# Experimental Study on the Risk Preference Characteristics of Members in Supply Chain Emergencies
## 2 Experimental Design and Methods
### Experiment 3: Risk Preference Test of Supply Chain Emergent Sub-Events  
In terms of the definition and classification of a supply chain emergency, a consistent opinion has not currently been formed in the academic circle. A representative study, such as [PERSON]'s [32] classification of a supply chain emergency, showed that emergencies include natural disasters, production accidents, and abnormal accidents (such as a robbery, artificial panic, and strike). Some scholars divided supply chain emergencies into subjective factors, objective factors, and environmental factors [33]. Based on the classified statistics of relevant studies, the supply chain emergency was divided into four sub-events in this study: natural disaster, production accident, economy field, and abnormal accident, and the risk preferences of subjects were tested in the corresponding sub-events. [PERSON] [13] (2010) made the subjects choose schemes in four scenarios of the financial risk field, including a deterministic return y and a risky return x (p chance of x). Therefore, our experiment had a profit and loss generated by the decision-making scheme of a supply chain emergency. Each pair of the chosen schemes was presented as two options A and B. The two options of the chart represented risky returns indicating the probabilities for gain versus nothing, respectively (see Appendix B). The value of the risk return x was represented by a risk probability (20%, 40%, 60%, 80%) and the corresponding return (300, 600, 900, 1200). Each risk scenario produced 16 schemes when y and x were crossed and paired to design risky schemes. The accompanying certainty was generated by using a power law utility function with power \(\gamma\) so that a person with power \(\gamma\) would be indifferent between the sure thing and the risk. The utility function was used to measure the relevance and dependence of risk preference in supply chain emergent sub-events. The utility function formula is shown in (3):  
\[\text{y}=\text{x}\ \text{p}^{(1/\gamma)}, \tag{3}\]  
In the above formula, p represents the probability of the risk return x. \(\gamma\) represents the utility bending degree of the utility function u(x) = x\({}^{\gamma}\), which is also the risk preference coefficient of the decision maker. \(\gamma\) = 1 means risk neutral. The smaller \(\gamma\) is, the more risk-averse the decision maker is. In a specific supply chain emergency scenario, four values of \(\gamma\) were used (0.35, 0.5, 0.65, 0.8) when someone much less risk-averse would select the sure thing when even the most risk-averse would select the risky option. The idea here is that a more risk-seeking person tends to choose the prospects in the \"risky\" options, while a more risk-averse person tends to choose the sure amounts in the \"risky\" options and the prospects of the \"safe\" choice schemes. Definitely, very risk-seeking persons would choose only the risky option and very risk-averse subjects will choose only the sure amounts. The value of \(\gamma\) corresponds to the given value of \(\gamma\) for each design scheme. The mean value of \(\gamma\) selected by all the subjects was calculated, which was also the risk preference coefficient of the subjects. Values of \(\gamma\) were randomly assigned to options with the constraint that each value of \(\gamma\) occurred once for each amount and once for each probability. There were 64 (4 \(\times\) 4 \(\times\) 4) kinds of possible schemes of risk decisions that could be generated by composing values of the \(\gamma\), prospect amount, and four levels of probability. Presenting all subjects with all 64 schemes in each scenario would be a demanding task. In order to facilitate the effective implementation of the experiment, 16 composition schemes were selected considering that all four kinds of \(\gamma\) values could be paired with x and p in each emergent sub-event. However, it is certain that at least each scenario presented all four levels of \(\gamma\) paired with every monetary amount and probability.