An agent-based model of trust in social networks

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Oxford Internet Institute, February 18th, 2013

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SCID researchers

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Sociology &The Institute for Social Change

Nick CrossleyEd Fieldhouse Laurence Lessard-Phillips Yaojun LiNick ShryaneHuw Vasey

Theoretical Physics Group, School of Physics and Astronomy

Alan McKaneLouise DysonLuis Fernandez Lafuerza

Centre for Policy Modelling

Bruce EdmondsRuth Meyer

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SCID Goals

Taking modelling tools & techniques from Computational Science and Statistical Physics…

…to combine data & theory from Sociology and Psychology

…applied to the topic domain of social diversity and cohesion

Complexity Science

Social Science

Ethnic & Religious diversity

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SCID topic: diversity and social trust

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When is trust required?

Consider x’s position:– “x wants y to do z in context c”; e.g. “Bill (x) wants bob (y)

to babysit (x) during half-term (c).”

If: – x will be better off if y does z; worse off if not.– y may or may not do z.– x cannot be sure if y will do z.

Then for x there is potential benefit, but also uncertainty and risk.To achieve z through y, x must trust y.

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Trust as benevolence

Trust involves x’s beliefs about the trustworthiness of y:

– Reliability: “Does y often do z?” – Competence: “Is y able to do z?” – Intentions: “Does y want do z?”

In social situations, people are particularly concerned about intentions; in particular, that y may want to cheat or exploit x.

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Ethnicity and trust

• Classification to and self-identification with a particular ethnic in-group predicts:– Judgements of trustworthniness of in- and out-group faces– fMRI neural correlates of fear/alertness and risk/reward– Trusting/trustworthy behaviours in so-called economic

“trust games”

• Patterns of social connectedness exhibit strong homophily for ethnicity

E.g. Smith, S. S. (2010). Race and Trust. Annual Review of Sociology, Vol 36, 36, 453-475. doi: 10.1146/annurev.soc.012809.102526

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Problem: Trust in diverse social networks

£

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SCID aims to bring together theory and evidence from different ‘levels’

Social Surveys Macro patterns

Case StudiesMeso level

Lab Trust

GamesMicro level

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SCID aims to bring together theory and evidence from different ‘levels’

Class, Wealt

hSocial structures

Social Networks

Social processes

Judgement &

Decision-Making

Cognitive processes

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Complexity as inter-level interaction

• Complexity is (in part) the science of how micro-processes can give rise to meso- and macro-level phenomena– Micro-level interactions may give rise to local

meso-level regularities and more global macro-level structures

– Macro- and miso-level structures shape and constrain how the lower-level processes may operate and evolve.

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An example: Boids

• Perceptual attributes– Field of vision– Recognition of similar

others

• Behaviours– Forward movement– Turning radius

• Goals– Be close to neighbours– Don’t bump into others

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An example: Boids

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An example: Boids

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Level-specific phenomena

• Micro level has– Perception and

cognition of the individuals boids

– No central ‘planning’ or control, only inter-agent feedback

• Meso-level has– Flocks – somewhat

persistent collections of boids

– Similar to social networks, but with

• Fungible (i.e. exchangeable) agents

• constantly changing ‘weights’ between agents

An example of the layering of related models in chemistry

• AdapGunsteren, W. F; Berendsen, H. J. C. (1990) Computational Simulation of Molecular Dynamics: Methodology, Applications and Perspectives in Chemistry. Angewandte Chemie - International Edition in English, 29:992-1023.

Applying the model to flocking

• AdapGunsteren, W. F; Berendsen, H. J. C. (1990) Computational Simulation of Molecular Dynamics: Methodology, Applications and Perspectives in Chemistry. Angewandte Chemie - International Edition in English, 29:992-1023.

Flocks of birdsCorrelations between bird distances

Existing models of bird perception and cognition

Simple boids modelFlocking theory

Abstraction of simple boids model

The SCID Modelling Approach

Data-Integration Simulation Model

Micro-Evidence Macro-Data

Abstract Simulation Model 1 Abstract Simulation Model 2

SNA Model Analytic Model

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Emancipation theory of trust Yamagishi (2011)

Co-operating exclusively with known associates in a close-knit social network reduces the chance of betrayal and exploitation because of the ease of monitoring and punishment/ exclusion.This strategy incurs opportunity costs, as potentially more profitable opportunities may exist outside of the network.

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Emancipation theory of trust Yamagishi (2011)

The opportunities outside the network may be realised by trusting strangers, i.e. co-operating under high uncertainty with regard to the trustworthiness of your partner. Trust therefore ‘emancipates’ actors from purely parochial co-operation.Trust risks exploitation, but this risk can be mitigated if actors display and can discriminate signs of trustworthiness.

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Emancipation theory of trust Yamagishi (2011)

The emancipation theory of trust makes no explicit reference to ethnicity and migration. But, it does assume that to avoid parochialism and mistrust requires learning about signs of trustworthiness. This requires some exposure to and familiarity with those you hope to co-operate with.Homophily and xenophobia, associated with ethnicity, would be expected to reduce intergroup interaction and so reduce trust.

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A proposed specification for an agent-based model of the

emancipation theory

Based upon:

Yamagishi, T. (2011). Trust: The evolutionary game of mind and society: Springer.

Macy, M. W., & Sato, Y. (2002). Trust, cooperation, and market formation in the US and Japan. Proceedings of the National Academy of Sciences of the United States of America, 99(Supp 3): 7214-7220.

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Aim

• This describes a ‘MK1’ model, which aims to represent just a few of the core processes that may be involved in trust.

• We shall build upon this in MK2, MK3…• This talk will focus on how some of these

processes are specified in the proposed ABM

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Stage 1: agents are allocated to networks

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Agents are given ‘tags’; fixed ones…

Representing e.g.sex, ethnicity

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…and labile ones

Representing e.g.wealth, politics

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…and labile ones

Representing e.g.wealth, politics

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Stage 2 – parochial or cosmopolitan?

Agents decide if they want to seek a transaction inside their network…

?

.. or outside of their network,?

based on an agent-specific propensity plocal

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Stage 3 –dyad formation

Within-network preference

Across-network preference

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Stage 3 –dyad formation

Within-network preference

Across-network preference

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Stage 4 – trust your partner?? ?

Agents have a propensity to trust, ptrust.

This is influenced by: i) Success in the past associated with trusting ii) Knowledge of acts of betrayal by your partner iii) Expectations based upon your partners tags

If either agent does not trust, the game is off.If both agents trust, the game is on.

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Stage 5 – cheat your partner?

Co-operate Cheat

Co-operate Reward

Reward

Temptation

SuckerCheat Sucker

Temptation

Punishment

Punishment

T > R > P > S

Agents have a propensity, pco-op,to co-operate

Payoffs are ordinal:

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Stage 5 – cheat your partner?

Co-operate Cheat

Co-operate Reward

Reward

Temptation

SuckerCheat Sucker

Temptation

Punishment

Punishment

T > R > P > S

Agents have a propensity, pco-op,to co-operate

Payoffs are ordinal:

If decisions are made ‘blind’, game is “Prisoner’sdilemma”. If one player moves first and the otherknows the move, it’s called the “Trust game”.

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Opportunity cost

Across-network preference

The pool of potential partners within networks is likely to be much smaller than that available across networks – interacting within-networks should incur an opportunitycost.

Within-network preference

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Opportunity cost

Across-network preference

opportunity cost

n = size of ‘pool’N = size of population

1

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N

nOC

Within-network preference

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Opportunity cost

Within-network preference

Across-network preference

92.0113

121

OC 17.0113

1111

OC

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Reinforcement learning

Propensities associated with good outcomes are reinforced.Bush-Mosteller stochastic learning algorithm:

Probability of a certain action at time t = Pt ;

Benefit of payoff at time t = βt (where -1 < βt < 1);

If βt >= 0, Pt+1 = Pt + (1-Pt)βt, and

if βt < 0, Pt+1 = Pt + Ptβt.

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Memory and reputation

All agents within a network know about and shun cheaters within the network. Knowledge of cheating by outside agents is gained through experience.Outside cheaters are shunned:

With certainty if he/she cheated you.With high probability if he/she cheated someone you have interacted with (i.e. third-party reputation).

Therefore, networks facilitate monitoring and punishment.

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Learning from social signals (tags)Agents construct a measure of association between a partner’s tags and good/bad outcomes:

– Based upon their own interaction history.– Influenced by their whole network’s interaction

history (i.e. stereotypes).

Agents/networks with a limited history of interaction (i.e. small sample size) will develop biases – ‘beliefs’ about tags that don’t reflect the true population associations.

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Learning from reputation and Social Signals

• Agents’ dispositional propensities, e.g. to trust or cooperate, are nudged up or down by contextual factors for each specific interaction, based upon:– Social ‘tag’ signals on display (and the

individual/group evaluation of them)– Memory of interactions with the individual agent

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Learning from trustworthinessIf the agents play the “trust game” rather than the “prisoner’s dilemma”, one of them “shows their hand” and moves first.This risks easy betrayal by the other player, but may be used as a costly ‘signal’ of trustworthiness by the first player. Co-operators may be able to find each other by displaying and learning from such signals.

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Evaluation stage – outcome measures

The simulation is run many times, allowing for summary statistics to be generated and research questions to be addressed, e.g.:

What is the relationship between within-network tag homophily and strategy choice/success?How does network size and interaction history influence tag learning?

One advantage of the games approach is that data from behavioural experiments is available - but almost always just dyads

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SummaryAgents exist in networks where they share information, monitor each other and shun within-network cheaters. But interacting within one’s own network carries an opportunity cost.Interacting with strangers outside the network (i.e. trusting) carries potentially greater payoffs, but has a greater risk of betrayal; this can be ameliorated if agents can tolerate these costs while learning to spot signs of trustworthiness.

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Summary• We give agents:

– Homophily, social monitoring, reinforcement learning, social signals (tags)

• Based on theory, we expect to see emerge:– Some networks settling into mutual co-operation

and distrust of strangers; other networks developing trust in outsiders and lots of out-group co-operation; different groups developing different stereotypes of social signals, because of their different levels of interaction with ‘outsiders’.

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Example networks

• Heterogeneous group ‘ethnicity’

• Heterogeneous group size

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Example networks

• Homogeneous group ‘ethnicity’

• Homogeneous group size– e.g. dyads only

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Some preliminary results

Homogeneous, parochial networks

– Passing is initially high, cooperation low

– Trust and cooperation evolve slowly

– Defecting evolves with cooperation as the global market is established

• With high N there is a low probability of cheaters being excluded from the market.

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Some preliminary results

Dyads with high sensitivity to defection

– Passing stays high; cooperation also high but hardly ever exercised!

– Trust never develops

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Next steps

• Evolving social networks– A central plank of the Emancipation Theory of

Trust is social uncertainty• ‘Trust + social intelligence’ and ‘strong social networks’

are both seen as solutions to this uncertainty.

– We could use uncertainty reduction as a driving process of network formation, e.g.

• Homophily = less uncertainty about social signals• Network closure = less uncertainty about network

monitoring

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Improving the model

This is Mk1 for the trust model; is not intended to comprehensively represent all aspects of social trust - it is a bare-bones model of a theory of trust. We will look to expand this into Mk2 & Mk3. What really important factors have we left out? E.g.:

Agents currently do not know their own tag status (e.g. ethnicity) and are free to develop ‘prejudices’ against their own kind. Is this a problem?There are no ‘legal institutions’ in the model, i.e. global agencies that monitor trust and promise punishment. A future Mk2 model may include these. (How?)

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Improving the model

Agents do not have internal models of others agent’s intentions – e.g. learning algorithm is ‘rearward facing’, not anticipatory.

I haven’t mentioned how the labile tags are updated/ changed. These tags may be seen as signs of group membership, or perhaps of social status. For example, high status has been found to be associated with perceptions of trustworthiness – perhaps because it is hard/risky to fake and costly if lost by abusing trust. How could we implement this?

Your thoughts appreciated