Social Learning in Networks:Extraction of Deterministic Rules

Rustam Tagiew1, Dmitry Ignatov2, Fadi Amroush3

1Qlaym GmbH, Dusseldorf, Germany2National Research University Higher School of Economics, Moscow, Russia

3Granada Lab of Behavioral Economics (GLOBE), Granada, Spain

EEML 2013 at IEEE ICDM 2013Dallas, TX, USA

1 Introduction

2 Related Work

3 Social Learning in Networks

4 Data set

5 Results and Interpretations

6 Conclusion

Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Economics and Data Mining – Same Goal, Different Mindsets

The goal regarding human intercation

Hinting causalitities, Prediction of outcomes

Mindset of EconomistsAs in physics, theoretical considerations lead to a model, whoseparameters are then fitted to the data

Mindset of Data MinersA set of validated relations is derived from the data for latertheoretical considerations

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Once standard Economic Theory

The “Homo Economicus” Assumption

Humans are egoistic and rational... and this is a common knowledgeThe preferences are settled by amounts of money

Don’t confuse it with Game Theory

Game Theory is just neutral math to use,if preferences are known and players are rational

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Failure led to Experimental Economics

Unsurprisingly, humans are

... neither throughout egoistic

... no correct in reasoning to be rational.

They therefore deviate from game theoretic equilibriabut in quite predictable ways.

Data situationEconomists continue to conduct laboratory experimentsExcessive field data available sinceOrwellian nightmare became reality

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Data used in this paper

Same data, different mindsetChoi et al., 2012“Social learning in networks: quantal response equilibriumanalysis of experimental data”

Tagiew et al., 2013“Social learning in networks: extraction of deterministic rules”

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Related workChoi et al., 2012

Quantal Response Equilibrium (QRE)

“trembling-hand” essentially “delutes” game theoretic equilibria

P (action1,i) =eλ

∑j∈Actions2

P (action2,j)u1(action1,i,action2,j)∑actionk

eλ∑

k∈Actions1P (action2,j)u1(action1,k,action2,j)

λ→∞ results in the game theoretic equilibriumλ→ 0 results in random choice

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Related workTagiew, 2012

The two cases of behavior modelling in games

Participation: payoff maximization→ Non-deterministic modelsSpectator: correctness maximization→ Deterministic models

PerformanceCross-validation results of support vector machine baseddeterministic models outperformed related work on two data sets

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Social Learning in Networks – Game rules

Social Learning is the process of acquiring knowledge by observationof other players’ turns.

3 chosen network types of observation for 3 playersA

B C

A

B C

A

B C

Complete Circle Star

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Social Learning in Networks – Game rules

Further DetailsThe hidden variable is either white (1) or red (-1)(state of the world)If a players’ action matches the hidden variable,(s)he gets on average $0.5 payoffA turn is a simultaneous action by 3 players,after what actions can be observedA round consists of 6 subsequent turnsAt start of a round, every player might secretly get a signal,

which equals the hidden variable in2

3of cases

A group of 3 players completes 15 rounds at a stretch

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Social Learning in Networks – Game rules

Information levelsfull: signals are always sent

high: signals are sent in2

3of cases

low: signals are sent in1

3of cases

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Data Set

Number of subjects’ groups for 9 game configurations.

Information/ Low High FullNetwork type

Complete 6 5 6Circle 5 6 6Star 6 6 6

Total Number of Human Decisions3 ∗ 6 ∗ 15 = 270 times the sum of the table results 14040

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Signal is not provided; first turn (747 samples)

Bias towards −1Information/ low high sum

Network typecomplete 62% 69% 64%

star 67% 55% 64%circle 53% 52% 53%sum 61% 59% 60%

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Signal is provided; first turn (1593 samples)

Deviation from Signal

Player’s decision significantly correlates to signal only (0.883)

Signal/ −1 1Decision−1 757 511 42 743

5.8% deviation from rational choice(first round is not significantly lower)

Either undergrad students at New York Universityfailed at elementary math or they were aware of others’ payoffs

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

“Awareness of others’ payoffs”Brosnan and de Waal, Nature, 2007

Capuchin monkey experiment

YouTube link

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Signal is provided; correlations between inputs and the decision.

1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SignalMaximally correlated own decision Maximally correlated observed decision

turn number

corr

elat

ion

to d

ecis

ion

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Is the sabotage successful?

The equilibrium in full information complete network

1th turn: Copy the signal!2-6 turns: Copy the last turns’ median!

The deviation makes it futile to observe others (270 samples)

Median’s correctness drops from 74% to 68%Median and signal equally correlate with state

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Correlation of the real state to the decision in general (2340 samples)

1 2 3 4 5 60

0.05

0.1

0.15

0.2

0.25

0.3

Real stateReal state with signalReal state without signal

turn

corr

elat

ion

to d

ecis

ion

Correlation to signal is 0.347

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Signal is not provided; correlations between inputs and the decision.

1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Maximally correlated own decision Maximally correlated observed decision

turn number

corr

elat

ion

to d

ecis

ion

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Generalization and fit correctness for rule extraction (JRip)

1 2 3 4 5 650

55

60

65

70

75

80

85

90

95

100

Null hypothesis with signalNull hypothesis without signalGeneralization with signalGeneralization without signalFit with signalFit without signal

turn number

corr

ectn

ess

in p

roce

nt

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Generalization and fit Kappa for rule extraction (JRip)

1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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1

Generalization with signalGeneralization without signalFit with signalFit without signal

turn number

Kap

pa s

tatic

to d

ecis

ion

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Example of rule extraction

IF (Own decision in turn 3 = -1)& (Own decision in turn 4 = -1) THEN -1

ELSEIF (Own decision in turn 3 = -1)& (Signal = -1) & (Player = B) THEN -1

ELSEIF (Own decision in turn 3 = -1)& (1th observed in turn 4 = -1)& (GType = star) THEN -1

ELSEIF (Own decision in turn 4 = -1)& (Own decision in turn 2 = 1)& (Player = C) & (Round <= 7)& (Observed in turn 2 = -1) THEN -1

ELSEIF (Observed in turn 3 = -1)& (Own decision in turn 3 = -1)& (Round <= 7) & (Round >= 5)& (Signal = -1) THEN -1

ELSEIF (Own decision in turn 4 = -1)& (Observed in turn 3 = -1)& (Player = B) THEN -1

ELSEIF (Own decision in turn 4 = -1)& (Own decision in turn 1 = -1)& (Player = C) THEN -1

ELSE 1

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Conclusion

Strong hint of pugnacious behavior

Deterministic rules are able to generalize human behavior

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Introduction Related Work Social Learning in Networks Data set Results and Interpretations Conclusion

Future work

Collecting more data from Experimental Economics domain on aWeb portalApplying other Data Mining & Machine Learning techniques forEconomics and Social Sciences data concerning humanbehaviorIn particular emergent sequential patterns seems to be a goodtool for Game Data Mining since we deal with sequences ofactions and their outcomesCollaboration with other research teams working in ExperimentalEconomics and Game Theory potentially interested in DM&MLmethods

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