play a game called the Traveler’s Dilemma

for real monetary rewards (Goeree and Holt, 1999;

Anderson et al., 2004). While the participants did

not play the strict equilibrium strategies predicted by

classical economics, they did make decisions that col-

lectively were in agreement with a form of bounded

rationality equilibrium described by statistical evo-

lutionary equations and whose stationary states are

again reminiscent of some probabilistic models used

in Artiﬁcial Intelligence (AI) and theoretical psychol-

ogy.

In the ﬁnal study considered here, Yoshida et

al. (Yoshida et al., 2008) recently proposed what they

called a Game Theory of Mind that uses bounded re-

cursion (of the sort: I’m thinking of you thinking of

me thinking of you etc. truncated at a certain level)

and value functions attributable to different players in

order to model depth of strategic reasoning.

2.2 A Stochastic Model of

Decision-making

Conventional game theory begins with a number of

players and the rewards they receive for their joint ac-

tions, in the simplest case there are two players (here

called A and B), each of which has two choices and

the payoff matrices are given by:

α =





, (1)

β =





. (2)

The expected utility to each player is given in terms of

the joint probability p(α

)q(β

) = p(A

)q(B

) = p

Here, A denotes the player, A

denotes a decision vari-

able that can take two different value, either α

denoting the ﬁrst or second row in equation 1,

and the A

are sometimes called cumulative decision

variables (see below for where this comes from) and

p(A

) = A

/(A

+ A

) etc. (equiv. for B), so:

(u) =

∑

i, j

, E

(u) =

∑

i, j

(3)

A further set of equations are needed as well, called

the conditional expected utilities (Wolpert et al.,

2012):

(u|α

) =

∑

, E

(u|β

) =

∑

(4)

in which the expected utility to α is conditional upon

α ﬁxing their choice to α

(similarly for β). Us-

ing these expressions we can represent how a single

player (A in what follows) models the theirs and their

opponents incremental changes in the decision vari-

ables during time interval dt in terms of a determinis-

tic drift term and a stochastic diffusion term (Bogacz

et al., 2006):

= (α

+ α

)dt + σ

(5)

= (

)dt + σ

(6)

Figure 1: The neuro-cognitive development of a ToM by

player A. In each panel A

signals before A

and A

then

laterally inhibits A

from signalling (inhibition connections

not shown). A: Two cell assemblies encode stochastic deci-

sion variables A

and A

that take early signals from other

regions of the brain. B: Two new cell assemblies are formed

that encode the decision variables B

and B

of another

player, these decision variables inﬂuence the A

decision

variables via black dashed connections. C: The A

are now

reciprocally connected to the B

through red dashed con-

nections such that dynamic changes in the activity of the

cell assemblies during the decision making process are

reﬂected in the activity of the B

cell assemblies.

Note the tilde in these equations indicating that it

is the A player’s estimate of the B player’s utility and

SocialCognitioninSilica-A'TheoryofMind'forSociallyAwareArtificialMinds

659

decision variable B, in game theory the utility is com-

mon knowledge between players, but in representing

the other player’s decision process each player has to

estimate the utility the other player will gain from the

interaction. Equations 5 and 6 represent a model of

how A has neurally encoded the constraints, their esti-

mates of B’s incentives as well as their decision mak-

ing process (it is the same as A’s). In this representa-

tion of stochastic neural signal accumulation, the dA

are only implicitly connected to each other through

their connection with the B

(no A

term appears on

the right hand side of equation 5), however each A

interacts with both B

terms. This is how the neural

network of A looks once it has fully developed, but the

intermediate steps to this ﬁnal form can be described

as:

A. dA

= µ

dt + σ

(7)

B. dA

= (α

+ α

)dt + σ

(8)

dt + σ

(9)

where the letter labels on the left reﬂect the panel la-

bels of Figure 1 and panel C. is modelled by equa-

tions 5 and 6. The µ

term of equation 7 represents

the weight the player attributes to each of their two

options, because the player is not accounting for the

other player’s strategies at this point, a plausible (but

by no means the only) strategy is to take the average

of the two payoff’s available for each choice for ex-

ample: µ

= (α

+ α

)/2 (similarly for B’s µ

). In

terms of strategic thinking (see as an example (Cori-

celli and Nagel, 2009)), option A. is level 0 thinking,

no account is made of the other player’s choices, the

choice of µ

= (α

+ α

)/2 implies A assumes the

other player equally weights their choices, but there

are obviously many other alternative formulations of

. Option B. is level 1 thinking, some account is

made of B’s strategy, but no attempt is made by A

to adjust their interpretation of B’s strategy by ac-

counting for how B might be strategically weighting

their choices based upon A’s likely strategy. Finally,

equations 5 and 6 represent A accounting for their es-

timation of the weighted strategies of B where B’s

weighted strategies accounts for A’s weighted strate-

gies (level 2 thinking).

It is not easy to see that there is necessarily a solu-

tion to these equations such that an equilibrium in the

dynamics might be achieved. However, it has recently

previously been shown that providing the drift terms

are linear in the decision variables (the terms that pre-

cede dt in equations 5- 6) there is a guaranteed set of

equilibrium probabilities given by:

p(A

) ∝ e

(u|α

)

(10)

p(B

) ∝ e

(u|β

)

(11)

where the γ

and γ

terms are proportional to the noise

terms σ in equations 5 and 6 and the remainder of

the terms in the exponents are simply the conditional

expected utilities of equation 4. The interpretation of

this form is that if A holds strategy A

ﬁxed then the

probability of choosing strategy A

is proportional to

the exponentiation of the utility condition on A

being

ﬁxed based upon A’s estimate of the distribution over

strategies B will choose.

In order to see how equations 10 and 11 can be

thought of as social perspective taking, simplify these

probabilities to only one variable for each player:

= 1 − 2p(A

) ∈ [−1, 1] and Q

= 1 − 2q(B

) ∈

[−1,1]. Now rewrite equations 10 and 11 in an ex-

plicit form in terms of an equilibrium involving only

for A:

= 1 −

(u|α

)

(u|α

)

+ e

(u|α

)

(12)

= tanh(

(u|α

) − E

(u|α

))) (13)

= tanh(

+ z

)) (14)

= tanh(

(tanh(

+ z

))))) (15)

The z terms are reduced constants derived from pay-

off matrices 1 and 2. Note that Q

can be written

as a function of Q

: Q

= F

) where F

(·) is

A’s decision model with A’s γ and z parameters, cf.

equation 14 and likewise Q

= F

). However,

these are implicit self-consistent equations for each

player’s choices: Q

= F

)) (cf. equation 15)

and Q

= F

)).

2.3 Social Networks, Decisions and ToM

Between players A and B a minimal 2-person social

network has been described, one of mutual and self

consistent comprehension between the two players

(when in equilibrium) based upon an accurate men-

tal model each has of the other. This small social

network can be expanded to multiple agents, to do

so label each new agent C, D, E etc. and like A

and B these new comers only have two options in a

game theory-like setting to choose from so that Q

, Q

etc. can be deﬁned similarly to Q

= F

Taking the perspective of how A needs to internally

model their social network in order to make decisions

that are ‘in equilibrium’, A’s model will depend upon

the local topology of their social network. For exam-

ple if A is connected to four other people and these

people do not know each other or anyone else other

ICAART2014-InternationalConferenceonAgentsandArtificialIntelligence

660

than A, then A can represent them as independent:

= F

),F

)), i.e.

= tanh

(tanh(

+ z

))) +

(tanh(

+ z

))) +

(tanh(

+ z

))) +

(tanh(

+ z

))))

(16)

where the z and γ notation has been extended to these

new players, see Figure 2, B. Alternatively, given

three agents that all know each other and interact with

each other, A’s model of their local social network

would be Q

= F

))), i.e.

= tanh

(tanh(

+ z

)))

(17)

see Figure 2, C. In this example it would not be a com-

plete representation of the local network topology for

A to simply have accounted for B and C as though

these two people were independent of each other, in

such a model: Q

= F

),F

)), but this does

not accurately reﬂect how A needs to consider the way

in which B and C adjust their decisions based upon the

connection they have with each other, as this connec-

tion indirectly inﬂuences how A needs to consider the

choices they make. More generally, in the case of B.

of Figure 2, while A is inﬂuenced by B (and C, D and

E), B might themselves be connected to other players

in their local network and these players are only indi-

rectly related to A through the inﬂuence they have on

B’s decisions.

3 CONCLUSIONS

How do agents, artiﬁcial or biological, coordi-

nate their actions in such a way that their collec-

tive decision-making is better than their individual

decision-making? People are both good and bad at

such aggregation: science is based on individuals co-

operating and competing in order to produce a body of

knowledge far greater than any one individual could

achieve, but the coordinated behaviour of traders in

Figure 2: The internal representations A has of the

other agents in different network topologies. Each

topology has a distinctive representation when A’s

choices are in equilibrium: A: Q

= F

)),

B: Q

= F

),F

)), C: Q

))).

ﬁnancial markets can lead to billions of dollars be-

ing lost in a market crash. More importantly for ar-

tiﬁcial agents, what are the theoretical foundations of

cooperation and competition that can lead to simple

agents making better decisions collectively than could

be achieved through every individual acting indepen-

dently of one another? So how do we engineer true

collective intelligence in societies of artiﬁcial agents?

One approach is outlined in this work: individual

agents make their decisions based on what they can

each individually and objectively know (or can ﬁnd

out) about the environment as well as how they be-

lieve other agents will make their choices and how

these choices subsequently impact on the quality of

their own decisions. In people, such cooperative di-

vision of labour leads to specialisation and expertise

amongst a population that is able to solve problems

that no individual could solve alone, replicating this

in a collection of artiﬁcial intelligences will open up

the possibilities of a symbiosis of bio-silica commu-

nities, where artiﬁcial agents are dynamically respon-

sive to the internal mental states of people, enhancing

the quality of our decision-making.

SocialCognitioninSilica-A'TheoryofMind'forSociallyAwareArtificialMinds

661

REFERENCES

Anderson, S. P., Goeree, J. K., and Holt, C. A. (2004).

Noisy directional learning and the logit equilibrium.

The Scandinavian Journal of Economics, 106(3):581–

602.

Baron-Cohen, S. E., Tager-Flusberg, H. E., and Cohen,

D. J. (2000). Understanding other minds: Perspec-

tives from developmental cognitive neuroscience . Ox-

ford University Press.

Bhatt, M. and Camerer, C. F. (2005). Self-referential think-

ing and equilibrium as states of mind in games: fmri

evidence. Games and Economic Behavior, 52(2):424–

459.

Bogacz, R., Brown, E., Moehlis, J., Holmes, P., and Cohen,

J. D. (2006). The physics of optimal decision making:

a formal analysis of models of performance in two-

alternative forced-choice tasks. Psychological review,

113(4):700.

Coricelli, G. and Nagel, R. (2009). Neural correlates of

depth of strategic reasoning in medial prefrontal cor-

tex. Proceedings of the National Academy of Sciences,

106(23):9163–9168.

Dunbar, R. (1992). Neocortex size as a constraint on

group size in primates. Journal of Human Evolution,

22(6):469–493.

Dunbar, R. I. and Shultz, S. (2007). Evolution in the social

brain. science, 317(5843):1344–1347.

Goeree, J. K. and Holt, C. A. (1999). Stochastic game

theory: For playing games, not just for doing the-

ory. Proceedings of the National Academy of Sciences,

96(19):10564–10567.

Goldman, A. I. (2005). Imitation, mind reading, and sim-

ulation. Perspectives on Imitation: Imitation, human

development, and culture, 2:79.

Harr

e, M. (2013). The neural circuitry of expertise: Percep-

tual learning and social cognition. Frontiers in Human

Neuroscience, 7:852.

Kudo, H. and Dunbar, R. (2001). Neocortex size and so-

cial network size in primates. Animal Behaviour,

62(4):711–722.

Lamm, C., Batson, C. D., and Decety, J. (2007). The neural

substrate of human empathy: Effects of perspective-

taking and cognitive appraisal. Journal of cognitive

neuroscience, 19(1):42–58.

Lehmann, J. and Dunbar, R. (2009). Network cohesion,

group size and neocortex size in female-bonded old

world primates. Proceedings of the Royal Society B:

Biological Sciences, 276(1677):4417–4422.

Lieberman, M. D. (2007). Social cognitive neuroscience: a

review of core processes. Annual Review of Psychol-

ogy, 58:259–289.

Powell, J., Lewis, P. A., Roberts, N., Garc

ıa-Fi

nana, M.,

and Dunbar, R. (2012). Orbital prefrontal cortex

volume predicts social network size: An imaging

study of individual differences in humans. Proceed-

ings of the Royal Society B: Biological Sciences,

279(1736):2157–2162.

Shultz, S. and Dunbar, R. (2007). The evolution of the so-

cial brain: Anthropoid primates contrast with other

vertebrates. Proceedings of the Royal Society B: Bio-

logical Sciences, 274(1624):2429–2436.

Tenenbaum, J. B., Kemp, C., Grifﬁths, T. L., and Goodman,

N. D. (2011). How to grow a mind: Statistics, struc-

ture, and abstraction. science, 331(6022):1279–1285.

Wolpert, D. H., Harr

e, M., Olbrich, E., Bertschinger, N.,

and Jost, J. (2012). Hysteresis effects of changing the

parameters of noncooperative games. Physical Review

E, 85(3):036102.

Yoshida, W., Dolan, R. J., and Friston, K. J. (2008).

Game theory of mind. PLoS computational biology,

4(12):e1000254.

Zacks, J. M. and Michelon, P. (2005). Transformations of

visuospatial images. Behavioral and Cognitive Neu-

roscience Reviews, 4(2):96–118.

ICAART2014-InternationalConferenceonAgentsandArtificialIntelligence

662