Shared Parking Decision Behavior of Parking Space Owners and Car Travelers Based on Prospect Theory—A Case Study of Nanchang City, China

Abstract

Shared parking improves the utilization rate of parking spaces by taking advantage of temporal and spatial differences, which is conducive to alleviating parking problems. From the perspective of bounded rationality, this paper studies the factors that influence the decision behavior of parking space owners and car travelers (non-residential drivers who have parking needs near residential areas) in sharing parking spaces. Prospect theory was used to analyze the bounded rational behavior characteristics of parking space owners and car travelers, and a value function model with rental price as the reference point was established. Combined with the survey data of the Xinhuangcheng district in Nanchang City, China, the shared parking space rental price that satisfied both parties was analyzed in this case study. The results of the study show that factors such as personal characteristics and behavioral habits affect the decision behavior of parking space owners and car travelers, and that rental price is a key factor. When the rental price of parking spaces is close to the maximum price desired by the owner, the owner feels the benefit and is willing to share the private parking space, but when the rental price differs greatly from the maximum price desired by the owner, the owner feels the loss and is not willing to share the parking space. From the survey data, it can be concluded that the ideal rental price of shared parking spaces around the survey area is 5 CNY/h. This paper provides a theoretical basis and guidance for the formulation of shared parking policies, which can help solve parking problems.

1. Introduction

As the number of motor vehicles increases year by year, parking problems are becoming increasingly serious [1]. There is a huge gap in the supply of parking spaces, and the phenomenon of parking chaos is intensifying. At present, many cities in China are trying to alleviate the parking problem by expanding the supply of parking spaces. However, land resources and funds are limited. With the continuous increase in motor vehicles, expanding the supply of parking spaces cannot fundamentally solve this problem [2]. How to scientifically and effectively alleviate the parking problem becomes increasingly important. For this problem, there are many theoretical studies and practical cases; for example, the development of a mechanical three-dimensional parking lot to improve space utilization, and enhancing the service quality of public transportation to induce drivers to use public transportation.

In recent years, mechanical three-dimensional parking lots have become an effective measure to solve parking problems. The biggest advantage of a three-dimensional parking lot is that it can make full use of urban land resources and improve space utilization. Due to the advantages of small footprint, high degree of automation and convenient access, three-dimensional parking is increasingly favored by urban traffic managers. Nevertheless, the costs of construction, operation, and post-maintenance of the three-dimensional parking lot requires a substantial amount of time and money, and the rate of return in the later period is relatively slow [3,4]. Therefore, the development of three-dimensional parking lots has been stagnant in China.

Inducing drivers to use public transportation by improving its service quality is also a common method to solve parking problems. Ai et al. have optimized the transfer conditions for parking at the periphery of the rail transit line to attract more passengers [5], and most low-income people will choose public transportation. However, the service time and frequency of public transportation are limited, and it is difficult to achieve “point-to-point” service; thus, it is hard to meet the requirements of some passengers [6,7,8,9,10]. In contrast, private cars are more flexible and comfortable. People whose travel routes are not well covered by public transportation have to drive private cars or take cabs. Drivers still face parking difficulties.

In the information age, ride-hailing has developed rapidly and it has been liked by people for its convenient and comfortable advantages. Therefore, many cities in China are trying to develop ride-hailing, people are more willing to choose ride-hailing by improving the quality of ride-hailing services. The parking demand can be effectively reduced by increasing the utilization rate of cars [11,12]. However, there are many illegal business phenomena in ride-hailing, and the safety of passengers is difficult to guarantee. This method still cannot solve parking problem.

Shoup [13] found that in the urban traffic network, on average, about 30% of the traffic congestion per day is caused by drivers looking for parking spaces. The problems of traffic congestion and environmental pollution caused by the process of finding parking spaces are obvious. Therefore, many scholars began to put forward the concept of parking reservation and studied it as a subsystem of the parking guidance system. Travelers can reserve a parking space online, thus reducing the problems in finding a parking space [14]. There is a lot of research on parking reservations: Xue [15] used the method of advance parking reservation to reduce the parking search time and established a prospect theory model with the reservation price as a variable; Mouskos proposed the use of parking reservation services to help travelers reserve parking spaces in advance, targeting the lowest parking costs for all users of the system [16]. However, the number of parking spaces is limited. Parking reservation is very effective in reducing a traveler’s parking time, but it cannot effectively solve the issue of insufficient parking spaces.

According to a survey conducted by the City of Davis (Davis, CA, USA), nearly 45% of parking spaces in residential areas are unused, while parking spaces in parking lots near malls, shopping centers, attractions, etc. are in short supply [17]. How to improve the utilization of parking spaces in a limited geographic space is a problem. Fortunately, sharing idle parking spaces with travelers who need to park nearby is an effective way to alleviate the parking problem [18,19,20,21]. Shared parking takes advantage of the temporal and spatial variability of parking demand around different buildings to integrate parking resources from different sites, effectively improving parking utilization.

The United States put forward the theory of berth sharing as early as 1983, it defines “shared parking” as “parking spaces of different land uses in a region at different times of the day” [22]. Under the mixed land use model, office, commercial, leisure and residential resources are intensively compounded, so that travelers can enjoy a convenient urban life with offices, shopping and entertainment in close proximity to each other. Parking spaces in residential areas are often vacant during the workdays during the day, while parking spaces near residential areas are in short supply. Parking utilization is improved by sharing parking spaces to drivers who need to park in the neighbor-hood. In this paper, the car travelers are non-residential drivers who have parking needs near residential areas.

After more than ten years of exploration and research, many scholars have verified its feasibility and effectiveness from different aspects. At present, the research on shared parking spaces mainly focuses on shared parking policies and pricing and demand prediction. In terms of policies, Zhang [23] analyzed the development of shared parking in China in three respects: the developmental history, service content, and profit model of shared parking, and put forward corresponding suggestions and guidance for a series of existing problems; Huang and Jian proposed an integrated operating strategy of car sharing and parking sharing that improves the welfare of operators and travelers [24,25]. Song [26] analyzed and summarized cases of the implementation of shared parking policies in 61 cities in China, and condensed the influence pedigree of the formulation and implementation of shared parking policy in China, which includes 25 categories and 45 concepts. In terms of pricing, Tan [27] introduced a one-sided Vickrey-Clarke-Groves (O-VCG) combinatorial auction mechanism to encourage travelers to tell the truth to maximize the benefits; Gao [28] considered the risk perception characteristics of individuals when sharing parking spaces and proposed a method based on the optimal risk-perception benefit. Wang [29] used the MP-DGS (modified agent Demange–Gale–Sotomayor) mechanism and a combined system (integration of direct and evolutionary approaches) to maximize social surplus by optimizing the allocation-pricing of parking permits. In terms of demand prediction, Tooraj [30] used historical and real-time data to predict parking availability and proposed a model that considers the temporal and spatial correlation of parking availability. Jin [31] proposed an LSTM recurrent neural network approach to predict parking demand. She et al. [32] used a combined prediction method of BP neural network and Markov chain to improve the prediction accuracy and timeliness.

The above-mentioned research on shared parking has produced many results, but there are many shortcomings in its implementation objects, effects, and specific implementation measures, mainly the following: (1) In terms of policies, the shared parking policies are mature and perfect, but it is difficult to achieve better results due to people’s low willingness to share and insufficient supervision [33,34]. (2) In terms of pricing, there is no pricing mechanism in the prior study that considers the heterogeneity of parking time patterns of space owners and car travelers [35]. (3) In terms of demand prediction, the first study only imported historical data into the model without considering the uncertainty of travelers’ behavior and the variability of parking demand time distribution, and ignored the variability between data leading to large prediction errors [36,37]. The question of how to deepen the personal heterogeneity of travelers and the variability of parking demand time should be addressed.

It can be seen that the research on shared parking has mainly focused on policies, pricing, and demand prediction, and not much research has been conducted on the decision behavior of parking space owners and travelers under uncertain conditions. Therefore, this paper considered the uncertainty of space owners’ and travelers’ decision behavior during the implementation of shared parking activities, and used prospect theory to study space owners’ and travelers’ shared parking decision-making behavior.

In the decision-making process, the decision maker’s personal perception and judgment ability is limited, and it is difficult to be completely rational [38,39]. In previous research, domestic and foreign scholars mostly applied expected utility theory to study parking behavior. However, expected utility theory assumes that decision makers are perfectly rational, which is inconsistent with the actual situation. The Allais and Ellsberg paradox explains to a certain extent that the actual decision behavior of decision makers is not completely consistent with expected utility theory [40]. In the decision behavior of shared parking spaces, parking space owners and car travelers cannot obtain complete information, because they are influenced by personal experience and personal characteristics (personality, age, mood, and hobbies), etc. [41]. At the same time, the environment in which decision makers live is complex and uncertain. For example, weather and road operation conditions can change at any time. Therefore, the decision behavior of shared parking spaces is carried out in an uncertain environment. Compared with the expected utility theory, prospect theory based on the perspective of bounded rationality describes the decision behavior of decision makers in an uncertain environment more closely to the actual situation. This paper adopted prospect theory based on a bounded rationality perspective, took human psychological characteristics into account, and analyzed the factors that influence the decision of shared parking by parking space owners and car travelers. Prospect theory was used to analyze the bounded rational behavior characteristics of the owners and travelers, to establish a value function model with the rental price as a reference point.

This paper analyzed shared parking decision behavior of parking space owners and car travelers under uncertain conditions based on prospect theory, and obtained the survey data by designing a questionnaire with a combination of SP (Stated-Preference) and RP (Revealed-Preference). Through this study, we hope to provide a relevant basis and guidance for the shared parking policy, which will contribute to the conservation of urban land and sustainable development, and alleviate the urban traffic congestion problem. The structure of this study is arranged as follows: Section 2 contains the research methodology; Section 3 contains the factors affecting decision behavior; Section 4 describes the data processing and analysis; Section 5 provides model calibration and discussion; and finally, Section 6 contains the conclusions and recommendations.

2. Research Methodology

In response to the questions raised above, this study conducted an SP (Stated-Preference) survey and an RP (Revealed-Preference) survey to obtain data on decision behaviors related to shared parking. The main survey methods for decision behaviors is RP/SP survey. The RP survey provides a basis for assessing the current traffic problems by investigating actual behaviors, and the SP survey provides a basis for future traffic trends by setting scenarios to predict behavioral preferences. The RP/ SP survey is complementary in terms of data reliability and availability. Therefore, in order to understand the factors influencing decision behavior of parking space owners and travelers, this paper adopted a combination of RP/ SP survey to investigate the shared parking behavior. According to the survey data, a value function model based on prospect theory was established. From this, the reference value of the rental price of shared parking was obtained and analyzed, which provided theoretical guidance and suggestions for the formulation of shared parking policies.

2.1. Prospect Theory

2.1.1. Characteristics of Prospect Theory

Kahneman and Tversky found that people’s decisions under uncertainty differed from those based on expected utility theory, and modified it to arrive at “prospect theory” [42]. Prospect theory incorporates a large body of psychological research that considers the different attitudes people hold toward losses and gains. Prospect theory divides the human decision process into two stages: the first stage is the collection and organization of event outcomes and related information; the second stage is evaluation and decision making [43]. The basic aspects of prospect theory are as follows:

• People are more sensitive to losses than gains.
• People tend to avoid risk when faced with gains, and tend to pursue risk in the face of losses.
• People attach importance not only to the absolute amount of wealth but also to the amount of change in wealth.
• The decision makers in the early stage will have a certain influence on the later stage. If people gain in the first period, people’s preference for risk will be enhanced; if people face loss in the first period, people’s aversion to risk will increase.

2.1.2. Prospect Theory Model

According to prospect theory, the value of decision behavior is measured by the value function $v(x)$ and the weight function $\pi (p)$ [43]. The expression of the value function (1) is as follows: This shows that the decision makers will be affected by the value function and the decision weight function in the decision-making process.

$$v(x)=\{\begin{array}{l}a{x}^{\alpha }(x>0,a>0,\alpha >0)\\ -b{x}^{\beta }(x>0,b>0,\beta >0)\end{array}$$

(1)

As can be seen from Figure 1, the shape of the curve of the value function presents an “S” type. The origin is the reference point. On the right side of the x-axis, the value function $v(x)>0$ is the gain area, and the graph is concave; on the left side of the x-axis, the value function $v(x)<0$ is the loss area, and the graph is convex. It is not difficult to establish that the slope of the curve in the gain area is smaller than that in the loss area, which means that the decision makers are more sensitive to the loss than the gain. In the same amount, the utility of the loss is greater than that of the gain. In short, decision makers are risk-pursuant in the loss area and risk-averse in the gain area.

As can be seen from Figure 2, the weight function is a strictly increasing nonlinear function. The convex part of the image indicates that the decision makers tend to overestimate low-probability events, and the lower concave part indicates that the decision makers tend to underestimate high-probability events. Among them, for extremely low-probability events, the weight value is 0; for extremely high-probability events, the weight value is 1.

Prospect theory states that under uncertainty, the total value $V$ (prospect value) of a decision event is represented by the product between the value function $v(x)$ and the weight function $\pi \left(p\right)$. Its expression (2) is as follows:

$$V=v(x_1)\pi \left(p_1\right)+v\left(x_2\right)\pi \left(p_2\right)$$

(2)

2.2. Shared Parking Decision Behavior Model

2.2.1. Analysis of the Decision Behavior of Parking Space Owners

Parking space owners are often influenced by personal experience, personal characteristics (personality, age, mood, hobbies), and many other factors when considering whether to rent out a private parking space. Parking space owners make different decisions about the rental price, so the rental price is an uncertain value. When faced with the choice of rental price, the psychological changes of parking space owners in an uncertain environment are consistent with the basic ideas of prospect theory. Therefore, this paper used prospect theory to study and analyze the decision behavior of the parking space owners.

2.2.2. Rental Price Reference Point

In prospect theory, there are two reference points for the rental price of shared parking spaces. One reference point is the lowest price at which the parking space owner is willing to rent the private parking space; the other is the highest price at which the owner is willing to rent it out. When the rental price lies between the two points, the rental is beneficial; when the rental price exceeds the highest rental price given by the space owner, the driver feels the loss and chooses to park in other parking lots, and the rental is a loss for parking space owners; when the rental price is below the lowest value given by the space owner, the space owner feels the loss and is not willing to rent out the parking space. Therefore, when the rental price is between the two references points, both space owners and car travelers feel the benefit and are willing to participate in shared parking activities, and the prospect value is positive. According to the survey data, the travel characteristics of parking space owners were analyzed, and a prospect-theory model with the rental price as a parameter was established. The value function graph is shown in Figure 3.

The variables in Figure 3 are defined as follows:

$K_a$ is the lowest price at which the parking space owner is willing to rent.

$K_b$ is the price that the parking space owner is most willing to offer.

$K_c$ is the highest price at which the parking space owner is willing to rent.

From Figure 3, there are three reference points, $K_a$ (the lowest price that the owner is willing to rent), $K_b$ (the price that the owner is most willing to offer), and $K_c$ (the highest price that the owner is willing to rent). When the rental price offered by the space owner is less than $K_a$, the space owner obtains very little revenue and cannot predict what will happen after the space is rented out. He or she feels loss and is not willing to rent out the space, so this situation is not considered. When the rental price offered by the owner is greater than $K_c$, car travelers find the rental price too high to accept and refuse to reserve the parking space, so the rental success rate is low and the value function is less than 0. In area II, as the price continues to rise, the willingness of car travelers to use the sharing parking space decreases, and the parking space owner’s gain also decreases. When the rental price offered by the parking space owner is between $K_a$ and $K_c$, the owner thinks that it is beneficial to rent the parking space and is willing to rent out, so the rental success rate is high and the value function is greater than 0.

From the value function graph, we can see that area I and area II are concave with positive value function, which is consistent with the prospect theory in which gain is a concave function. Area III is convex with a negative value function, which is consistent with prospect theory in which loss is a convex function.

2.2.3. Shared Parking Model of the Rental Price Based on Prospect Theory

According to the introduction of prospect theory and value function in the previous section, the sensitivity to rental price is also different considering the different personality preferences and life perception levels of the owners. Therefore, the decision behavior of the rental price will be different. Its value function Equation (3) is as follows:

$$V(K)=\{\begin{array}{l}{V}_1(K)={\delta }_1{(K-K_a)}^{{\phi }_1}+{\sigma }_1,\hspace{1em} 0\le K_a\le K\le K_b\\ V_2(K)={\delta }_2{(K_c-K)}^{{\phi }_2}+{\sigma }_2,\hspace{1em}\hspace{1em}\hspace{1em}{K}_b\le K\le K_c\\ V_3(K)={\delta }_3{(K-K_c)}^{{\phi }_3}+{\sigma }_3,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{K}_c\le K\end{array}$$

(3)

$V(K)$ is a function of the revenue gained by the parking space owner. When $V(K)>0$, it means that the owner considers the rental as a gain; when $V(K)<0$, it means that the owner considers the rental as a loss.

$V_1(K)$ and $V_2(K)$ are the gain regions, and $V_3(K)$ is the loss region.

${\delta }_i(i=1,2,3)$ is the coefficient of value weighting function. In areas I and II (gain area), the larger the absolute value of ${\delta }_i$, the more sensitive the parking space owner is to gain; similarly, in area III (loss area), the larger the absolute value of ${\delta }_i$, the more sensitive the parking space owner is to loss.

${\phi }_i(i=1,2,3)$ is the risk pursuit coefficient, and ${\phi }_i\in (0,1)$. When the value of ${\phi }_i$ is larger, the parking space owner is more willing to pursue risk.

${\sigma }_i(i=1,2,3)$ is the perceived error of the parking space owner during the decision behavior of the rental price. Assume that ${\sigma }_i$ obeys a dual exponential distribution with an expectation value of 0.

From Equation (3), the value function $V(K)>0$ for area I and area II are beneficial to the parking space owners. If the owners are satisfied with shared parking activities, they may not change their decision behavior in the next decision. According to the statistical theory, the probability expression is as follows:

$$P(V_1>0)=\exp (-\exp (u_1({\delta }_1{(K_b-K)}^{{\alpha }_1}+{\sigma }_1\left)\right))$$

(4)

$$P(V_1>0)=\exp (-\exp (u_2({\delta }_2{(K-K_b)}^{{\alpha }_2}+{\sigma }_2)))$$

(5)

The value function $V(K)<0$ for area III is a loss for the parking space owner. The shared parking space management platform should adjust the rental price. If it is not adjusted, the travelers feel the loss and refuse to participate in this activity. According to the statistical theory, the probability expression is as follows:

3. Affecting Factors of Shared Parking Decision Behavior

3.1. Factors Influencing Travelers’ Decisions

3.1.1. Individual Attributes

The personal characteristics of the traveler include gender, age, personal attributes (mood, feelings, hobbies, etc.), and monthly income.

Generally, women are delicate, consider more factors, and tend to be conservative and cautious, making it difficult to choose. Men, on the other hand, behave more boldly and actively, bravely and adventurously. As a result, male travelers are more likely to participate in shared parking activities.

Generally, young people have a strong curiosity about the outside world and are willing to try new things. They are more direct, impulsive, and adventurous, so they are more likely to participate in shared parking activities. Older travelers are more experienced and have more factors to consider, so they do not easily accept the new model of shared parking spaces.

As travelers are affected by external factors such as work, family, and weather, it can lead to changes in their moods, feelings, and preferences. In particular, changes in mood have a greater impact on travelers. When they are in a good mood, they are more willing to accept shared parking activities; however, when they are in a bad mood, they are more reluctant to accept new things and less likely to participate in shared parking activities.

3.1.2. Cost of Shared Parking Spaces

The cost of shared parking spaces refers to the cost of pedestrians from the moment they start parking to the time they leave, usually in CNY/h. In general, if the cost of shared parking spaces is high, travelers will not consider it; if the cost of shared parking spaces is low or similar to the price of parking in nearby parking lots, travelers are more likely to consider it.

3.1.3. Parking Environment

If the parking lot is clean and tidy, with good lighting and good traffic facilities, travelers will feel safer and less concerned about parking problems. Conversely, if the parking lot is lacking in all aspects and does not meet the traveler’s psychological expectations, they are less likely to choose shared parking spaces.

3.1.4. Road Environment

The road traffic conditions around the parking lot also have a large impact on the traveler’s choice. If the surrounding roads are heavily congested, the traveler spends more time on the road, which increases the car traveler’s time cost, and the traveler is less likely to choose shared parking spaces next time. Conversely, if the traveler has a smooth ride on the roads around the parking lot, they are more likely to accept shared parking spaces next time.

3.2. Factors Influencing Parking Space Owners’ Decisions

3.2.1. Individual Attributes

Personal characteristics of the parking space owner include gender, age, personal attributes (mood, feelings, hobbies, etc.), and monthly income.

Generally, women are delicate, consider more factors, and tend to be conservative and cautious, making it difficult to choose. Men, on the other hand, behave more boldly and actively, bravely and adventurously. As a result, male owners are more likely to be willing to rent out private parking spaces.

Age also has a certain influence on the parking space rental behavior of parking space owners. Older owners with more driving experience may encounter more difficult parking problems and are more able to understand the difficulty of finding a parking space, so they are more likely to be willing to share theirs. People with a lower driving age, on the other hand, have less experience in parking and do not have a deep understanding of the difficulties encountered when parking out. In addition, younger people have just entered society with limited living conditions and most cannot afford to own cars or private parking spaces, whereas older people’s careers are generally stable and have a good standard of living, so they can afford to own cars and private parking spaces.

Personal attributes also affect decisions about renting shared parking spaces. Some people are lively and cheerful, simple and kind, and are usually more willing to rent private parking spaces, while others are introverted and reluctant to communicate with outsiders, and are usually reluctant to try new things and refuse to rent private parking spaces.

Monthly income is also an important factor that influences the decision of parking space owners. People with relatively high monthly income have an inner desire for a high quality of life and do not care much about small profits. People with lower monthly income, who want more income, are more likely to rent out.

3.2.2. Rental Prices

In general, if the rental price is low, the parking space owners are not satisfied with the rental price and are not willing to rent out the private spaces; when the rental price is too high, the car travelers may refuse to reserve the spaces and go elsewhere to park.

3.2.3. Parking Space Management Level

If the parking lot has a good management mode, and the management personnel are very strict and responsible for the parking lot, this will bring a sense of security and satisfaction to the parking space owners and car travelers. On the contrary, lax management of parking spaces in parking lots will lead to confusion in the district, which will create greater safety risks for both vehicles and pedestrians, and parking space owners are not willing to rent out private parking spaces.

3.2.4. The Quality of Travelers

The quality of travelers is a very important factor for parking space owners. If a traveler is of good quality, can park reasonably at the specific location, and leave within the reservation time, this will encourage more space owners to rent out. Conversely, if a traveler is of poor quality and not only takes up other people’s parking spaces but also litters and spits, this will make the owner reluctant to rent out.

3.2.5. Number of Parking Spaces for Rent

If there are many owners renting parking spaces in the neighborhood, the parking space owners will be more willing to rent out. Conversely, if there are few owners renting parking spaces, they are less likely to rent out.

4. Data Processing and Analysis

4.1. Survey Design

The survey method used a combination of SP and RP questionnaire. From 18 March to 24 March 2019, an RP and SP questionnaire survey was conducted in Xinhuangcheng District, Nanchang City, China (Figure 4). The community is located around the Shengjin Pagoda scenic spot, surrounded by a large number of residential areas. The daily traffic involves a large number of people and a large amount of traffic flow, and the parking problem is very serious.

The total sample of this survey questionnaire is 101, comprising 97 valid samples and 4 invalid samples. One study [44] has shown that a survey sample of about 100 is representative if the sampling is reasonable. By solving the gradient vector and Hessian matrix of the unknown parameters, and then using the NR (Newton-Raphson) method or the DGP (Davidon-Fletcher-Powell) method, the sample size that meets the accuracy requirements can be obtained after several iterations. Among them, there were 49 males and 48 females, and the ratio of males to females was close to 1:1, which was consistent with the statistical characteristics.

By setting the relative scenarios, the questionnaire was uniformly distributed online due to the pandemic. The specific contents include the personal characteristics of parking space owners (gender, age, personal hobbies and monthly income, etc.), time slots for renting parking spaces, external factors, and the change in rental prices (see Supplementary Materials File S1 for survey contents). The detailed survey questions and the statistical results of the survey data are listed in

Table 1. Survey statistics of the respondents’ personal characteristics and choice behaviors.

Serial Number	Survey Content	Options	Number of Respondents	Percentage
1	Gender	Male	49	51.00%
		Female	48	49.00%
2	Age	18–25	7	7.22%
		26–35	22	22.68%
		36–45	50	51.55%
		>45	18	18.55%
3	Monthly income (CNY)	<3000	0	0%
		3000–4999	16	16.00%
		5000–6999	46	47.00%
		7000–10,000	29	30.00%
		>10,000	6	6.00%
4	Driving experience	One year or less	3	88.37%
		Two to five years	27
		Six to ten years	54
		More than ten years	13	11.63%
5	Emotional factors (Multiple choice)	Mood	66	40.50%
		Feelings	49	30.06%
		Hobbies	22	13.49%
		None	26	15.95%
6	Time slots for renting parking spaces	8:00~10:00	8	2.69%
		10:00~12:00	48	16.16%
		12:00~14:00	83	27.95%
		14:00~16:00	92	30.98%
		16:00~18:00	60	20.20%
		18:00~20:00	6	2.02%
7	Parking difficulty affect choice	Yes	64	66.00%
		No	33	34.00%
8	Influence of external factors on parking space rental	Fill in	97	18.60%
9	Nearby parking lot prices	Fill in	97	——
10	Acceptable lowest rental prices	Fill in	97	——
11	Acceptable highest rental prices	Fill in	97	——
12	Rental prices for 50% success	Fill in	97	——
13	Rental prices for 80% success	Fill in	97	——

. The first five questions belong to the RP (Revealed-Preference) survey, and the rest of the questions belong to the SP (Stated-Preference) survey. The most significant difference between the SP survey and RP survey is that the RP survey is designed to obtain objective and realistic data, while the SP survey is designed to obtain the choices made by the respondents under hypothetical conditions. The statistical results of the survey data are shown in Table 1.

4.2. Data Analysis

4.2.1. Personal Characteristics Analysis

As can be seen from Table 1, the largest number of people in this survey are in the age group of 36 to 45 years old, accounting for 51.55%. This indicates that most middle-aged people have reached a good stage of their career and can afford to own private cars. The percentage of people in the age group of 18 to 25 years old, on the other hand, is 7.22%, indicating that young people have just entered the workforce, have little savings, and cannot afford to own a private motor vehicle. Overall, the results of this survey are more in line with the age distribution of motorists in China.

The number of people with a monthly income of RMB 5000–6999 is the largest, accounting for 47%; the number of people with a monthly income of less than RMB 3000 is 0; and the number of people with a monthly income of more than RMB 10,000 is 6, accounting for 6%. This indicates that most of the people who own private cars have a medium or upper monthly income.

There is also an influence of personal characteristics on the rental choice of parking space owners. As seen in Table 1, mood has the greatest influence on parking space owners’ rental choices. Sixty-six of those surveyed believe that mood has a direct impact on their choice, followed by feelings and hobbies.

4.2.2. Analysis of External Factors

Parking space owners are also influenced by external factors when considering whether to rent a space, such as the revenue gained from renting a shared space, the level of management of the parking space, the number of owners in the parking lot who choose to rent a space, and the quality of the space users. From the survey data, it can be concluded that the respondents care most about the quality of the parking space users, which indicates that the parking space owners pay more attention to the sense of responsibility of the users.

4.2.3. Rental Price Analysis

Figure 5 shows that nearly half of the respondents think that the price charged by the nearby parking lots in their own area is 5 CNY/h, which has the highest percentage. The charge price is mainly distributed between (4, 6), and the average value of this charge price is 4.77 CNY/h based on statistics. Since the charge price of 5 CNY/h accounts for the largest proportion, it is assumed that the charge price of the surrounding parking lot is 5 CNY/h in the scenario assumption of the questionnaire survey.

As shown in Figure 6, the minimum rental price that respondents could accept was mainly concentrated between (2, 4), with a percentage of 87.6%, with 3 CNY/h being the most. The average value of the minimum rental price accepted by the respondents was 3.01 CNY/h based on the statistics.

As shown in Figure 7, the maximum rental price desired by the respondents was mainly concentrated between (6, 10), with a percentage of 85.6%. The maximum percentage of 8 CNY/h was 27.83%. The maximum rental price was 20 CNY/h, while the minimum rental price was 5 CNY/h. The average value of the maximum price that parking space owners wanted to rent out was 8.53 CNY/h based on the statistics.

As shown in Figure 8, if there is a 50% probability that the parking space can be rented successfully, most respondents would choose to rent the private parking space at a price of 5 CNY/h, and the majority of respondents would rent it at a price of 4 to 6 CNY/h. Statistically calculated, if there is a 50% probability that the parking space can be rented out successfully, the average of the respondents’ desired rental price is 5.54 CNY/h. This indicates that in order to ensure a higher rental success rate, parking space owners are willing to lower their prices appropriately to gain revenue.

As shown in Figure 9, if there is an 80% probability that the parking space can be rented successfully, most respondents would choose to rent it at a price of 4 CNY/h, and the majority of respondents would rent it at a price of 3 to 6 CNY/h. Statistically calculated, if there is an 80% probability that the parking space can be rented out successfully, the average of the respondents’ desired rental price is 4.51 CNY/h. This indicates that in order to ensure a higher rental success rate, parking space owners are willing to lower their prices appropriately to gain revenue.

5. Model Calibration and Discussion

5.1. Value Function Analysis

From the previous data analysis, it is clear that if there is an 80% probability that a parking space will be rented out successfully compared to the maximum rental price, the owner will choose to lower the price to obtain a profit. Therefore, the concavity of the value function can be examined based on the trend of the cumulative distribution curve of the owner’s change in rental price. Although the cumulative distribution curve of the owner’s rental price change is not exactly the same as the value function curve, the probability of the owner’s rental price change can be deduced from the value function. The cumulative distribution curve of the owner’s change from the desired maximum rental price to the price that has an 80% probability of guaranteeing successful rental of the space is shown in Figure 10.

The horizontal coordinate of the graph is the relative price difference between the maximum price that the space owner wants to rent and the price with 80% probability of successful rental. There are two reference points, 0 CNY/h and 6 CNY/h. A reference point of 0 CNY/h means that the maximum price the owner wants to rent and the 80% probability of successful rental are the same, which means that the owner feels the benefit when the shared parking space rental price reaches the owner’s desired price, while 6 CNY/h means that the difference between the maximum price the owner wants to rent and the 80% probability of successful rental is 6 CNY/h. This is the critical price difference that is unacceptable to the parking space owner. As can be seen from the figure, between the two reference points, this curve is concave and the space owner considers this rental price as a gain; when the price difference is greater than 6 CNY/h, this curve is convex and the space owner considers this rental price as a loss. The gaining area curve is concave and the losing area curve is convex. The results of the data analysis are consistent with the value function form of prospect theory.

5.2. Parameter Calibration of Value Function Model

For the model parameter ${\phi }_i(i=1,2,3)$, this paper used the calibration result of Kahneman and Tversky, that is, ${\phi }_i$ = 0.88 [43]. To calibrate the model parameter ${\delta }_i\left(i=1,2,3\right)$, the least-squares method was used (see Supplementary Materials File S2 for least-squares method). The calibrated results are ${\delta }_1$ = 0.154, ${\delta }_2$ = 0.205, and ${\delta }_3$ = −0.022. The relative errors calculated from the calibration results are shown in

Table 2. Relative error calculation table.

Price of Difference (CNY/h)	True Value of Cumulative Frequency (%)	Theoretical Value of Cumulative Frequency (%)	Relative Error (%)
1	15.46%	15.43%	0.25%
2	28.87%	28.39%	1.66%
3	40.21%	40.56%	−0.88%
4	37.11%	37.74%	−1.68%
5	21.65%	20.50%	5.29%
7	3.09%	2.20%	29.03%
8	5.15%	4.04%	21.63%
9	6.19%	5.77%	6.69%
10	7.22%	7.43%	−3.02%
11	8.25%	9.05%	−9.70%

.

As can be seen from Table 2, the relative error in the calibration of the value function model using the least-squares method is within 30%. According to the value of ${\delta }_i\left(i=1,2,3\right)$, the value function equation can be obtained as follows.

$$V(K)=\{\begin{array}{l}{V}_1(K)=0.154{(K-K_a)}^{0.88},\hspace{1em} 0\le K_a\le K\le K_b\\ V_2(K)=0.205{(K_c-K)}^{0.88},\hspace{1em}\hspace{1em}\hspace{1em}{K}_b\le K\le K_c\\ V_3(K)=-0.022{(K-K_c)}^{0.88},\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} K_c<K\end{array}$$

(6)

From the above formula, it can be seen that, in first two lines of Equation (6), the curve is concave and the value function is positive. In this case, a price with 80% probability of rental success is close to the maximum price at which the owner wants to rent out the parking space, and the owner feels the benefit and is willing to rent; in last line of Equation (6), the curve is convex and the value function is negative. At this time, a price with 80% probability of rental success is different from the highest price at which the space owner wants to rent, and the space owner feels loss and is not willing to rent the space. The results of the analysis are consistent with the form of the value function of prospect theory.

6. Conclusions and Recommendations

This study helps to identify the main influencing factors of decision behavior of parking space owners and car travelers in shared parking activities, and can provide theoretical guidance for the promotion and application of subsequent shared parking activities. By analyzing the survey data, the following conclusions can be drawn.

The data analysis shows that factors such as personal characteristics and behavioral habits -affect the decision behavior of parking space owners and travelers. Rental price is a key factor that influences the decision behavior of parking space owners. Different owners perceive the value of rental price differently. The rental price should be adjusted to a moderate price. The price is too high for travelers to accept, and the price is too low for parking space owners to rent.

The average price charged for parking spaces near this surveyed neighborhood is 4.77 CNY/h, the average minimum rental price acceptable to the space owner is 3.01 CNY/h, and the average maximum rental price desired is 8.53 CNY/h. Compared with the maximum rental price, if there is an 80% probability that the parking space can be rented successfully, the owner will choose to lower the price to gain revenue.

When the rental price of a shared space is close to the maximum price desired by the owner, the owner feels the benefit and is willing to rent out the private parking space. However, when the difference between the rental price and the maximum price desired by the owner is too large, the owner feels the loss and is not willing to rent out the parking space.

Most of the travelers who need parking are middle-aged, and they pay more attention to the parking experience. Therefore, operators should focus on improving the parking services and safety. When considering whether to rent a private parking space, space owners are vulnerable to external factors, such as the quality of parking space users and the level of management of the parking spaces. Therefore, the management level of parking spaces should be improved, and parking space users who do not follow the rules should be punished. However, there are limitations in this study, the survey of this paper has a small amount of data, and the total sample of this survey questionnaire is 101, with a valid sample of 97. To ensure the accuracy of the model, the amount of data in the survey sample should be expanded. This paper focuses on the analysis of rental price on the decision behavior of parking space owners. Other factors, such as the impact of travelers’ parking length on the decision behavior of owners, should be considered in future research.