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A Model of Observational Learning
Bikhchandani Et Al (1998) "Learning from the behavior of others: conformity, fads, and informational cascades" Journal of Econ
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0 20 40 60 80 100 120
If we could count the private signals,
the observed proportion of them set to "High" (1)
would be our best estimate for the source chance.
Source chance
0.51
Decision Rand Private Signal Signal History Proportion
1 0.413 1 1 1
2 0.723 -1 0 0.5
3 0.028 1 1 0.666666667
4 0.84 -1 0 0.5
5 0.471 1 1 0.6
6 0.245 1 2 0.666666667
7 0.804 -1 1 0.571428571
8 0.637 -1 0 0.5
9 0.142 1 1 0.555555556
10 0.321 1 2 0.6
11 0.736 -1 1 0.545454545
12 0.64 -1 0 0.5
13 0.224 1 1 0.538461538
14 0.355 1 2 0.571428571
15 0.661 -1 1 0.533333333
16 0.679 -1 0 0.5
17 0.135 1 1 0.529411765
18 0.863 -1 0 0.5
19 0.712 -1 -1 0.473684211
20 0.244 1 0 0.5
21 0.96 -1 -1 0.476190476
22 0.634 -1 -2 0.454545455
23 0.593 -1 -3 0.434782609
24 0.655 -1 -4 0.416666667
25 0.311 1 -3 0.44
26 0.067 1 -2 0.461538462
27 0.832 -1 -3 0.444444444
28 0.466 1 -2 0.464285714
29 0.564 -1 -3 0.448275862
30 0.322 1 -2 0.466666667
31 0.569 -1 -3 0.451612903
32 0.997 -1 -4 0.4375
33 0.786 -1 -5 0.424242424
34 0.081 1 -4 0.441176471
35 0.917 -1 -5 0.428571429
36 0.091 1 -4 0.444444444
37 0.738 -1 -5 0.432432432
38 0.352 1 -4 0.447368421
39 0.402 1 -3 0.461538462
40 0.868 -1 -4 0.45
41 0.909 -1 -5 0.43902439
42 0.804 -1 -6 0.428571429
43 0.673 -1 -7 0.418604651
44 0.002 1 -6 0.431818182
45 0.953 -1 -7 0.422222222
46 0.283 1 -6 0.434782609
47 0.975 -1 -7 0.425531915
48 0.174 1 -6 0.4375
49 0.587 -1 -7 0.428571429
50 0.482 1 -6 0.44
51 0.852 -1 -7 0.431372549
52 0.688 -1 -8 0.423076923
53 0.926 -1 -9 0.41509434
54 0.697 -1 -10 0.407407407
55 0.704 -1 -11 0.4
56 0.956 -1 -12 0.392857143
57 0.78 -1 -13 0.385964912
58 7E-04 1 -12 0.396551724
59 0.058 1 -11 0.406779661
60 0.435 1 -10 0.416666667
61 0.847 -1 -11 0.409836066
62 0.009 1 -10 0.419354839
63 0.694 -1 -11 0.412698413
64 0.56 -1 -12 0.40625
65 0.374 1 -11 0.415384615
66 0.111 1 -10 0.424242424
67 0.703 -1 -11 0.417910448
68 0.08 1 -10 0.426470588
69 0.511 -1 -11 0.420289855
70 0.406 1 -10 0.428571429
71 0.48 1 -9 0.436619718
72 0.25 1 -8 0.444444444
73 0.153 1 -7 0.452054795
74 0.713 -1 -8 0.445945946
75 0.158 1 -7 0.453333333
76 0.951 -1 -8 0.447368421
77 0.762 -1 -9 0.441558442
78 0.349 1 -8 0.448717949
79 0.414 1 -7 0.455696203
80 0.59 -1 -8 0.45
81 0.474 1 -7 0.456790123
82 0.836 -1 -8 0.451219512
83 0.23 1 -7 0.457831325
84 0.514 -1 -8 0.452380952
85 0.216 1 -7 0.458823529
86 0.664 -1 -8 0.453488372
87 0.452 1 -7 0.459770115
88 0.463 1 -6 0.465909091
89 0.231 1 -5 0.471910112
90 0.806 -1 -6 0.466666667
91 0.688 -1 -7 0.461538462
92 0.46 1 -6 0.467391304
93 0.332 1 -5 0.47311828
94 0.196 1 -4 0.478723404
95 0.297 1 -3 0.484210526
96 0.217 1 -2 0.489583333
97 0.655 -1 -3 0.484536082
98 0.136 1 -2 0.489795918
99 0.902 -1 -3 0.484848485
100 0.093 1 -2 0.49
nal cascades" Journal of Economic Perspectives, 12(3), 151-170
A Model of Observational Learning
Bikhchandani Et Al (1998) "Learning from the behavior of others: conformity, fads, and informational cascades" Journal of Economi
There exists some phenomenon, about
1.0 We either act as if it is High (1) or as if i
Interpretations: Adopt/Don't; Buy/Sell; T
0.8
To make our decision, we have informa
(a) Personal experience - a signal;
0.6
(b) Past actions (by others) - learning;
(c) A 50:50 coin toss.
0.4 However, actions may suffer from some
0.2
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0 5 10 15 20 25 30 35
Action Proportion Signal Proportion
Source chance Coin toss chance History threshold
0.51 0.5 2
Decision Rand Private Signal Rand CoinToss Learning FromLearning Predictable Learning+Signal
1 0.095 1 0.422 1 0 0 0 1
2 0.102 1 0.058 1 1 1 0 1
3 0.674 -1 0.275 1 2 1 1 1
4 0.454 1 0.391 1 2 1 1 1
5 0.693 -1 0.664 -1 2 1 1 1
6 0.624 -1 0.276 1 2 1 1 1
7 0.557 -1 0.495 1 2 1 1 1
8 0.675 -1 0.874 -1 2 1 1 1
9 0.548 -1 0.739 -1 2 1 1 1
10 0.88 -1 0.145 1 2 1 1 1
11 0.27 1 0.96 -1 2 1 1 1
12 0.688 -1 0.281 1 2 1 1 1
13 0.442 1 0.518 -1 2 1 1 1
14 0.844 -1 0.873 -1 2 1 1 1
15 0.487 1 0.896 -1 2 1 1 1
16 0.135 1 0.814 -1 2 1 1 1
17 0.26 1 0.73 -1 2 1 1 1
18 0.742 -1 0.487 1 2 1 1 1
19 0.999 -1 0.587 -1 2 1 1 1
20 0.601 -1 0.538 -1 2 1 1 1
21 0.728 -1 0.416 1 2 1 1 1
22 0.745 -1 0.61 -1 2 1 1 1
23 0.618 -1 0.3 1 2 1 1 1
24 0.067 1 0.198 1 2 1 1 1
25 0.334 1 0.67 -1 2 1 1 1
26 0.389 1 0.965 -1 2 1 1 1
27 0.46 1 0.718 -1 2 1 1 1
28 0.442 1 0.836 -1 2 1 1 1
29 0.876 -1 0.302 1 2 1 1 1
30 0.578 -1 0.817 -1 2 1 1 1
nformational cascades" Journal of Economic Perspectives, 12(3), 151-170
There exists some phenomenon, about which we want to act.
We either act as if it is High (1) or as if it is Low (-1). 35
Interpretations: Adopt/Don't; Buy/Sell; True/False. 30
25
To make our decision, we have information on:
(a) Personal experience - a signal; 20
(b) Past actions (by others) - learning; 15
(c) A 50:50 coin toss. 10
However, actions may suffer from some noise.
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Action History Signal History
Method2 chance Noise chance
0 0
Use learning+signal Use own signal Reverses action
Method1 Method2 Rand Method Decision Rand WithNoise Surprise
1 1 0.288 1 1 0.139 1 1
1 1 0.241 1 1 0.934 1 1
1 -1 0.28 1 1 0.437 1 0
1 1 0.836 1 1 0.811 1 0
1 -1 0.193 1 1 0.954 1 0
1 -1 0.293 1 1 0.158 1 0
1 -1 0.857 1 1 0.043 1 0
1 -1 0.737 1 1 0.983 1 0
1 -1 0.321 1 1 0.252 1 0
1 -1 0.342 1 1 0.903 1 0
1 1 0.927 1 1 0.198 1 0
1 -1 0.858 1 1 0.605 1 0
1 1 0.448 1 1 0.009 1 0
1 -1 0.549 1 1 0.071 1 0
1 1 0.03 1 1 0.935 1 0
1 1 0.142 1 1 0.189 1 0
1 1 0.603 1 1 0.708 1 0
1 -1 0.837 1 1 0.591 1 0
1 -1 0.094 1 1 0.682 1 0
1 -1 0.981 1 1 0.446 1 0
1 -1 0.05 1 1 0.965 1 0
1 -1 0.086 1 1 0.11 1 0
1 -1 0.004 1 1 0.066 1 0
1 1 0.795 1 1 0.974 1 0
1 1 0.039 1 1 0.256 1 0
1 1 0.804 1 1 0.625 1 0
1 1 0.708 1 1 0.024 1 0
1 1 0.097 1 1 0.397 1 0
1 -1 0.413 1 1 0.015 1 0
1 -1 0.631 1 1 0.103 1 0
25 30 35
Signal History
Signal History Action History Signal Proportion Action Proportion
1 1 1 1
2 2 1 1
1 3 0.666666667 1
2 4 0.75 1
1 5 0.6 1
0 6 0.5 1
-1 7 0.428571429 1
-2 8 0.375 1
-3 9 0.333333333 1
-4 10 0.3 1
-3 11 0.363636364 1
-4 12 0.333333333 1
-3 13 0.384615385 1
-4 14 0.357142857 1
-3 15 0.4 1
-2 16 0.4375 1
-1 17 0.470588235 1
-2 18 0.444444444 1
-3 19 0.421052632 1
-4 20 0.4 1
-5 21 0.380952381 1
-6 22 0.363636364 1
-7 23 0.347826087 1
-6 24 0.375 1
-5 25 0.4 1
-4 26 0.423076923 1
-3 27 0.444444444 1
-2 28 0.464285714 1
-3 29 0.448275862 1
-4 30 0.433333333 1
