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53
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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
Graph 3 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 4 Evolution of the Bid Factor Monte Carlo Simulations NFB Treatment 1.5
Bid Factor
1 0.5 0 0
16
32
48
64
-0.5 -1 Period Played
Mean
Standard Deviation
Std
80
TABLE I 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 II ESTIMATION OF THE BENCHMARK MODEL α 0CRL FB Sample NFB Sample
α1CRL
α 2CRL
0.928* 0.084 0.734* (0.066) (0.187) (0.047) 0.816* 0.111 0.826* (0.097) (0.179) (0.104)
µ σ α1IM α 2IM α 0IM θ IM 0.902* 0.154 0.638* 0.831* 0.226 3.281* (0.118) (0.212) (0.079) (0.114) (0.134) (1.132) 0.374 0.141 0.431 0.322 0.241 4.065* (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 III 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 IV 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)
