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Figure 1
Evolution of the Bid Factor
Sample with Feed Back
1.5
Bid Factor
1
0.5
0
0
16
32
48
64
80
-0.5
-1
Period Played
Mean
Standard Deviation
Std
Figure 2
Evolution of the Bid Factor
Sample with No Feed Back
1.5
Bid Factor
1
0.5
0
0
16
32
48
64
-0.5
-1
Period Played
Mean
Standard Deviation
Std
80
Figure 3
Evolution of the Bid Factor
Sample with Feed Back
Good Players
1.5
Bid Factor
1
0.5
0
0
4
8
12
16
-0.5
-1
Period Played
Mean
Standard Deviation
Std
Figure 4
Evolution of the Bid Factor
Sample with Feed Back
Bad Players
1.5
Bid Factor
1
0.5
0
0
4
8
12
16
-0.5
-1
Period Played
Mean
Standard Deviation
Std
Figure 5
Evolution of the Bid Factor
Sample with No Feed Back
Good Players
1.5
Bid Factor
1
0.5
0
0
4
8
12
16
-0.5
-1
Period Played
Mean
Standard Deviation
Std
Figure 6
Evolution of the Bid Factor
Sample with No Feed Back
Bad Players
1.5
Bid Factor
1
0.5
0
0
4
8
12
16
-0.5
-1
Period Played
Mean
Standard Deviation
Std
Figure 7
Continuous Reinforcement
Model
Positive
0.8
Strategy
Distribution at
period t
0.7
0.6
Density
0.5
Reinforcement
at period t
0.4
0.3
Strategy
Distribution at
period t+1
0.2
0.1
0
-1
mt
0
st
1
Bid Factor
Figure 8
Continuous Reinforcement Model
Positive and Large Payoff
1.4
Strategy
Distribution at
period t
1.2
Density
1
Reinforcement at
period t
0.8
0.6
0.4
Strategy
Distribution at
period t+1
0.2
0
-1
mt
0
Bid Factor
st
1
Figure 9
Continuous Reinforcement Model
Negative and Small Payoff
0.8
Strategy
Distribution at
period t
0.7
0.6
Density
0.5
Reinforcement
at period t
0.4
0.3
Strategy
Distribution at
period t+1
0.2
0.1
0
-1
mt
0 st
1
Bid Factor
Figure 10
Continuous Reinforcement Model
Negative and Large Payoff
1.6
Strategy
Distribution at
period t
1.4
1.2
Density
1
Reinforcement at
period t
0.8
0.6
Strategy
Distribution at
period t+1
0.4
0.2
0
-1
mt
0 st
Bid Factor
1
Graph 11
Evolution of the Bid Factor
Monte Carlo Simulations
FB Treatment
1.5
Bid Factor
1
0.5
0
0
16
32
48
64
80
-0.5
-1
Period Played
Mean
Standard Deviation
Std
Graph 12
Evolution of the Bid Factor
Monte Carlo Simulations
NFB Treatment
1.5
Bid Factor
1
0.5
0
-0.5
0
16
32
48
64
-1
Period Played
Mean
Standard Deviation
Std
80
TABLE 1
EXPERIMENTAL OUTCOMES
Total Number of Periods Played
Total Number
of Participating Subjects
Average Number
of Periods Played
Number of Bankruptcies
Number of Subjects who
Participated for the Entire Session
Average Profit
(Includes the Starting Balance)
Percentage of Auctions
with Negative Profits
Average Number
of Periods Before Bankruptcy*
Average Profit
of an Auction Winner
Percentage of Auctions
Won by the High Value Bidder
FB
Sample
80
28
NFB
Sample
78
31
Mann-Whitney
Test Statistic
.
.
p-Value
68.57
(8.3)
4
20
60.38
(12.4)
7
18
-3.08
2.64E-3
.
.
.
.
54 (12.8)
43 (13.3)
-3.734
1.88E-4
18
29
-3.234
1.23E-4
13 (6.1)
22 (12.5)
-2.079
0.037
2.6 (0.7)
1.7 (0.7)
-3.544
3.84E-4
36
28
-2.017
0.043
.
.
Numbers in parenthesis refer to standard deviations.
The FB and NFB samples have the same distribution under the null hypothesis in the Mann-Whitney test.
* The average is taken over the participants who experienced bankruptcy.
TABLE 2
THE EVOLUTION OF THE BID FACTOR
Feed Back Sample
No Feed Back Sample
Good Players in
Feed Back Sample
Bad Players in
Feed Back Sample
Good Players in
No Feed Back Sample
Bad Players in
No Feed Back Sample
α
β
σ
0.371
(0.241)
0.413
(0.471)
0.281*
(0.101)
0.126
(0.212)
0.178*
(0.049)
0.219*
(0.096)
1.48E-2*
(3.45E-4)
5.41E-3*
(1.26E-3)
3.17E-2*
(7.31E-4)
1.94E-2*
(2.11E-3)
2.32E-2*
(4.69E-3)
1.44E-2*
(6.68E-3)
22.025
(17.123)
5.173
(8.735)
1.027*
(0.368)
1.785*
(0.582)
1.245*
(0.514)
1.628*
(0.627)
H 0 : {β ≤ 0}
Test
p-Value
Statistic
-1.796* 5.262 7.12E-8
(0.327)
-1.069* 4.277 9.48E-6
(0.421)
-0.988* 3.832 6.36E-5
(0.217)
-0.789* 3.124 8.92E-4
(0.225)
-0.800* 3.668 1.22E-4
(0.176)
-0.559* 2.127 1.67E-2
(0.204)
γ
Numbers in parenthesis refer to standard deviations. * Indicates parameters significant at a 5% level.
TABLE 3
ESTIMATION OF THE BENCHMARK MODEL
µ
σ
α 0IM
α1IM
α 2IM
θ IM
α 0CRL α1CRL α 2CRL
FB
0.928* 0.084 0.734* 0.902* 0.154 0.638* 0.831* 0.226 3.281*
Sample (0.066) (0.187) (0.047) (0.118) (0.212) (0.079) (0.114) (0.134) (1.132)
NFB
0.816* 0.111 0.826* 0.374
0.141
0.431
0.322
0.241 4.065*
Sample (0.097) (0.179) (0.104) (0.478) (0.206) (0.294) (0.216) (0.171) (1.469)
Numbers in parenthesis refer to standard deviations. * Indicates parameters significant at a 5% level.
TABLE 4
NESTED MODELS COMPARISON
H0
No Heterogeneity FB Sample
No Heterogeneity NFB Sample
Experiential and Observational Parameters
are Equal
CRL
Payoff Dependent Imitation
Exogenous Learning
Nash Equilibrium with Errors
Imitation of Successful Behavior
Imitation of Successful Behavior with Errors
Imitation of Average Behavior
Imitation of Average Behavior with Errors
Imitation of Mode Behavior
Imitation of Mode Behavior with Errors
No Reinforcement of Best Strategies
Wald
Test
Statistic
Degrees
of
Freedom
Chi-square
statistic
( α = 0.05 )
p-value
197.776
228.046
16.245
189
210
3
222.074
244.806
7.814
0.316
0.187
1.01E-3
19.355
21.437
46.378
59.719
52.957
59.719
62.662
73.084
41.084
53.120
6.083
4
3
7
8
7
7
7
7
7
7
4
7.814
7.814
14.067
15.507
14.067
14.067
14.067
14.067
14.067
14.067
9.488
6.69E-4
8.54E-5
7.38E-8
5.29E-10
3.78E-9
5.12E-11
4.43E-11
1.06E-13
7.80E-7
3.51E-9
0.193
TABLE 5
MONTE CARLO SIMULATIONS OUTCOMES
Total Number of Periods Played
Average Number of Participating Subjects
Average Number of Periods Played
Average Number of Bankruptcies
Average Number of Subjects who
Participated for the Entire Session
Average Profit (Includes the Starting Balance)
Percentage of Auctions with Negative Profits
Average Number of Periods Before Bankruptcy
Average Profit of an Auction Winner
Percentage of Auctions Won by the High Value Bidder
FB Sample
80
26.8 (3.8)
71.6 (6.1)
2.8 (1.6)
21.2
(2.7)
59 (9.4)
15.2
11.2 (4.8)
2.55 (0.53)
38.4 (8.3)
Numbers in parenthesis refer to standard deviations
NFB Sample
78
32.7 (5.7)
57.3 (15.7)
8.7 (3.3)
16.1
(4.0)
40.4 (15.6)
28.7
20.5 (10.5)
1.58 (0.79)
25.7 (13.2)