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立 政 治 大 學
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Chapter 4 Experiment design and procedures
4.1 Ultimatum game
The ultimatum game experiments were run in the NCCU EEL (National Cheng-Chi University, Experimental Economics Lab). There are three sequential stages different on the medium of bid administered in this study, which were based on repeated ultimatum game. In stage 1 (S1), the money treatment, a normal ultimatum game is played in this stage, the proposer was asked to allocate NT$100 to the responder. If the responder states acceptance for the offer, they share the money;
otherwise, both receive nothing. In stage 2 (S2), the chocolate treatment, the proposer was allowed to make allocate 10 chocolates to the responder. Every piece of chocolate is worth NT$10 which was also informed to the players ahead of the game and the total value of all chocolate are NT$100, the same as the amount of cash in stage 1. To reduce further uncertainty which may come with the use of chocolates as the medium, we use a well-branded chocolate in Taiwan, i.e., Ferrero Rocher. In the final stage (S3), the medium in stage l and 2 are combined in use. The proposer has NT$100 and 10 chocolates in hand and is asked to propose one offer including both money and chocolate. We repeatedly play ultimatum game ten times in each stage. Given the complexity of how to analysis and model the final combinatorial game, our analysis in this research is only based on the first two stages.
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All experimental stages began with an introductory talk. Subjects then were encouraged to ask questions. All participants were fully informed on all features of the experimental design and the procedures. The subjects were randomly assigned to be as the proposers and responders at beginning and the pair relationship will be maintained in all three stages.
Table 3 Subjects: Gender and the Role-to-Play Proposer Responder
Male 40 39
Female 43 44
Total 166 individuals were recruited to join our experiments, 79 male and 87 female (see Table 3). These subjects all enrolled from the NCCU EEL Recruiting System and mostly are students coming from different schools. Their ages were ranged from 18 to 30. Subjects received a show-up fee of NT$1501 that was independent of their earnings in the experiment. Participants could receive a bonus calculated as the average amount of the money or chocolate they actually acquired during the ten rounds ultimatum game of each stage. Hence, if there is a half-half deal accepted by both side through the whole 30 periods of the game, the bonus will be a total pay of NT$ 100 and 10 10-dollar chocolates. Considering that the total duration of our experiment was 90 minutes (including pre-experiment information session, 3-stage game, post-experiment questionnaire and payment), this structure of pay should be reasonably attractive.
1 The normal on-campus work-study hourly rate, NT$95
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立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
All test procedures were conducted and controlled by the z-Tree 3.2.12 (Fischbacher, 2007). It means that the subjects interaction through the monitor and they don’t know the gender of his/her partner.
4.2 Monte Carlo simulation
To show how the Monte Carol simulation is implemented, we use Table 4 as an illustration. In this research, our results will be presented by the following categorizations: money experiment and chocolate experiment, each then subgrouped by gender. Therefore, there are six categories as structured in Table 4. The simulation is repeated 10 times, but the first time is reserved for the initialization for the emotion dynamics (1) and (2) or (3). We, therefore, have nine observations for each subject.
There are a total of 83 subjects, 40 male subjects and 43 female subjects. The number of observations for each category is, accordingly, shown in the last row of the table.
Let us take the money experiment with all subjects, the first category, as an example.
As shown in the second column of the last row, there are a total of 747 observations.
For each single run of the Monte Carlo simulation, the emotion index X and Y are developed based on these 747 observations. For each single run the four parameters,
αx+, αx−,
α
y+,α
y− are randomly sampled from the given range (Table 2). An example is given in Table 4: (αx+,α
y+) = (1.1608, 1.3908), and (αx−,α
y−) = (2.2355, 4.7792). By the homogeneity assumption applied in this research, in this specific run, we assume that these parameter values are applied to all subjects when estimating their emotions.30
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We shall repeat this process for 2,000 times2 for each of the assumed reference R. In this specific example, R is assumed to be 40. When all this is done, we move to the next category, for example, the money experiment with male proposers only, then with female proposers only, then moving to the chocolate experiments in the order as demonstrated in Table 4.
Table 4 Monte Carlo Simulation: One Specific Runs
At the end of each run, what we have is the derived (
X
i t, ,Y
i t, ) for eachindividual
i
and the observedZ
i t, (i =1, ..., 83, t = 2, ..., 9). We then pool these variables together and apply the maximum likelihood estimator to estimate the coefficients of the ordered logit model (8). The statistical software applied to this estimation is Matlab 2008b. The estimates of these specific runs are given in the first row of the fourth block of Table 4. Immediately below it is the p-value of the2 We had test to repeat the simulation for 2000, 10000, and 20000 times and the outcomes were quite similar. Therefore, we believe that repeating the Monte Carlo simulation for 2000 times is enough for our model to get convergence results.
Proposer
Money Chocolate
all subjects male female all subjects male female
α x αx αy αx αy αx αy αx αy αx αy αx αy
*, ** and *** denote the significance of estimates at the 10 percent, 5 percent and 1 percent levels, respectively.
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estimated coefficients. Again, taking the all-subject case as an example,
b
ˆ1 andb
ˆ2are -0.0718 and 0.0747, with only
b
ˆ1 being statistically significant. Therefore, we have this run for the significance of X as well as one for the insignificance of Y. In the end of the 2,000 trials, we shall count how many runs having significant X and how many runs having significant Y. These will be main results to be reported in the next section. Also, to make sure that both X and Y are measuring different parts of emotions, we calculate the correlation coefficient between X and Y, as shown in the last row of the fourth block, to confirm that they are not highly correlated. As shown in these specific runs, X and Y in general are not highly correlated, which indicates that they are not measuring the same kind of emotions.32