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Chapter 5 Ultimatum game experiment results
In this chapter, we show the fundament results in our ultimatum game experiments.
Table 5 represents regarding proposers and Table 6regards responders. There are a few points deserving to be highlighted. First, our mean offer rate for the money experiment is 43.52%. In an international context, this number is very close to our neighboring country, Japan, where the mean offer rate is 44.73% (a survey from Oosterbeek et al., 2004).
Second, the mean offer rate of chocolates, 45.6%, is slightly, but statistically significantly, higher than that of money (Table 7). This may concur positively with the observation made by Bowles et al. (1997). Third, if we separate the group by gender, an issue which have received tremendous attention in experimental economics (Croson & Gneezy, 2009;
García-Gallego et al., 2012; McGee & Constantinides, 2013), we find that the mean offer rates between men (43.43%) and women (43.60%) are very close and the difference is not significant (Table 7), while the rate offered by women is significantly higher. However, in the chocolate experiment, the result is opposite; now men become more generous (47.1%) than women (44.1%), and the difference is also statistically significant (Table 7). At the same time, both in money and chocolate treatments, the male responders ask for higher offer (Table 8). Hence, as already noticed in the literature, the gender effect can be context sensitive (Croson & Gneezy, 2009), and, in this case, the medium can play a role.
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Table 5 Descriptive Statistics of the Ultimatum Game: Proposers
Table 6 Descriptive Statistics of the Ultimatum Game: Responders
money
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Table 7 Stastics test in defferent Medium and gender : proposer
Table 8 Stastics test in defferent Medium and gender : responder
Table 9 Average Offer Rates in Money and Chocolate Experiments Mean offer
money 43.52 (43.52%) 0.000013*** 0.000004***
chocolate 4.56 (45.6%)
m_male 43.43 (43.43%) 0.801924 0.655700
m_female 43.6 (43.6%)
money 45.55 (45.55%) 0.000102*** 0.000026***
chocolate 4.80 (48.00%)
m_male 46.95 (46.95%) 0.000191*** 0.000048***
m_female 44.29 (44.29%)
c_male 4.89 (48.9%) 0.068248* 0.004977***
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Table 9 shows the basic statistics of the responders’ behavior under the condition when the offers were accepted (the upper panel) and when the offers were rejected (the lower panel). In the upper panel, we show the statistics of the offers accepted by the respective responders. For the money experiment, we see that men are more demanding by requesting a statistically significant higher offer rate (46.95%) than women (44.29%);
nonetheless, the acceptance rates between men and women (72.05% vs. 70.68%) are not significantly different. When coming to the chocolate experiment, unlike their corresponding proposers, men were not getting generous here. Instead, they were still statistically significantly more demanding (48.9%) than women (47.0%), while the resultant acceptance rates (78.21% vs. 76.36%) are not statistically significantly different.
Comparing the proposers’ offer behavior in our experiments (Figure 4) to an international meta-survey (Figure 3)(Cooper & Dutcher, 2011), our data show some difference. In Cooper’s survey, for the two leftmost categories of offers, acceptance rates are lower for Rounds 6–10 than in Rounds 1–5, but we have reverse results. The magnitude of the increase for small offers is larger, but given the infrequency of low offers we would once again struggle to identify the effect without a sizable dataset.
The lower panel of Table 6 gives the result conditional on the rejection. Basically, the result can be read similarly to those conditional on the acceptance. The mean offer rate under rejection is higher for men than women in both the money and chocolate experiments. The rejection rate of the money experiment is high, up to 28.67%, and the rejection rate of the chocolate experiment is 22.77%. An international comparison of the rejection rate in repeated ultimatum game is not known to us.
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Figure 3 Acceptance rate as a function of experience. Note: The numbers above the bars give the number of observations for that bar (Cooper & Dutcher, 2011)
Figure 4 Acceptance rate as a function of experience in our experiments. (M) means the money treatment and (C) means the chocolate treatment.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0≦offer<10% 10%≦offer<20% 20%≦offer<30% 30%≦offer<40% 40%≦offer<50% 50%≦offer Acceptance rate
Offer rate
(M) 1-5 rounds (M) 6-10 rounds (C) 1-5 rounds (C) 6-10 rounds
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Since we don’t get data about rejection rate in repeated ultimatum games across countries, and we could not test if there are any difference between our subjects and literatures. We enrolled subjects to play one-shot ultimatum game, not reported the details here, our rejection rate is 13.24% for the money experiment and 5.88% for the chocolate experiment. Therefore, our result of having a higher rejection rate in the repeated game than in the one-shot game is consistent with the findings in other studies, e.g., Slembeck (1999).
Figure 5 Offer Rates through Time
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Since what we run is a multiple-round ultimatum game, we, therefore, also briefly summarize the key statistics over time. Figure 5 gives the time series of the average offer rates made by proposers (the upper panel) and the average acceptance rate accepted by responders (the lower panel). The average offer rate started low around 40 to 45, then gradually moved up to the level of the average and fluctuated around there.
Except in the third and the fifth period, the average offer rate in the chocolate experiment is always higher than that in the money experiment.
Also, in Figure 5 (the lower panel), we can see that the accepted offer rate, from the beginning to the end, is very much fluctuating around their mean level, with no noticeable tendency to increase or decrease. Except in round 5, the accepted offer rate in the chocolate experiment is either equal to or larger than that in the money experiment.
Table 9 shows the gender difference over time in both money and chocolate experiments. In the money experiment, except in the first two periods, women’s generosities compared to men were consistently shown in the rest of the remaining periods. On the other hand, men’s generosities in the chocolate experiment were also consistently shown in all periods except round 3. In sum, the inequality properties shown in Table 4 and 5 are consistent in each individual round over time to a substantial extent. In sum, even though the difference between men and women observed through these two tables is limited, the evidence is slightly in line with our understanding of gender differences in fairness preference or social preference. There are more basic statistics tables and figures on Appendix B for reference.
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