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April 8, 2004 1 Teck H. Ho
Outline In-Class Experiment and Motivation
Adaptive Experience-Weighted Attraction (EWA) Learning in Games: Camerer and Ho (Econometrica, 1999)
Sophisticated EWA Learning and Strategic Teaching: Camerer, Ho, and Chong (JET, 2002)
Self-tuning EWA Learning (EWA Lite): Ho, Camerer, and Chong (2004)
April 8, 2004 2 Teck H. Ho
Actual versus Belief-Based Model Frequencies: pBC (inexperienced subjects)
0
1~10
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Choices
Round
Figure 2a: Actual Choice Frequencies for Inexperienced Subjects
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1~10
11~2
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Choices
Round
Figure 3d: Belief Learning Model Frequencies for Inexperienced Subjects
April 8, 2004 3 Teck H. Ho
Actual versus Reinforcement Model Frequencies: pBC (inexperienced subjects)
0
1~10
11~2
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21~3
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31~4
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41~5
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51~6
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61~7
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Choices
Round
Figure 2a: Actual Choice Frequencies for Inexperienced Subjects
0
1~
10
11
~2
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21
~3
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31
~4
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41
~5
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~6
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~7
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~8
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~9
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~1
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0.55
0.60
Choices
Round
Figure 3e: Reinforcement Model Frequencies for Inexperienced Subjects
April 8, 2004 4 Teck H. Ho
Actual versus EWA Model Frequencies: pBC (inexperienced subjects)
0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
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61~7
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71~8
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Choices
Round
Figure 2b: Adaptive EWA Model Frequencies for Inexperienced Subjects
0
1~10
11~2
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21~3
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31~4
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41~5
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51~6
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61~7
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0.40
Choices
Round
Figure 2a: Actual Choice Frequencies for Inexperienced Subjects
April 8, 2004 5 Teck H. Ho
Actual versus Belief-Based Model Frequencies: pBC (experienced subjects)
0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
0
61~7
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71~8
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0.0
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Choices
Round
Figure 4d: Belief Learning Model Frequencies for Experienced Subjects
0
1~10
11~2
0
21~3
0
31~4
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41~5
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51~6
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61~7
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71~8
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0.0
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Choices
Round
Figure 3a: Actual Choice Frequencies for Experienced Subjects
April 8, 2004 6 Teck H. Ho
Actual versus Reinforcement Model Frequencies: pBC (experienced subjects)
0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
0
61~7
0
71~8
0
81~9
0
91~1
00
1
3
5
7
9
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Choices
Round
Figure 4e: Reinforcement Model Frequencies for Experienced Subjects
0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
0
61~7
0
71~8
0
81~9
0
91~1
00
1
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
Choices
Round
Figure 3a: Actual Choice Frequencies for Experienced Subjects
April 8, 2004 7 Teck H. Ho
Actual versus EWA Model Frequencies: pBC (experienced subjects)
0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
0
61~7
0
71~8
0
81~9
0
91~1
00
1
3
5
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9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Choices
Round
Figure 3a: Actual Choice Frequencies for Experienced Subjects
0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
0
61~7
0
71~8
0
81~9
0
91~1
00
1
3
5
7
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
Choices
Round
Figure 3b: Adaptive EWA Model Frequencies for Experienced Subjects
April 8, 2004 8 Teck H. Ho
Three User Complaints of EWA 1.0
Experience matters.
EWA 1.0 prediction is not sensitive to the structure of the learning setting (e.g., matching protocol).
EWA 1.0 model does not use opponents’ payoff matrix to predict behavior.
April 8, 2004 9 Teck H. Ho
Sophisticated EWA Learning (EWA 2.0)
The population consists of both adaptive and sophisticated players.
The proportion of sophisticated players is denoted by . Each sophisticated player however believes the proportion of sophisticated players to be ’
Use latent class to estimate parameters.
April 8, 2004 10 Teck H. Ho
The EWA 2.0 Model: Adaptive players
Adaptive ( ) + sophisticated ( )
Adaptive players
)( )(
))(,()1,()1(
)( )(
))(,()1,()1(
),(
tsstN
tsstaAtN
tsstN
tsstaAtN
taA
iijiijiij
iijiijiij
ij
1
i
ik
ij
m
k
tA
tA
ij
e
etaP
1
)(
)(
)1,(
April 8, 2004 11 Teck H. Ho
The EWA 2.0 Model: Sophisticated Players
1 Adaptive ( ) + sophisticated ( )
Sophisticated players believe ( )proportion of the players are adaptive and best respond based on that belief:
Better-than-others ( ); false consensus ( )
im
kkiijkikiij sstsPtaPtsA
1,,, ),()]1,()1,(1[(),(
i
ik
ij
m
k
tsA
tsA
ij
e
etsP
1
),(
),(
)1,(
1
April 8, 2004 12 Teck H. Ho
Well-known Special Cases
Nash equilibrium: ’ = 1 and = infinity
Quanta response equilibrium: ’ = 1
Rational expectation model: ’
Better-than-others model: ’
April 8, 2004 13 Teck H. Ho
Results 0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
0
61~7
0
71~8
0
81~9
0
91~1
00
1
3
5
7
9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Choices
Round
Figure 3a: Actual Choice Frequencies for Experienced Subjects
0
1~10
11~2
0
21~3
0
31~4
0
41~5
0
51~6
0
61~7
0
71~8
0
81~9
0
91~1
00
1
3
5
7
9
0
0.1
0.2
0.3
0.4
0.5
0.6
Choices
Round
Figure 3c: Sophisticated EWA Model Frequencies for Experienced Subjects
April 8, 2004 14 Teck H. Ho
MLE Estimates
April 8, 2004 15 Teck H. Ho
Strategic Teaching So far, all players are myopic. They only care about immediate
payoffs.
Sophisticated players would want to “control” or “manipulate” the learning paths of the adaptive players if they are non-myopic (i.e., care beyond immediate payoffs).
In evaluating the attractiveness of a strategy, a strategic teacher compute its NPV, taking into account the potential of the strategy in influencing adaptive players to evolve into desirable outcomes in the future.
April 8, 2004 16 Teck H. Ho
April 8, 2004 17 Teck H. Ho
Out-of-Sample Prediction
April 8, 2004 18 Teck H. Ho
April 8, 2004 19 Teck H. Ho
In-Sample Calibration
April 8, 2004 20 Teck H. Ho
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