coordination and learning in dynamic global games: experimental evidence olga shurchkov mit the...
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June 2007 Coordination and Learning3 Intro: Literature Review Coordination models with complete information (Obstfeld, 1996) Global coordination models with heterogeneous information (static framework) Carlsson and van Damme, 1993 Morris and Shin, 1998 Global coordination models with heterogeneous information (multi-period framework) Angeletos et al., 2006 Experimental Evidence Cooper, DeJong, Forsythe, and Ross, AER 1990, 1992 Van Huyck, Battalio, and Beil, AER 1990 Cabrales, Nagel, and Armenter, 2002 Heinemann, Nagel, and Ockenfels, EMA 2004 Cheung and Friedman, Working paper 2006TRANSCRIPT
Coordination and Learning in Dynamic Global Games:
Experimental Evidence
Olga ShurchkovMIT
The Economic Science AssociationWorld Meeting 2007
June 2007 Coordination and Learning 2
Intro: Motivation• 3 features of currency crises
• Strategic complementarities (coordination games)• Heterogeneous expectations (global coordination games)• Dynamic nature (dynamic global coordination games)
• Goals • Structure of equilibrium strategies• Impact of learning on dynamics of coordination
– “exogenous learning”– “endogenous learning”
• Multiplicity detection• Rationality assessment
• Approach • First study to test the predictions of dynamic global coordination models with a
laboratory experiment• Why a laboratory experiment?
June 2007 Coordination and Learning 3
Intro: Literature Review• Coordination models with complete information (Obstfeld, 1996)
• Global coordination models with heterogeneous information (static framework)• Carlsson and van Damme, 1993• Morris and Shin, 1998
• Global coordination models with heterogeneous information (multi-period framework)
• Angeletos et al., 2006
• Experimental Evidence• Cooper, DeJong, Forsythe, and Ross, AER 1990, 1992• Van Huyck, Battalio, and Beil, AER 1990• Cabrales, Nagel, and Armenter, 2002• Heinemann, Nagel, and Ockenfels, EMA 2004• Cheung and Friedman, Working paper 2006
June 2007 Coordination and Learning 4
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 5
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 6
The Model: Setup• Two-period version of Angeletos-Hellwig-Pavan (2006)
• Players indexed by i take actions: A (“attack”) (ait = 1) or B (“not attack”) (ait = 0).
• Status quo collapses iff the mass of agents attacking is A >
• Individual payoffs
• Information structure:• is drawn from N( z,1/) and is not observed by the agents• z is the prior – the public signal• Additional private signal: xit = + it where
)/1,0(~ tit N
A > A <
Attack (a i = 1) 100 – c – cNot Attack (a i = 0) 0 0
June 2007 Coordination and Learning 7
• Prediction 1: There exists a unique x1* such that in any equilibrium of the dynamic
game, an agent chooses action A (“attack”) in the 1st period iff x1 < x1*, which
implies that there exists a unique 1* such that the status quo is abandoned
iff < 1*.
• Implications for experiment: • A1() is decreasing in
• The thresholds 1* and x1
* are decreasing in the cost of attacking, c
The Model: Period 1 Predictions
A
Everyone
0
June 2007 Coordination and Learning 8
The Model: Period 2 Predictions
• Prediction 2: No new information not attacking is the unique equilibrium.
Implication for experiment: Probability of attack should be greatly reduced in the second stage.
• Prediction 3: Sufficient new information (2 is sufficiently large) new attack becomes possible, if z is sufficiently high.
Implication for experiment:
Probability of attack should be higher with new information in second stage thanwith no new information.
Notes: z is the prior ( is drawn from N( z,1/)) 2 is the precision of private signal, x, in period 2
June 2007 Coordination and Learning 9
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 10
The Experiment: Treatments
Table 1: Session Overview Table 2: Parameterization
• 6 sessions at the Institute for Empirical Research in Economics, Zurich
• 30 subjects in each session
• 2 groups of 15 subjects each
• Different treatments for cost of attacking and information in Stage 2
Notes: is drawn from N( z,1/ ))
is the precision of private signal, x
• Elicitation of beliefs
Session z, 1/ 1/1 1/2
1-4 65, 50 7 N/A5-6 75, 55 10 1S
First 20 Rounds
Last 20 Rounds
First 20 Rounds
Last 20 Rounds
1,2 20 50 No No3,4 50 20 No No5 60 60 No Yes6 60 60 Yes No
Information in Stage 2Cost of Action A
June 2007 Coordination and Learning 11
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 12
Data Analysis: First Period Predictions
Figure 1: Kernel Regression: Fraction of Agents Attacking vs. Theta (pooled data for sessions 1-4, cost 50)
Attack Fraction is monotonically decreasing in
0
0.2
0.4
0.6
0.8
1
-100 -50 0 50 100 150 200
Att
ack
Frac
tion
June 2007 Coordination and Learning 13
1 2 3Private signal, x -0.007*** -0.007*** -0.001***
(0.0001) (0.0001) (0.0001)Cost of action A -0.003*** -0.0004**
(0.0003) (0.0002)Belief 0.067***
(0.0010)R2 0.58 0.59 0.84No. of observations 6000 6000 6000Note: Robust standard errors in parentheses. Regressions include group,subject, and round fixed effects. For sessions 5 and 6, only the no-new-information treatment data are used. Significance levels: ** 5%, *** 1%.
Dependent Variable: Action
Data Analysis: First Period Predictions Table 3: OLS Regressions of individual action on x in Stage 1, all data for sessions 1-4
June 2007 Coordination and Learning 14
Session CostPercent Using
Thresholds1, 2 20 81.5 88.8 87.8 84.3 93%1, 2 50 48.1 82.8 47.8 82.5 93%3, 4 20 81.5 89.0 87.8 85.3 95%3, 4 50 48.1 77.3 47.8 77.1 95%5, 6 60 34.8 71.6 30.9 72.9 92%
Data Analysis: Static Predictions
*x̂
Table 4: Estimated Aggregate Threshold Summary
Note:
• Estimated thresholds vary only slightly with cost
x̂*
June 2007 Coordination and Learning 15
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 16
Data Analysis: Endogenous Learning
Figure 2: Average Probability of Attack for the No-New Information Treatments
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Stage 1 Ave Prob of Attack Stage 2 Ave Prob of Attack
June 2007 Coordination and Learning 17
1 2 3Private signal, x -0.006*** -0.006*** -0.0008***
(0.0001) (0.0001) (0.0001)Cost of action A -0.0026*** -0.0005**
(0.0003) (0.0002)Belief 0.0655***
(0.0008)Stage -0.2307*** -0.2272*** -0.0399***
(0.0073) (0.0073) (0.0054)R2 0.62 0.62 0.85No. of observations 8820 8820 8820Note: Robust standard errors in parentheses. Regressions include group,subject, and round fixed effects. For sessions 5 and 6, only the no-new-information treatment data are used. Significance levels: ** 5%, *** 1%.
Dependent Variable: Action
Data Analysis: Endogenous Learning Table 5: OLS Regressions of individual action on x, all data for sessions 1-4
June 2007 Coordination and Learning 18
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 19
Figure 3: Average Probability of Attack for the No-New-Information (NNI) Treatments and the New-Information (NI) Treatments (only for rounds that continue into Stage 2 and for which x<100)
Data Analysis: New Information
0.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
NNI NI NNI NI
Stage 1 Stage 2
June 2007 Coordination and Learning 20
Table 6: Effect of the New Information Treatment on Stage 2 Actions
Data Analysis: New Information
Dependent Variable: Action
Private signal, x -0.0021***
(0.0002)NI dummy 0.0842***
(0.0145)R2 0.20No. of observations 1395Note: Robust standard errors in parentheses. Regressions include group, subject, and round fixed effects. Significance level: *** 1%.
June 2007 Coordination and Learning 21
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 22
Data Analysis: Rationality
0
0.25
0.5
0.75
1
0 20 40 60 80 100x
Belief about E[A|x] Theory E[A|x]
0
0.25
0.5
0.75
1
0 20 40 60 80 100x
Belief about E[A|x] Theory E[A|x]
Figure 4: Cost 20
Belief about Fraction of Agents Attacking vs. Theory Prediction
0
0.25
0.5
0.75
1
0 20 40 60 80 100x
Belief about E[A|x] Theory E[A|x]
Figure 5: Cost 50
Figure 6: Cost 60
Results of Rationality Test:
c=20: 76.98% rational
c=50: 90.79% rational
c=60: 89.44% rational
June 2007 Coordination and Learning 23
Data Analysis: Consistency Measure of Consistency:
LHS: Average size of attack
RHS: E[A()|x] is the
belief of subject i
E[E[A()|x]] is the
average belief
]]|)([[)]([ xAEEAE Cost Treatment
Average Realized Attack Fraction
Beliefs Averaged Across x
20 0.5857 0.535450 0.5799 0.534760 0.5071 0.4615
Cost & Info Treatment
Average Realized Attack Fraction
Beliefs Averaged Across x
20 NNI 0.0227 0.061050 NNI 0.0769 0.210160 NNI 0.0461 0.150560 NI 0.1248 0.1484
Table 7: Test of Consistency in Stage 1
Table 8: Test of Consistency in Stage 2
June 2007 Coordination and Learning 24
Presentation Agenda• Introduction and Motivation
• The Model Predictions
• The Experiment
• Data Analysis• First Period Predictions• Dynamic Predictions: Endogenous Learning• Dynamic Predictions: New Information• Rationality and Consistency
• Discussion
June 2007 Coordination and Learning 25
Discussion
• Static Predictions• Subjects follow monotone threshold strategies • Subjects act more aggressively than the theory predicts
• Dynamic Predictions• Subjects’ behavior exhibits learning• Less learning than the theory predicts (cost of attacking matters)
• Rationality• Given their aggressive beliefs, agents seem to behave rationally• Actions seem to be consistent with beliefs
June 2007 Coordination and Learning 26
Extra Slides
June 2007 Coordination and Learning 27
First Period Predictions: “Mistakes”
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35 40
0
0.05
0.1
0.15
0.2
0.25
0.3
0 10 20 30 400
0.05
0.1
0.15
0.2
0.25
0.3
0 10 20 30 40
Notes:• Estimated thresholds exhibit a slight upward trend
• Behavior that is not consistent with best-response strategy does not decrease significantly over rounds
• On average, in 91% of cases subjects followed a strategy that was a best response to the estimated threshold
Figure A1: Estimated thresholds vs. rounds (pooled data for sessions 1-4)
Figure A2: Proportion of “mistakes” relative to the best-response vs. rounds (Sessions 1-2)Figure A2: Proportion of “mistakes” relative to the best-response vs. rounds (Sessions 3-4)
)ˆ(
June 2007 Coordination and Learning 28
Endogenous Learning: Strategy Space
Figure A3: Probability of Attack vs. x by Stage for cost 50 treatments
Figure A4: Probability of Attack vs. x by Stage for cost 20 treatments
0
0.1
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0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
<50 50-60 60-70 70-80 80-90 90-100 >100x
Pr(A
ctio
n A
)
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<50 50-60 60-70 70-80 80-90 90-100 >100x
Pr(A
ctio
n A
)
June 2007 Coordination and Learning 29
0.00
0.10
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0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
<40 40-50 50-60 60-70 70-80 80-90 90-100 >100x
Pr(A
ctio
n A
)
First-Stage Probability of A, NI and NNI Average
Second-Stage Probability of A, NNI
New Information: Strategy Space
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
<40 40-50 50-60 60-70 70-80 80-90 90-100 >100x
Pr(A
ctio
n A
)
First-Stage Probability of A, NI and NNI Average
Second-Stage Probability of A, NNI
Second-Stage Probability of A, NI
Figure A5: Probability of Attack vs. x by Stage for the NNI TreatmentsFigure A5: Probability of Attack vs. x by Stage for the NNI and the NI Treatments
June 2007 Coordination and Learning 30
Calculation of Measure of Rationality
ix
ix
czxii
11
11
Figure A6: Thresholds for Different Cost Treatments
0
20
40
60
80
100
-200 -100 0 100 200 300
Cost 20 Cost 50 Cost 60
ix
ix
Measure of Rationality:
Expected payoff vs. Cost of attacking
Attack iff
Results:
Treatment c=20:
76.98% rational
Treatment c=50:
90.79% rational
Treatment c=60:
89.44% rational
);()(ˆ.. iiii xxgxgtsx
Threshold
June 2007 Coordination and Learning 31
Further Research: Theory• Correction for “mistakes”
• Justification for excess aggressiveness Optimism
0
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0.75
1
0 20 40 60 80 100
x
Bel
ief A
bout
Fra
ctio
n C
hoos
ing
A
Data Theory
0
0.25
0.5
0.75
1
0 20 40 60 80 100
x
Bel
ief A
bout
Fra
ctio
n C
hoos
ing
A
Data Theory Theory w ith Mistakes
0
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1
0 20 40 60 80 100
x
Bel
ief A
bout
Fra
ctio
n C
hoos
ing
A
Data TheoryTheory w ith Mistakes Theory w ith Mistakes & Optimism
Figure A7: Modified Theoretical Beliefs for Cost-50 Treatment
June 2007 Coordination and Learning 32
Further Research: Experimental
• Allowing for communication “generic sunspot”
• Effects of gender on coordination