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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
0.9
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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