A Finite Precision of Private Information Precision of Private Information Approaching Infinity 0 θ1 * θ

Session Cost of Action A First 20 Last 20 Rounds Rounds Information in Stage 2 First 20 Last 20 Rounds Rounds 1,2 20 50 No No 3,4 50 20 No No 5 60 60 No Yes 6 60 60 Yes No Session z, 1/α 1/β 1 1/β 2 1-4 65, 50 7 N/A 5-6 75, 55 10 1

1 0.8 Attack Fraction 0.6 0.4 0.2 0-100 -50 0 50 100 150 200 θ Pr(Action A) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 <0 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 >100 x

Dependent Variable: Action 1 2 3 Private signal, x -0.0065 *** -0.0066 *** -0.0012 *** (0.0001) (0.0001) (0.0001) Cost of action A -0.0026 *** -0.0005 ** (0.0003) (0.0002) Belief 0.0646 *** (0.0011) R 2 0.57 0.58 0.83 No. of observations 6000 6000 6000 Note: Robust standard errors in parentheses. Regressions include group and round fixed effects. For sessions 5 and 6, only the no-new-information treatment data are used. Significance levels: ** 5%, *** 1%.

120 100 Threshold 80 60 40 20 0 0 10 20 30 40 Round

0.3 0.25 0.2 0.15 0.1 0.05 0 0 10 20 30 40 0.3 0.25 0.2 0.15 0.1 0.05 0 0 10 20 30 40

0.7 0.6 Pr(Action A) 0.5 0.4 0.3 0.2 0.1 0 Stage 1 Ave Prob of Action A Stage 2 Ave Prob of Action A

Dependent Variable: Action 1 2 3 Private signal, x -0.006 *** -0.006 *** -0.001 *** (0.0001) (0.0001) (0.0001) Cost of action A -0.0026 *** -0.0006 ** (0.0003) (0.0002) Belief 0.0632 *** (0.0011) Stage -0.2308 *** -0.2272 *** -0.0466 *** (0.0073) (0.0073) (0.0057) R 2 0.61 0.62 0.84 No. of observations 8820 8820 8820 Note: Robust standard errors in parentheses. Regressions include group and round fixed effects. For sessions 5 and 6, only the no-new-information treatment data are used. Significance levels: ** 5%, *** 1%. Pr(Action A) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 <50 50-60 60-70 70-80 80-90 90-100 >100 x First-Stage Probability of A Second-Stage Probability of A

Pr(Action A) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 <50 50-60 60-70 70-80 80-90 90-100 >100 x First-Stage Probability of A Second-Stage Probability of A

0.30 0.25 Pr(Action A) 0.20 0.15 0.10 0.05 0.00 NNI NI NNI NI Stage 1 Stage 2

Dependent Variable: Action Private signal, x -0.0021 *** (0.0002) NI dummy 0.0842 *** (0.0145) R 2 0.20 No. of observations 1395 Note: Robust standard errors in parentheses. Regressions include group, subject, and round fixed effects. Significance level: *** 1%. Pr(Action A) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 <40 40-50 50-60 60-70 70-80 80-90 90-100 >100 x First-Stage Probability of A, NI and NNI Average Second-Stage Probability of A, NNI Second-Stage Probability of A, NI

1 1 Belief About Fraction Choosing A 0.75 0.5 0.25 Belief About Fraction Choosing A 0.75 0.5 0.25 0 x 0 x 0 20 40 60 80 100 0 20 40 60 80 100 g ( x ) i * g( x, x ) i g ( x ) i * g( x, x ) i 1 Belief About Fraction Choosing A 0.75 0.5 0.25 0 x 0 20 40 60 80 100 g ( x ) i * g( x, x ) i

100 x i 80 60 40 20 0-200 -100 0 100 200 300 Cost 20 Cost 50 Cost 60 x i

Cost Treatment Average Realized Attack Fraction Beliefs Averaged Across x 20 0.5857 0.5354 50 0.5799 0.5347 60 0.5071 0.4615 Cost & Info Treatment Average Realized Attack Fraction Beliefs Averaged Across x 20 NNI 0.0227 0.0610 50 NNI 0.0769 0.2101 60 NNI 0.0461 0.1505 60 NI 0.1248 0.1484

Sessions 1-4 Cost 20 Sessions 1-4 Cost 50 Sessions 5-6 No New Info Sessions 5-6 New Info Mean θ 73.48 64.40 77.78 74.10 Min θ -73.83-92.73-107.48-49.06 Max θ 208.46 188.30 256.30 256.68 Mean x (Stage 1) 73.37 64.45 77.80 74.25 Min x (Stage 1) -82.55-106.92-128.23-71.84 Max x (Stage 1) 220.85 201.84 277.64 281.59 Mean # Attackers Stage 1 9.16 8.89 6.88 7.18 Mean # Attackers Stage 2 1.28 0.89 0.50 1.94 Mean Belief (Stage 1) 8.57 8.35 6.62 7.03 Mean Belief (Stage 2) 1.76 1.58 1.08 2.71 % Successful Attacks (Stage 1) 0.57 0.54 0.43 0.41 % Successful Attacks (Stage 2) 0.019 0.00 0.00 0.021 Median Comfort Level with Stats 4 4 4 4 Number of Subjects 120 120 60 60

1 0.8 Attack Fraction 0.6 0.4 0.2 0-150 -100-50 0 50 100 150 200 θ 1 0.8 Attack Fraction 0.6 0.4 0.2 0-150 -100-50 0 50 100 150 200 θ

Pr(Action A) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 <0 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 >100 x Pr(Action A) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 <0 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 >100 x

Dependent Variable: Action 1 2 3 Private signal, x -0.1046 *** -0.1064 *** -0.0603 *** (0.0100) (0.0104) (0.0091) Cost of action A -0.0306 *** -0.0115 * (0.0046) (0.0065) Belief 0.6842 *** (0.0511) Pseudo R 2 0.74 0.75 0.91 No. of observations 6000 6000 6000 Note: Standard errors in parentheses. Regressions include group and round fixed effects. For sessions 5 and 6, only the no-new-information treatment data are used. Significance levels: * 10%, ** 5%, *** 1%. Dependent Variable: Action 1 2 3 Private signal, x -0.0065 *** -0.0066 *** -0.001 *** (0.0001) (0.0001) (0.0001) Cost of action A -0.0026 *** -0.0004 ** (0.0003) (0.0002) Belief 0.0668 *** (0.0010) R 2 0.58 0.59 0.84 No. of observations 6000 6000 6000 Note: Robust standard errors in parentheses. Regressions include group, subject, and round fixed effects. For sessions 5 and 6, only the no-newinformation treatment data are used. Significance levels: ** 5%, *** 1%.

Dependent Variable: Action 1 2 3 Private signal, x -0.1052 *** -0.1078 *** -0.0614 *** (0.0090) (0.0096) (0.0097) Cost of action A -0.0339 *** -0.0148 ** (0.0044) (0.0064) Belief 0.7079 *** (0.0485) Stage -1.6341 *** -1.5964 *** -0.8440 *** (0.1157) (0.1145) (0.1785) R 2 0.75 0.76 0.92 No. of observations 8820 8820 8820 Note: Standard errors in parentheses. Regressions include group and round fixed effects. For sessions 5 and 6, only the no-new-information treatment data are used. Significance levels: ** 5%, *** 1%. Dependent Variable: Action 1 2 3 Private signal, x -0.006 *** -0.006 *** -0.0008 *** (0.0001) (0.0001) (0.0001) Cost of action A -0.0026 *** -0.0005 ** (0.0003) (0.0002) Belief 0.0655 *** (0.0008) Stage -0.2307 *** -0.2272 *** -0.0399 *** (0.0073) (0.0073) (0.0054) R 2 0.62 0.62 0.85 No. of observations 8820 8820 8820 Note: Robust standard errors in parentheses. Regressions include group, subject, and round fixed effects. For sessions 5 and 6, only the no-newinformation treatment data are used. Significance levels: ** 5%, *** 1%.

Dependent Variable: Action Private signal, x -0.1428 *** (0.0199) NI dummy 0.7783 * (0.4518) R 2 0.67 No. of observations 1395 Note: Standard errors in parentheses. Regressions include group, subject, and round fixed effects. Significance level: * 10%, *** 1%. Dependent Variable: Average Fraction of Mistakes Sessions 1-2 Sessions 3-4 Round*Cost -0.0024-0.0011 (0.0019) (0.0021) Constant 0.1148 ** -0.071 ** (0.0261) (0.0044) R 2 0.04 0.01 No. of observations 40 40 Note: Robust standard errors in parentheses. Significance levels: ** 5%, *** 1%.