Ion Juvina found an error in our manuscript published in Games [1]. The error led to overestimation (by about 3%) of the alternation rate presented in Table 2 (in page 120). The correction does not change the main conclusions, but it slightly changes five exhibits. The corrected exhibits are presented below, and in the competition website (http://sites.google.com/site/gpredcomp).
Table 2.The 40 market entry games that were studied in the estimation experiment. At each trial, each of 4 players has to decide (individually) between “entering a risky market”, or “staying out” (a safer prospect). The payoffs depended on a realization of a binary gamble (the realization at trial t is denoted Gt, and yields “H with probability Ph; and L otherwise”), the number of entrants (E), and two additional parameters (k and S). The exact payoff for player i at trial t is:
The left hand-columns present the exact value of the different parameters in the 40 games, the right hand columns present the equilibrium predictions, and the main experimental results in the first and second block (B1 and B2).
Table 2.The 40 market entry games that were studied in the estimation experiment. At each trial, each of 4 players has to decide (individually) between “entering a risky market”, or “staying out” (a safer prospect). The payoffs depended on a realization of a binary gamble (the realization at trial t is denoted Gt, and yields “H with probability Ph; and L otherwise”), the number of entrants (E), and two additional parameters (k and S). The exact payoff for player i at trial t is:
The left hand-columns present the exact value of the different parameters in the 40 games, the right hand columns present the equilibrium predictions, and the main experimental results in the first and second block (B1 and B2).
Experimental results
The games
Entry at eq.
Entry rates
Efficiency
Alternations
#
K
ph
H
L
S
pure
symmetric
B1
B2
B1
B2
B1
B2
1
2
0.04
70
-3
5
1.00
1.00
0.71
0.80
2.77
2.66
0.16
0.16
2
2
0.23
30
-9
4
1.00
1.00
0.55
0.62
2.64
2.75
0.25
0.23
3
2
0.67
1
-2
3
1.00
1.00
0.88
0.94
2.39
2.24
0.10
0.04
4
2
0.73
30
-80
4
1.00
1.00
0.71
0.64
2.58
2.57
0.28
0.27
5
2
0.80
20
-80
5
1.00
1.00
0.66
0.67
2.50
2.67
0.29
0.27
6
2
0.83
4
-20
3
1.00
1.00
0.73
0.82
2.45
2.50
0.24
0.18
7
2
0.94
6
-90
5
1.00
1.00
0.86
0.87
2.34
2.38
0.13
0.11
8
2
0.95
1
-20
5
1.00
1.00
0.86
0.91
2.48
2.31
0.12
0.08
9
2
0.96
4
-90
3
1.00
1.00
0.87
0.90
2.36
2.34
0.14
0.08
10
3
0.10
70
-8
4
0.75
0.77
0.42
0.48
1.22
1.11
0.29
0.25
11
3
0.90
9
-80
4
0.75
0.77
0.80
0.73
-0.33
0.29
0.18
0.25
12
3
0.91
7
-70
6
0.75
0.77
0.76
0.83
0.10
-0.41
0.19
0.12
13
4
0.06
60
-4
2
0.50
0.50
0.42
0.41
0.52
0.84
0.22
0.15
14
4
0.20
40
-10
4
0.50
0.50
0.48
0.46
-0.34
0.04
0.31
0.31
15
4
0.31
20
-9
4
0.50
0.50
0.49
0.44
-0.07
0.30
0.34
0.38
16
4
0.60
4
-6
2
0.50
0.50
0.56
0.58
-0.27
-0.26
0.22
0.26
17
4
0.60
40
-60
3
0.50
0.50
0.58
0.55
-0.96
-0.20
0.28
0.25
18
4
0.73
3
-8
2
0.50
0.50
0.57
0.55
-0.29
0.09
0.24
0.20
19
4
0.80
20
-80
2
0.50
0.50
0.64
0.63
-1.30
-1.21
0.28
0.27
20
4
0.90
1
-9
6
0.50
0.50
0.53
0.48
0.12
0.63
0.21
0.16
21
4
0.96
3
-70
3
0.50
0.50
0.65
0.62
-0.84
-0.38
0.23
0.18
22
5
0.02
80
-2
3
0.25
0.33
0.36
0.31
0.24
0.64
0.17
0.17
23
5
0.07
90
-7
3
0.25
0.33
0.39
0.24
-0.81
0.34
0.19
0.13
24
5
0.53
80
-90
5
0.25
0.33
0.65
0.58
-3.41
-2.44
0.27
0.36
25
5
0.80
1
-4
2
0.25
0.33
0.45
0.42
-0.31
0.11
0.20
0.18
26
5
0.88
4
-30
3
0.25
0.33
0.52
0.49
-0.95
-0.57
0.22
0.21
27
5
0.93
5
-70
4
0.25
0.33
0.57
0.57
-1.63
-1.43
0.27
0.20
28
6
0.10
90
-10
5
0.25
0.22
0.26
0.27
-0.13
0.07
0.22
0.19
29
6
0.19
30
-7
3
0.25
0.22
0.39
0.32
-1.35
-0.45
0.27
0.26
30
6
0.29
50
-20
3
0.25
0.22
0.47
0.48
-2.74
-2.43
0.38
0.36
31
6
0.46
7
-6
6
0.25
0.22
0.38
0.34
-0.90
-0.38
0.23
0.24
32
6
0.57
6
-8
4
0.25
0.22
0.44
0.39
-1.56
-0.59
0.26
0.27
33
6
0.82
20
-90
3
0.25
0.22
0.63
0.55
-5.33
-3.14
0.26
0.21
34
6
0.88
8
-60
4
0.25
0.22
0.57
0.50
-3.30
-1.96
0.16
0.19
35
7
0.06
90
-6
4
0.25
0.14
0.31
0.35
-1.40
-1.43
0.29
0.21
36
7
0.21
30
-8
3
0.25
0.14
0.39
0.31
-2.20
-1.04
0.30
0.23
37
7
0.50
80
-80
5
0.25
0.14
0.51
0.55
-4.18
-4.78
0.34
0.32
38
7
0.69
9
-20
5
0.25
0.14
0.46
0.34
-2.62
-0.88
0.25
0.23
39
7
0.81
7
-30
2
0.25
0.14
0.41
0.34
-2.25
-0.93
0.22
0.21
40
7
0.91
1
-10
2
0.25
0.14
0.34
0.27
-0.71
-0.30
0.19
0.17
Means
0.51
0.51
0.56
0.54
-0.39
0.04
0.23
0.21
Estimated error variance
.0016
.0015
.1370
.1188
.0012
.0015
Figure 1.Proportion of alternation as a function of Ph. Each data point summarizes the results of one game. The outlier (alternation rate of 0.07 when Ph = 0.67) is Problem 3: The problem with the lowest payoff variance, and the only problem in which entry cannot lead to losses.
Figure 1.Proportion of alternation as a function of Ph. Each data point summarizes the results of one game. The outlier (alternation rate of 0.07 when Ph = 0.67) is Problem 3: The problem with the lowest payoff variance, and the only problem in which entry cannot lead to losses.
Table 3.Summary of correlation analyses that examine the possibility of consistent individual differences. The summary scores are based on 180 correlation analyses (180 pairs of games) for each of the four variables.
Table 3.Summary of correlation analyses that examine the possibility of consistent individual differences. The summary scores are based on 180 correlation analyses (180 pairs of games) for each of the four variables.
Variable
Mean correlation
Proportion of positive correlations
Entry rate
0.249
0.844
Maximization
0.058
0.611
Alternation
0.415
0.983
Recency
0.281
0.888
Table 4.The baseline models, the estimated parameters, and the implied normalized MSD scores by statistic and block.
Table 4.The baseline models, the estimated parameters, and the implied normalized MSD scores by statistic and block.
Model
Fitted parameters
Normalized Mean Squared Deviation Scores by statistic and block
Entry rates
Efficiency
Alteration
Mean
Block:
1
2
1
2
1
2
Pure
26.52
21.56
39.41
28.01
49.50
35.26
33.38
Symmetric
29.57
25.11
21.13
13.24
30.59
25.95
24.26
RL
λ = 4, w = 0.01
8.57
16.37
5.19
8.84
19.14
12.22
11.72
NRL
λ = 12, w = 0.025
6.36
14.03
3.59
7.35
4.58
1.53
6.24
SFP
λ = 1.5, w = 0.1
5.91
5.36
9.37
14.99
6.53
3.79
7.66
NFP
λ = 4, w = 0.15
4.75
4.16
3.60
6.13
2.70
3.80
4.19
EWA
λ = 0.7, φ = 0.8, δ = 0.5, ρ = 0.4
10.06
8.91
4.69
9.22
4.38
2.49
6.62
SAW
εi ~ U[0,0.02], wi ~ U[0,1], ρi ~ U[0,0.02], and µi = {1, 2, or 3}.
3.93
2.49
1.87
2.04
4.18
5.37
3.31
I-SAW
εi ~ U[0,0.24], wi ~ U[0,0.8], ρi ~ U[0,0.2], πi ~ U[0,0.6], and µi = {1, 2, or 3}.
1.56
1.19
1.37
1.47
1.43
1.30
1.38
Table 5.The predictions of the best baseline models (I-SAW): The lowest row presents the correlation with the experimental results by statistic.
Table 5.The predictions of the best baseline models (I-SAW): The lowest row presents the correlation with the experimental results by statistic.
The games
Entry rates
Efficiency
Alternations
#
K
Ph
h
l
Sf
B1
B2
B1
B2
B1
B2
1
2
0.04
70
-3
5
0.78
0.81
2.60
2.56
0.17
0.13
2
2
0.23
30
-9
4
0.58
0.62
2.39
2.62
0.24
0.22
3
2
0.67
1
-2
3
0.90
0.91
2.33
2.32
0.10
0.08
4
2
0.73
30
-80
4
0.64
0.64
2.47
2.59
0.26
0.25
5
2
0.80
20
-80
5
0.67
0.67
2.47
2.61
0.24
0.23
6
2
0.83
4
-20
3
0.77
0.78
2.49
2.57
0.20
0.18
7
2
0.94
6
-90
5
0.82
0.82
2.39
2.49
0.15
0.14
8
2
0.95
1
-20
5
0.84
0.85
2.42
2.47
0.13
0.11
9
2
0.96
4
-90
3
0.84
0.86
2.35
2.43
0.13
0.11
10
3
0.10
70
-8
4
0.42
0.45
0.97
1.23
0.23
0.21
11
3
0.90
9
-80
4
0.74
0.75
-0.06
0.11
0.19
0.18
12
3
0.91
7
-70
6
0.76
0.76
-0.15
0.05
0.18
0.17
13
4
0.06
60
-4
2
0.41
0.43
0.22
0.34
0.24
0.22
14
4
0.20
40
-10
4
0.43
0.44
-0.04
0.25
0.27
0.25
15
4
0.31
20
-9
4
0.48
0.49
-0.22
0.01
0.29
0.28
16
4
0.60
4
-6
2
0.52
0.52
-0.20
-0.05
0.30
0.28
17
4
0.60
40
-60
3
0.55
0.55
-0.78
-0.47
0.29
0.28
18
4
0.73
3
-8
2
0.53
0.52
-0.20
-0.08
0.29
0.27
19
4
0.80
20
-80
2
0.65
0.64
-1.65
-1.23
0.24
0.24
20
4
0.90
1
-9
6
0.52
0.52
0.07
0.06
0.25
0.23
21
4
0.96
3
-70
3
0.61
0.59
-0.80
-0.51
0.21
0.19
22
5
0.02
80
-2
3
0.35
0.35
-0.08
0.06
0.23
0.20
23
5
0.07
90
-7
3
0.31
0.32
-0.42
-0.05
0.21
0.19
24
5
0.53
80
-90
5
0.52
0.52
-2.03
-1.59
0.29
0.28
25
5
0.80
1
-4
2
0.40
0.40
-0.24
-0.10
0.25
0.23
26
5
0.88
4
-30
3
0.47
0.46
-0.89
-0.73
0.25
0.22
27
5
0.93
5
-70
4
0.51
0.50
-1.43
-1.08
0.24
0.21
28
6
0.10
90
-10
5
0.31
0.31
-1.08
-0.63
0.22
0.20
29
6
0.19
30
-7
3
0.36
0.36
-1.28
-0.90
0.26
0.24
30
6
0.29
50
-20
3
0.42
0.42
-2.05
-1.62
0.29
0.27
31
6
0.46
7
-6
6
0.35
0.35
-0.86
-0.67
0.27
0.24
32
6
0.57
6
-8
4
0.36
0.35
-0.94
-0.70
0.27
0.25
33
6
0.82
20
-90
3
0.60
0.57
-4.69
-3.73
0.25
0.24
34
6
0.88
8
-60
4
0.47
0.46
-2.20
-1.83
0.25
0.22
35
7
0.06
90
-6
4
0.26
0.26
-1.19
-0.68
0.20
0.18
36
7
0.21
30
-8
3
0.34
0.33
-1.77
-1.32
0.26
0.24
37
7
0.50
80
-80
5
0.49
0.48
-4.31
-3.61
0.29
0.28
38
7
0.69
9
-20
5
0.37
0.36
-1.84
-1.52
0.26
0.24
39
7
0.81
7
-30
2
0.37
0.36
-1.81
-1.50
0.26
0.23
40
7
0.91
1
-10
2
0.29
0.28
-0.76
-0.58
0.22
0.19
Means
0.525
0.526
-0.270
-0.011
0.234
0.215
Correlation with the experimental results
0.973
0.979
0.982
0.970
0.750
0.834
References and Notes
Erev, I.; Ert, E.; Roth, A.E. A choice prediction competition for market entry games: An introduction. Games2010, 1, 117–136. [Google Scholar]