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Erev, I. et al. A Choice Prediction Competition for Market Entry Games: An Introduction. Games 2010, 1, 117-136

1
Max Wertheimer Minerva Center for Cognitive Studies, Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel
2
Computer Laboratory for Experimental Research, Harvard Business School, Boston, MA, 02163, USA
3
Department of Economics, 308 Littauer, Harvard University, Cambridge, MA 02138, USA
4
Harvard Business School, 441 Baker Library, Boston, MA 02163, USA
*
Author to whom correspondence should be addressed.
Games 2010, 1(3), 221-225; https://doi.org/10.3390/g1030221
Submission received: 13 July 2010 / Accepted: 14 July 2010 / Published: 21 July 2010
(This article belongs to the Special Issue Predicting Behavior in Games)
Ion Juvina found an error in our manuscript published in Games [1]. The error led to overestimation (by about 3%) of the alternation rate presented in Table 2 (in page 120). The correction does not change the main conclusions, but it slightly changes five exhibits. The corrected exhibits are presented below, and in the competition website (http://sites.google.com/site/gpredcomp).
Table 2. The 40 market entry games that were studied in the estimation experiment. At each trial, each of 4 players has to decide (individually) between “entering a risky market”, or “staying out” (a safer prospect). The payoffs depended on a realization of a binary gamble (the realization at trial t is denoted Gt, and yields “H with probability Ph; and L otherwise”), the number of entrants (E), and two additional parameters (k and S). The exact payoff for player i at trial t is: V i (t)={ round(G t /S) with p= .5; -round(G t /S) otherwise   if i does not enter                        10-k(E)+G t                                          if i enters } The left hand-columns present the exact value of the different parameters in the 40 games, the right hand columns present the equilibrium predictions, and the main experimental results in the first and second block (B1 and B2).
Table 2. The 40 market entry games that were studied in the estimation experiment. At each trial, each of 4 players has to decide (individually) between “entering a risky market”, or “staying out” (a safer prospect). The payoffs depended on a realization of a binary gamble (the realization at trial t is denoted Gt, and yields “H with probability Ph; and L otherwise”), the number of entrants (E), and two additional parameters (k and S). The exact payoff for player i at trial t is: V i (t)={ round(G t /S) with p= .5; -round(G t /S) otherwise   if i does not enter                        10-k(E)+G t                                          if i enters } The left hand-columns present the exact value of the different parameters in the 40 games, the right hand columns present the equilibrium predictions, and the main experimental results in the first and second block (B1 and B2).
Experimental results
The gamesEntry at eq.Entry ratesEfficiencyAlternations
#KphHLSpuresymmetricB1B2B1B2B1B2
120.0470-351.001.000.710.802.772.660.160.16
220.2330-941.001.000.550.622.642.750.250.23
320.671-231.001.000.880.942.392.240.100.04
420.7330-8041.001.000.710.642.582.570.280.27
520.8020-8051.001.000.660.672.502.670.290.27
620.834-2031.001.000.730.822.452.500.240.18
720.946-9051.001.000.860.872.342.380.130.11
820.951-2051.001.000.860.912.482.310.120.08
920.964-9031.001.000.870.902.362.340.140.08
1030.1070-840.750.770.420.481.221.110.290.25
1130.909-8040.750.770.800.73-0.330.290.180.25
1230.917-7060.750.770.760.830.10-0.410.190.12
1340.0660-420.500.500.420.410.520.840.220.15
1440.2040-1040.500.500.480.46-0.340.040.310.31
1540.3120-940.500.500.490.44-0.070.300.340.38
1640.604-620.500.500.560.58-0.27-0.260.220.26
1740.6040-6030.500.500.580.55-0.96-0.200.280.25
1840.733-820.500.500.570.55-0.290.090.240.20
1940.8020-8020.500.500.640.63-1.30-1.210.280.27
2040.901-960.500.500.530.480.120.630.210.16
2140.963-7030.500.500.650.62-0.84-0.380.230.18
2250.0280-230.250.330.360.310.240.640.170.17
2350.0790-730.250.330.390.24-0.810.340.190.13
2450.5380-9050.250.330.650.58-3.41-2.440.270.36
2550.801-420.250.330.450.42-0.310.110.200.18
2650.884-3030.250.330.520.49-0.95-0.570.220.21
2750.935-7040.250.330.570.57-1.63-1.430.270.20
2860.1090-1050.250.220.260.27-0.130.070.220.19
2960.1930-730.250.220.390.32-1.35-0.450.270.26
3060.2950-2030.250.220.470.48-2.74-2.430.380.36
3160.467-660.250.220.380.34-0.90-0.380.230.24
3260.576-840.250.220.440.39-1.56-0.590.260.27
3360.8220-9030.250.220.630.55-5.33-3.140.260.21
3460.888-6040.250.220.570.50-3.30-1.960.160.19
3570.0690-640.250.140.310.35-1.40-1.430.290.21
3670.2130-830.250.140.390.31-2.20-1.040.300.23
3770.5080-8050.250.140.510.55-4.18-4.780.340.32
3870.699-2050.250.140.460.34-2.62-0.880.250.23
3970.817-3020.250.140.410.34-2.25-0.930.220.21
4070.911-1020.250.140.340.27-0.71-0.300.190.17
Means0.510.510.560.54-0.390.040.230.21
Estimated error variance .0016.0015.1370.1188.0012.0015
Figure 1. Proportion of alternation as a function of Ph. Each data point summarizes the results of one game. The outlier (alternation rate of 0.07 when Ph = 0.67) is Problem 3: The problem with the lowest payoff variance, and the only problem in which entry cannot lead to losses.
Figure 1. Proportion of alternation as a function of Ph. Each data point summarizes the results of one game. The outlier (alternation rate of 0.07 when Ph = 0.67) is Problem 3: The problem with the lowest payoff variance, and the only problem in which entry cannot lead to losses.
Games 01 00221 g001
Table 3. Summary of correlation analyses that examine the possibility of consistent individual differences. The summary scores are based on 180 correlation analyses (180 pairs of games) for each of the four variables.
Table 3. Summary of correlation analyses that examine the possibility of consistent individual differences. The summary scores are based on 180 correlation analyses (180 pairs of games) for each of the four variables.
VariableMean correlationProportion of positive correlations
Entry rate0.2490.844
Maximization0.0580.611
Alternation0.4150.983
Recency0.2810.888
Table 4. The baseline models, the estimated parameters, and the implied normalized MSD scores by statistic and block.
Table 4. The baseline models, the estimated parameters, and the implied normalized MSD scores by statistic and block.
ModelFitted parametersNormalized Mean Squared Deviation Scores by statistic and block
Entry ratesEfficiencyAlterationMean
Block:121212
Pure 26.5221.5639.4128.0149.5035.2633.38
Symmetric 29.5725.1121.1313.2430.5925.9524.26
RL λ = 4, w = 0.018.5716.375.198.8419.1412.2211.72
NRLλ = 12, w = 0.0256.3614.033.597.354.581.536.24
SFPλ = 1.5, w = 0.15.915.369.3714.996.533.797.66
NFPλ = 4, w = 0.154.754.163.606.132.703.804.19
EWAλ = 0.7, φ = 0.8,
δ = 0.5, ρ = 0.4
10.068.914.699.224.382.496.62
SAWεi ~ U[0,0.02], wi ~ U[0,1],
ρi ~ U[0,0.02],
and µi = {1, 2, or 3}.
3.932.491.872.044.185.373.31
I-SAWεi ~ U[0,0.24], wi ~ U[0,0.8],
ρi ~ U[0,0.2], πi ~ U[0,0.6],
and µi = {1, 2, or 3}.
1.561.191.371.471.431.301.38
Table 5. The predictions of the best baseline models (I-SAW): The lowest row presents the correlation with the experimental results by statistic.
Table 5. The predictions of the best baseline models (I-SAW): The lowest row presents the correlation with the experimental results by statistic.
The gamesEntry ratesEfficiencyAlternations
#KPhhlSfB1B2B1B2B1B2
120.0470-350.780.812.602.560.170.13
220.2330-940.580.622.392.620.240.22
320.671-230.900.912.332.320.100.08
420.7330-8040.640.642.472.590.260.25
520.8020-8050.670.672.472.610.240.23
620.834-2030.770.782.492.570.200.18
720.946-9050.820.822.392.490.150.14
820.951-2050.840.852.422.470.130.11
920.964-9030.840.862.352.430.130.11
1030.1070-840.420.450.971.230.230.21
1130.909-8040.740.75-0.060.110.190.18
1230.917-7060.760.76-0.150.050.180.17
1340.0660-420.410.430.220.340.240.22
1440.2040-1040.430.44-0.040.250.270.25
1540.3120-940.480.49-0.220.010.290.28
1640.604-620.520.52-0.20-0.050.300.28
1740.6040-6030.550.55-0.78-0.470.290.28
1840.733-820.530.52-0.20-0.080.290.27
1940.8020-8020.650.64-1.65-1.230.240.24
2040.901-960.520.520.070.060.250.23
2140.963-7030.610.59-0.80-0.510.210.19
2250.0280-230.350.35-0.080.060.230.20
2350.0790-730.310.32-0.42-0.050.210.19
2450.5380-9050.520.52-2.03-1.590.290.28
2550.801-420.400.40-0.24-0.100.250.23
2650.884-3030.470.46-0.89-0.730.250.22
2750.935-7040.510.50-1.43-1.080.240.21
2860.1090-1050.310.31-1.08-0.630.220.20
2960.1930-730.360.36-1.28-0.900.260.24
3060.2950-2030.420.42-2.05-1.620.290.27
3160.467-660.350.35-0.86-0.670.270.24
3260.576-840.360.35-0.94-0.700.270.25
3360.8220-9030.600.57-4.69-3.730.250.24
3460.888-6040.470.46-2.20-1.830.250.22
3570.0690-640.260.26-1.19-0.680.200.18
3670.2130-830.340.33-1.77-1.320.260.24
3770.5080-8050.490.48-4.31-3.610.290.28
3870.699-2050.370.36-1.84-1.520.260.24
3970.817-3020.370.36-1.81-1.500.260.23
4070.911-1020.290.28-0.76-0.580.220.19
Means0.525 0.526 -0.270 -0.011 0.234 0.215
Correlation with the experimental results0.9730.9790.9820.9700.7500.834

References and Notes

  1. Erev, I.; Ert, E.; Roth, A.E. A choice prediction competition for market entry games: An introduction. Games 2010, 1, 117–136. [Google Scholar]

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MDPI and ACS Style

Erev, I.; Ert, E.; Roth, A.E. Erev, I. et al. A Choice Prediction Competition for Market Entry Games: An Introduction. Games 2010, 1, 117-136. Games 2010, 1, 221-225. https://doi.org/10.3390/g1030221

AMA Style

Erev I, Ert E, Roth AE. Erev, I. et al. A Choice Prediction Competition for Market Entry Games: An Introduction. Games 2010, 1, 117-136. Games. 2010; 1(3):221-225. https://doi.org/10.3390/g1030221

Chicago/Turabian Style

Erev, Ido, Eyal Ert, and Alvin E. Roth. 2010. "Erev, I. et al. A Choice Prediction Competition for Market Entry Games: An Introduction. Games 2010, 1, 117-136" Games 1, no. 3: 221-225. https://doi.org/10.3390/g1030221

APA Style

Erev, I., Ert, E., & Roth, A. E. (2010). Erev, I. et al. A Choice Prediction Competition for Market Entry Games: An Introduction. Games 2010, 1, 117-136. Games, 1(3), 221-225. https://doi.org/10.3390/g1030221

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