Coordination and Learning in Dynamic Global Games: Experimental Evidence

Coordination and Learning in Dynamic Global Games:

Experimental Evidence

Olga Shurchkov

MIT

The Economic Science Association

World 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?


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


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




• The Experiment


• Discussion


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


• 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


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




• The Experiment


• Discussion


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




• The Experiment


• Discussion


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


1 2 3

Private 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


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*




• The Experiment


• Discussion


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


1 2 3

Private 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%.


Data Analysis: Endogenous Learning Table 5: OLS Regressions of individual action on x, all data for sessions 1-4




• The Experiment


• Discussion


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


Table 6: Effect of the New Information Treatment on Stage 2 Actions

Data Analysis: New Information


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%.




• The Experiment


• Discussion


Data Analysis: Rationality

0

0.25

0.5

0.75

1

0 20 40 60 80 100

x

Belief about E[A|x] Theory E[A|x]

0

0.25

0.5

0.75

1

0 20 40 60 80 100

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 80 100

x


Figure 5: Cost 50

Figure 6: Cost 60

Results of Rationality Test:

c=20: 76.98% rational




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




• The Experiment


• Discussion


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


Extra Slides


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(


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

0.2

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(

Ac

tio

n A

)

0

0.1

0.2

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(

Ac

tio

n A

)


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(

Ac

tio

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(

Ac

tio

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


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


Further Research: Theory

• Correction for “mistakes”

• Justification for excess aggressiveness Optimism

0

0.25

0.5

0.75

1

0 20 40 60 80 100

x

Be

lief

Ab

ou

t F

rac

tio

n

Ch

oo

sin

g A

Data Theory

0

0.25

0.5

0.75

1

0 20 40 60 80 100

x

Be

lief

Ab

ou

t F

rac

tio

n

Ch

oo

sin

g A

Data Theory Theory w ith Mistakes

0

0.25

0.5

0.75

1

0 20 40 60 80 100

x

Be

lief

Ab

ou

t F

rac

tio

n

Ch

oo

sin

g A

Data Theory

Theory w ith Mistakes Theory w ith Mistakes & Optimism

Figure A7: Modified Theoretical Beliefs for Cost-50 Treatment


Further Research: Experimental

• Allowing for communication “generic sunspot”

• Effects of gender on coordination

Documents

Coordination and Learning in Dynamic Global Games: Experimental Evidence