# Experimental Study on the Risk Preference Characteristics of Members in Supply Chain Emergencies
## 2 Experimental Design and Methods
### Experiment 2: Risk Preference Test of Supply Chain Members in Emergencies  
According to cumulative prospect theory and the axiomatic weight parameters derived by [PERSON] [31] (1998), the values of a piecewise power function were obtained as follows:  
\[\
u(x)= \begin{cases}\ \ \ (x)^{1-\sigma};\ \ if\ x\geq 0\\ -\lambda(-x)^{1-\sigma};\ \ if\ x<0\end{cases}  \tag{1}\]  
The equation probability weighting function is shown in Equation (2):  
\[\pi(p)=1/\exp[\ln[(1/p)]\ ^{\alpha} \tag{2}\]  
The concavity of the value function is represented by \(\sigma\), and the degree of loss aversion is represented by \(\lambda\). If \(\lambda>1\), the decision maker is more sensitive to the loss. If \(\alpha=1\), then the probability weighting function is linear. If \(\alpha>1\), then the weighting function is S-shaped, i.e., individuals underweight small probabilities and overweight large probabilities, as shown by [PERSON] and [PERSON] [9]. If \(\alpha<1\), the weighting function is an inverted S-shape, i.e., individuals overweight small probabilities and underweight large probabilities. The above model reduces to EU (with a reflected utility function at zero) if \(\alpha=1\) and \(\lambda=1\). \(p\) is the probability of outcome x. In order to calculate the prospect theory parameters, two options programs (two series) of the supplies were designed in the rainstorm environment. Different selection programs determined the risk preference of subjects. As shown in Table 1, each series consisted of 14 questions and was divided into options A and B. The difference in the expected value between the programs (A relative to B), that is, the theoretical advantages and disadvantages of option A and option B, is shown in the right column. The probability and expected benefits of A and B were described by referring to [PERSON]'s design method. The choices were carefully designed so that any combination of choices in the two series determined a particular interval of prospect theory parameter values. In the test of each series, the subject would switch from option A to option B, and the switching point would have values of one or none for each series. Combinations of approximate values of \(\alpha\), \(\sigma\), and \(\lambda\) are illustrated in Table 2 for each switching point. \"Never\" indicates the cases in which a subject does not switch to option B (i.e., always chooses A). The switching points in series 1 and 2 jointly determined \(\alpha\) and \(\sigma\). If multiple switching points appeared, the experiment was considered invalid. From the switching table, two data matching the switching point were analyzed to obtain \(\alpha\) and \(\sigma\), which determined the risk preference of the subjects. The combinations of \(\alpha\) and \(\sigma\) of each switching point are shown in Table 2. For example, if the switching point was considered for question 6 in series 1, the combinations of (\(\alpha\), \(\sigma\)) were (0.4, 0.5), (0.5, 0.6), (0.6, 0.7), (0.7, 0.8), (0.8, 0.9), and (0.9, 1.0). If the switching point was considered for question 4 in series 2, the combinations of (\(\alpha\), \(\sigma\)) were (1.0, 0.7), (0.9, 0.8), (0.8, 0.9), and (0.9, 1.0). By combining the two series of turning points, the value of (\(\alpha\), \(\sigma\)) was (0.8, 0.9). With the time pressure value setting being considered, the research methods put forward by [PERSON] and [PERSON] were applied [27]. In order to verify the influence of time pressure on decision-making behavior, [PERSON] and [PERSON] defined the value obtained by subtracting one standard deviation from the mean decision time with no time pressure record as the low time pressure and 1/2 of the mean as the high time pressure. In this experiment, the mean time and standard deviation of the subjects in the two series were 220 s and 50 s, respectively, with no time pressure.