Coordination and Learning in Dynamic Global Games: Experimental Evidence

1
Coordination and Learning in Dynamic Global
GamesExperimental Evidence

• Olga Shurchkov
• MIT
• The Economic Science Association
• World Meeting 2007

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?

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

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

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

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 gt q
• Individual payoffs
• Information structure
• is drawn from N( z,1/a ) and is not observed
  by the agents
• z is the prior the public signal
• Additional private signal xit q xit where

7
The Model Period 1 Predictions

• 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 lt x1, which implies that there exists a
  unique q1 such that the status quo is abandoned
• iff q lt q1.
• Implications for experiment
• A1(q ) is decreasing in q
• The thresholds q1 and x1 are decreasing in the
  cost of attacking, c

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 (b2 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 than
• with no new information.
• Notes z is the prior (q is drawn from N(
  z,1/a ))
• b2 is the precision of private signal, x, in
  period 2

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

10
The Experiment Treatments

• 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 q is drawn from N(
  z,1/a ))
• b is the precision of private signal,
  x
• Elicitation of beliefs

Table 1 Session Overview
Table 2 Parameterization
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

12
Data Analysis First Period Predictions
Attack Fraction is monotonically decreasing in q
Figure 1 Kernel Regression Fraction of Agents
Attacking vs. Theta (pooled data for sessions
1-4, cost 50)
13
Data Analysis First Period Predictions
Table 3 OLS Regressions of individual action on
x in Stage 1, all data for sessions 1-4
14
Data Analysis Static Predictions
Table 4 Estimated Aggregate Threshold Summary

• Note
• Estimated thresholds vary only slightly with cost

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

16
Data Analysis Endogenous Learning
Figure 2 Average Probability of Attack for the
No-New Information Treatments
17
Data Analysis Endogenous Learning
Table 5 OLS Regressions of individual action on
x, all data for sessions 1-4
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

19
Data Analysis New Information
Stage 2
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 xlt100)
20
Data Analysis New Information
Table 6 Effect of the New Information Treatment
on Stage 2 Actions
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

22
Data Analysis Rationality
Belief about Fraction of Agents Attacking vs.
Theory Prediction
Figure 4 Cost 20
Figure 5 Cost 50
Results of Rationality Test c20 76.98
rational c50 90.79 rational c60 89.44
rational
Figure 6 Cost 60
23
Data Analysis Consistency
Measure of Consistency
Table 7 Test of Consistency in Stage 1
LHS Average size of attack RHS EA(q )x is
the belief of subject i
EEA(q )x is the average belief
Table 8 Test of Consistency in Stage 2
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

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

26
Extra Slides
27
First Period Predictions Mistakes
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)
Figure A1 Estimated thresholds vs. rounds
(pooled data for sessions 1-4)

• 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

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
29
New Information Strategy Space
Figure A5 Probability of Attack vs. x by Stage
for the NNI and the NI Treatments
Figure A5 Probability of Attack vs. x by Stage
for the NNI Treatments
30
Calculation of Measure of Rationality
Threshold
Measure of Rationality Expected payoff vs.
Cost of attacking
Results Treatment c20 76.98
rational Treatment c50 90.79
rational Treatment c60 89.44 rational
Figure A6 Thresholds for Different Cost
Treatments
Attack iff
31
Further Research Theory

• Correction for mistakes
• Justification for excess aggressiveness ?
  Optimism

Figure A7 Modified Theoretical Beliefs for
Cost-50 Treatment
32
Further Research Experimental

• Allowing for communication ? generic sunspot
• Effects of gender on coordination