## 5 Numerical Analysis
### Impact of Dynamic Pricing Mechanism on Ride-Hailing Platform's Order Allocation Strategy
#### 5.3.2 Impact of Taxi Unit Cost Changes on Ride-Hailing Platform's Order Allocation Strategy  
Although taxi fares are uniformly regulated by the government, ride-hailing platforms flexibly reduce the actual cost of taxi rides on their platforms through subsidies and other means or moderately increase taxi prices during periods of tight vehicle supply to ensure order responsiveness and attractiveness to passengers. Therefore, when taxis implement differentiated pricing strategies between online and offline services, their impact on the probability of passenger order cancellation is illustrated in Figure 10.  
When online taxi fares are advantageous, the probability of passenger order cancellation quickly approaches zero, with only a slight increase in cancellation probability at the penalty point for cancellations if the online taxi pick-up time exceeds 0.2 h. When online and offline prices are the same, the probability of passenger order cancellation remains unchanged for online taxi pick-up times within 0.1 h, but wait times exceeding 0.1 h make passengers more willing to take cruising taxis. When online taxi prices are higher than offline prices, the impact of cancellation penalties on passengers' decision to cancel orders decreases significantly. Beyond the penalty point, the probability of passenger order cancellation increases with the length of online taxi pick-up time, showing marginal diminishing increases, with the function value remaining high. Figure 9: Optimal order allocation ratio \(\alpha\) for social welfare when \(M_{C}\) changes. In cases of differentiated pricing between online and offline taxis, when online prices are lower or higher than offline prices, ride-hailing platforms allocate different proportions of orders to taxis, and changes in driver earnings are shown in Figure 11. In general, an increase in online vehicle arrival times leads to a decline in driver income. Specifically, when online taxis can pick up passengers within 0.05 h, higher online prices than offline can actually reduce driver income in the period before the cancellation penalty point. However, when online taxi pick-up times increase to 0.1 h, raising online taxi prices always prompts drivers to earn higher incomes. In view of this, when online vehicle pick-up times are relatively short, increasing online taxi prices is generally beneficial for improving driver income. If pick-up times extend to 0.15 h, the high-pricing model for online taxis will experience a significant decline in income after the cancellation penalty point, with the decline becoming more pronounced as the dispatch ratio increases. Meanwhile, driver income in the low-pricing model shows an upward trend. When pick-up times exceed 0.2 h, driver income will decline for both high and low online pricing models, with the high-pricing model lasting longer and showing a more significant decline. Therefore, to reduce the driver income risk, the low-pricing model can be selected at this point. Figure 11: Impact of differentiated pricing between online and offline taxi services on drivers’ income. Figure 10: Impact of differentiated pricing between online and offline taxi services on the probability of passenger order cancellation. When the taxi unit price, \(M_{T}\), fluctuates, changes in the optimal order allocation ratio, \(\alpha\), for maximizing social welfare are shown in Figure 12. For cases where the arrival time of cruising taxis, \(T_{X}\), precedes the penalty time, \(T_{P}\), for passenger order cancellation, an increase in taxi fares, \(M_{T}\), significantly affects the order allocation ratio, \(\alpha\), when ride-hailing vehicles arrive later. An increase in taxi fares, \(M_{T}\), raises the cost of switching to another mode for passengers, reducing the probability of order cancellation. Therefore, when taxi fares are higher, ride-hailing platforms need to allocate as many orders as possible to taxis.