We replicate the experiment of Wang et al. (2010). Furthermore, we conduct a simplified version and compare the results of both Treatments. The results of direct Replication are similar to that Wang et al. (2010). The behavior of subjects in the Simplified Treatment are closer to babbling equilibrium than in b = 2 of Replicate Treatment. The type of senders are classified as only L0 to L2. In addition, more senders are classified as L2 in the Simplified Treatment than in the Replicate Treatment. In the same way, more senders increase their proportion of choosing High (L2 or above) types in the Simplified Treatment than decrease, likely because it simpler game.
We could classified the choices of a L1 or L2 type sender into 3 cases in Simplified Treatment (see Table 14). First, when b = 0, the sender will tell the truth and will be trusted. Then, when b = 1 and s = 1 or 2, the sender usually tell a lie and will not be trusted. Finally, when b = 1 and e = 3, the sender will tell the truth but will not be trusted. Hope we can find some difference of brain activities in the potential fMRI research.12
12 In the paper-based post experimental questionnaire, we asked subjects, “Could you finish the tasks in the Simplified Treatment in 6 seconds? If not in the beginning, how many rounds of practice do you need to finish it in 6 seconds?”
78% of senders said they could finish it on time, or require at most 7 rounds of practice. The remaining 22% reported that they need 10 or more rounds before they can finish it on time.
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Table 18：Identify 3 cases for potential fMRI research
Cases Bias State Message Prediction True and be
trusted
0 1, 2, 3 M=S P=M
True but not be trusted
1 3 M=3 P=2
Lie and not be trusted
1 1, 2 M=3 P=2
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Reference
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Appendix:
Table A1: The number of total trials, given on bias, Replicate
Bias 0 1 2
Frequency 245 475 460
Table A2: Bias＝0, Sender matrix, Replicate
Message 1 Message 2 Message 3 Message 4 Message 5 Total
Table A3: Bias＝1, Sender matrix, Replicate
Message 1 Message 2 Message 3 Message 4 Message 5 Total
Table A4: Bias＝2, Sender matrix, Replicate
Message 1 Message 2 Message 3 Message 4 Message 5 Total
Table A5: Bias＝0, Receiver matrix, Replicate
Table A6: Bias＝1, Receiver matrix, Replicate
Action 1 Action 2 Action 3 Action 4 Action 5 Total
Table A7: Bias＝2, Receiver matrix, Replicate
Action 1 Action 2 Action 3 Action 4 Action 5 Total
Table A8: Bias＝1, Expect Payoff of Sender, Replicate
Message 1 Message 2 Message 3 Message 4 Message 5
Table A9: Bias＝2, Expect Payoff of Sender, Replicate
Table A10: Bias＝1, Expect Payoff of Receiver, Replicate
Action 1 Action 2 Action 3 Action 4 Action 5
Table A11: Bias＝2, Expect Payoff of Receiver, Replicate
Action 1 Action 2 Action 3 Action 4 Action 5
Table A12: The number of total trials without exchange role, given on bias, Simplified
Bias 0 1 -1
Frequency 542 1542 118
Table A13: Bias＝-1, Sender matrix, Simplified
Message 1 Message 2 Message 3 Total
Table A14: Bias＝0, Sender matrix, Simplified
Table A15: Bias＝1, Sender matrix and reversed matrix of bias=-1, Simplified Message 1 Message 2 Message 3 Total
Table A16: Bias＝-1, Prediction matrix, Simplified
Prediction 1 Prediction 2 Prediction 3 Total
Message 1 33 44 5 82
Message 2 6 13 4 23
Message 3 1 6 6 13
Total 40 63 15 118
Table A17: Bias＝0, Prediction matrix, Simplified
Prediction 1 Prediction 2 Prediction 3 Total
Message 1 177 0 1 178
Message 2 0 181 0 181
Message 3 0 0 183 183
Total 177 181 184 542
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Table A18: Bias＝1, Prediction matrix and reversed matrix of bias=-1, Simplified Prediction 1 Prediction 2 Prediction 3 Total
Message 1 58 98 23 179
Message 2 96 121 41 258
Message 3 56 881 168 1105
Total 210 1100 232 1542
Reverse bias = -1
Prediction 1 Prediction 2 Prediction 3
Message 1 6 6 1
Message 2 4 13 6
Message 3 6 6 1
Table A19: Bias＝-1, Receiver matrix, Simplified
Action 1 Action 2 Action 3 Total
Message 1 22 56 4 82
Message 2 1 8 14 23
Message 3 0 4 9 13
Total 23 68 27 118
Table A20: Bias＝0, Receiver matrix, Simplified
Action 1 Action 2 Action 3 Total
Message 1 177 1 0 178
Message 2 0 180 1 181
Message 3 0 0 183 183
Total 177 181 184 542
Table A21: Bias＝1, Receiver matrix and reserved matrix of bias=-1, Simplified Action 1 Action 2 Action 3 Total
Table A22：Sender Matrix, Robustness Check, bias=0 Without Catch Trials (Baseline) All Data
M=1 M=2 M=3 M=1 M=2 M=3
S=1 178 0 0 179 0 0
S=2 0 181 0 0 182 0
S=3 0 0 183 0 0 187
Table A23：Sender Matrix, Robustness Check, bias=1 Without Catch Trials (Baseline) All Data
M=1 M=2 M=3 M=1 M=2 M=3
S=1 107 133 311 121 145 348
S=2 35 81 385 42 97 434
S=3 37 44 409 49 62 450
Table A24：Receiver Matrix, Robustness Check, bias=0 Without Catch Trials (Baseline) All Data
A=1 A=2 A=3 A=1 A=2 A=3
M=1 177 1 0 188 1 0
M=2 0 180 1 0 186 1
M=3 0 0 183 0 0 196
Table A25：Receiver Matrix, Robustness Check, bias=1 Without Catch Trials (Baseline) All Data
A=1 A=2 A=3 A=1 A=2 A=3
M=1 123 52 4 143 64 5
M=2 140 112 6 167 130 7
M=3 167 739 199 180 818 234
Table A26：Prediction Matrix, Robustness Check, bias=0 Without Catch Trials (Baseline) All Data
=1 =2 =3 =1 =2 =3
M=1 177 0 1 188 0 1
M=2 0 181 0 0 187 0
M=3 0 0 183 0 0 196
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Table A27：Prediction Matrix, Robustness Check, bias=1 Without Catch Trials (Baseline) All Data
=1 =2 =3 =1 =2 =3
M=1 58 98 23 72 116 24
M=2 96 121 41 102 151 51
M=3 56 881 168 62 920 181
Table A28: Bias＝1, Expect Payoff of Sender, Simplified
Message 1 Message 2 Message 3
State 1 79 83 90
State 2 37 44 68
State 3 -20 -11 21
Table A29: Bias＝1, Expect Payoff of Receiver, Simplified
Action 1 Action 2 Action 3
Message 1 78 76 47
Message 2 77 79 50
Message 3 60 80 67
Table A30：Learning Results: Correlation in Replicate Treatment Rounds Bias CorrSM CorrMA CorrSA
Table A31：Learning Results: Payoffs in Replicate Treatment
Rounds Bias u_S (std) u_R (std)
Table A32：Learning Results: Correlation in Simplified Treatment Rounds Bias CorrSM CorrMA CorrSA
1-20
0 1.000 0.995 0.995
21-40 1.000 1.000 1.000
1-20
1 0.260 0.439 0.127
21-40 0.219 0.404 0.104
Table A33：Learning Results: Correlation in Simplified Treatment
Rounds Bias u_S (std) u_R (std)
1-20
0 99.79 2.49 99.79 2.49
21-40 100.00 0.00 100.00 0.00
1-20
1 53.23 40.52 75.19 24.90
21-40 58.12 38.01 76.52 22.84
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Experimental Instructions
4. 報酬決定