## 5 Nested Logit and Game Modeling Proposed  
### User Behavioral Choices  
A nested logit model is used to analyze the user's reservation slot selection behavior. As the first choice layer, in making appointment choices, users make the following choices based on travel costs [28; 29; 30]:  
Option 1: Select reservation parking. Option 2: Choose other parking lots in the neighborhood. Option 3: Choosing other modes of travel. This paper focuses on the analysis of the probability of the user's choice of time slot in the first case, and other parking lots and travel modes will not be categorized and analyzed in detail. Therefore, the second-choice tier unfolds under the first choice option of the first-choice tier (choosing reserved parking), including the choice of the combination j for the operation period, where J = {any combination of consecutive numbers contained in the maximum number of reservation periods}, j \(\in\) J. The overall nested logit tree structure is shown in Figure 3.  
The factors affecting the user's choice by considering the travel utility, perceived utility. The main subjective factors considered in the travel costs are the distance (km), cost (CNY), and time (min) required by the user to park. The parking time in the parking lot is categorized into peak and flat, and users weigh the time metrics according to their needs. The factors to be considered for the perceived cost of user trips were categorized into the convenience of parking, dependability of the garage, and user behavioral habits for trips to commercial areas. These factors were categorized in our questionnaire into five levels according to the degree of intensity, e.g., very convenient, relatively convenient, average, relatively inconvenient, and very inconvenient. In the process of travel parking behavior selection, among the inherent attributes of the user itself, the user's age (years), income (CNY), and purpose of travel are mainly considered. Figure 3: Nested logit selection tree. Based on the above factors, the user's travel utility function that considers their own preference habits is established as follows:  
\[ \begin{split} V_{i}=\alpha_{1}\text{distance}+\alpha_{2}\text{ cost}+\alpha_{3}\text{travel time}+\beta_{1}\text{preferences}+\beta_{2}\text{dependability}\\ +\beta_{3}\text{convenience}+\gamma_{1}\text{age}+\gamma_{2} \text{purpose}+\gamma_{3}\text{income}\end{split}  \tag{1}\]  
where \(\alpha\) is the parameter corresponding to travel utility; \(\beta\) is the parameter corresponding to perceived utility; and \(\gamma\) is the parameter corresponding to attribute utility. The utility functions in the last two choice branches of the first tier (choosing another parking lot vs. choosing another mode of travel) are all the above forms. Since the choice tree of the logit model is constructed in the form of a nested logit, the utility of the first choice branch of the first level (choosing to book a parking reservation) is affected by the utility of its nested branch, whose utility function is:  
\[V_{a}=V_{i(a)}+\beta_{logsum}logsum_{a} \tag{2}\]  
\[logsum_{a}=\ln(\sum_{l=1}^{n!}e^{V_{l}}) \tag{3}\]  
where \(V_{a}\) is the utility function of the user who chooses to reserve parking; \(V_{i(a)}\) is the corresponding basic utility function of the user in the same form as \(V_{i}\) where \(V_{a}\) is the user utility function for choosing reservation parking; \(V_{i(a)}\) is the corresponding user basic utility function in the same form as \(V_{i}\); \(\beta_{logsum}\) is a dissimilarity parameter reflecting the degree of correlation among the lower choice branches; \(logsum\) is the nested additional utility; and \(V_{l}\) is the utility function for selecting each reservation period in the same form as \(V_{i}\). Under the assumption that the number of reservation periods is n, in the first level of choice branches, the user has a total of three choices. In the second level of choice branches, the user has a total of (n!) choices.