Abstract
Shared parking effectively optimizes urban parking resources while making full use of private parking spaces and satisfying the growing demand for parking in large cities. However, some owners are unwilling to share private parking spaces and oppose the community in conducting shared parking projects. To promote the sharing of private parking spaces, we use a complex network evolutionary game method to depict the impact of owners’ unfavourable relationships on individuals’ decision processes in real time and explore the impact of management mechanisms on owners’ willingness to share. The results demonstrate that the EWA algorithm, which focuses on experiential learning and adaptability, is more conducive to promoting owner cooperation, whereas neighbour-avoidance conflict costs resulting from interactions between owners restrict cooperative behaviour, and a higher number of network owners is detrimental to cooperation. A platform improves the rejection rate of parking requests and overtime inconvenience cost is conducive to cooperation, but overtime probability and time window conflict cost reduce owners’ willingness to share. The government can lessen these adverse effects by adding compensation to all owners and increasing the public opinion adjustment coefficient to promote cooperative behaviour and increase the number of shared parking spaces.
Highlights
Studying the impact of owners’ relations and network topology characteristics on their propensity to share parking spaces.
The government provides subsidies to non-sharing owners to reduce neighbor-avoidance conflicts.
Compare the Fermi updating rule with the EWA algorithm and choose the better rule to update owners' strategy.
1. Introduction
The increasing number of vehicles and fierce competition for parking spaces have caused existing parking spaces to no longer meet parking demands in large urban cities [1]. A shortage of parking spaces will lead to adverse consequences owing to users’ long parking search times, which may have negative implications for the sustainable development of cities and the quality of life of residents [2,3]. Therefore, the mounting urban parking pressure needs to be solved urgently, and adding parking spaces or improving the utilization efficiency of parking spaces are effective solutions. According to the spatio-temporal differences and parking demands of different functional areas of a city, substantial idle parking spaces in residential areas can be utilized to satisfy the increasing demand for parking [4].
To address the problem of parking difficulties, shared parking is developing rapidly worldwide. The Parkme, Q-park, Mobypark, and JustPark platforms have huge parking demand every day, gathering parking users and owners who have the willingness to share private parking space, and rapidly promoting the scale development of shared parking. In shared parking environments, the behavioural decisions of owners affect their own and other owners’ interests, the relationships between owners, and community environmental safety, such as a decrease in the parking flexibility of owners, a decrease in community safety and unclear responsibility for the collision of vehicles from outside. Thus, private parking spaces need to be agreed upon by the owners’ committee to be open to the public [5,6]. Ultimately, owing to the significant number of owners opposing community sharing initiatives, the owners’ committees face difficulties in mediating adverse relationships between owners, resulting in the closure of the communities' external accessibility.
Most previous studies have primarily considered shared parking users, assuming a fixed supply of shared parking spaces, researching users’ travel behaviour or using various measures to encourage users to utilize shared parking spaces, which is followed by optimizing allocation mechanisms for optimal resource distribution [7,8]. Other research is related to the intention of two-sided users to engage in shared parking, such as the empirical analysis of users utilizing shared parking space [6,9] and the willingness of owners to share [10,11]. Some studies have conducted empirical analyses to explore the factors influencing individual owners’ willingness to share. However, none of them have focused on the impact of interpersonal relationships among community owners on their inclination to participate in shared parking, and the social dynamic relations that could influence the decision to open the community to outsiders. Therefore, based on the uncertainty in shared parking supply within residential areas, this study employs neighbour-avoidance conflict to illustrate the adverse relationships among owners, explore the neighbourhood relationship of community owners, study the impact of other owners’ sharing choices on individuals’ choice behaviours and enable owners to adjust their sharing decisions in real time.
The sharing of private parking spaces requires not only the coordination of owners but also the guidance and management of the government and the sharing platform [12]. Thus, based on the relationship between community owners, the social network, government and platform craft policies guided by the determinants of owners’ willingness to share parking, providing more idle parking space, which can alleviate the issue of uneven parking supply and demand.
2. Literature review
In this section, a systematic review of shared parking research is conducted to better understand the current development status of shared parking. We aim to alleviate the problem of parking resource constraints from a methodological perspective of parking allocation optimization models (Section 2.2) and parking management policies (Section 2.3). This is followed by an analysis of the influencing factors and parking space sharing behaviours (Section 2.4). Based on the above research, we derived the research gap and contribution (Section 2.5). A flowchart of the literature review is presented in Fig. 1.
The flowchart of the literature review.
2.1. Systematic literature review
A systematic review was conducted using the Web of Science database to obtain shared parking research. Employing specific keywords yielded 3102 search results, comprising 2666 journal articles, 348 conference papers and 19 editorials. By analysing publications from 2010 to 2023, 29 journal articles out of the initial 3102 search results were retained. Furthermore, the research focus in each cluster was revealed intuitively via keyword cluster analysis of the remaining results of the 29 papers. The systematic review framework and content are shown in Fig. 2. The development process of shared parking is revealed, and the diversification of periodical types and trends in interdisciplinary research is highlighted. A comparison of the research content and method is presented in Table 1.
The systematic review framework.
Brief description of the literature.
| Field | Research paper | Method | Result |
|---|---|---|---|
| Parking demand and supply matching | Ma and Zhang [13] | Traffic flow analysis | Dynamic parking and ridesharing fees improve traffic flow and system performance |
| Tang et al. [28] | Lagrangian relaxation algorithm | High computational efficiency and accuracy in addressing the shared parking problem | |
| Radvand et al. [20] | System of ordinary differential equations | Dynamic time-based tolling and parking provision optimize parking management for automated vehicles | |
| Parking management methods and policies | Kim et al. [22] | Alternating direction method of multipliers (ADMM) | ADMM excels in balancing parking demand and reducing parking expenses |
| Han et al. [23] | Joint model design and simulation | Shared parking increases utilization and profits | |
| Bao and Ng [25] | Online experiments | Tradable parking permit schemes are effective; environmental consciousness boosts their effectiveness | |
| Parking space sharing behaviour | Zhang et al. [11] | CART models | Owners' self-use behaviour etc. influences sharing willingness |
| Lai et al. [26] | New model and stable exchange scheme | Trade network theory optimizes welfare in shared parking | |
| Yan et al. [29] | Multinomial logit model including cumulative prospect | Sociodemographic characteristics, context variables, revenues and psychological concerns are all important factors |
| Field | Research paper | Method | Result |
|---|---|---|---|
| Parking demand and supply matching | Ma and Zhang [13] | Traffic flow analysis | Dynamic parking and ridesharing fees improve traffic flow and system performance |
| Tang et al. [28] | Lagrangian relaxation algorithm | High computational efficiency and accuracy in addressing the shared parking problem | |
| Radvand et al. [20] | System of ordinary differential equations | Dynamic time-based tolling and parking provision optimize parking management for automated vehicles | |
| Parking management methods and policies | Kim et al. [22] | Alternating direction method of multipliers (ADMM) | ADMM excels in balancing parking demand and reducing parking expenses |
| Han et al. [23] | Joint model design and simulation | Shared parking increases utilization and profits | |
| Bao and Ng [25] | Online experiments | Tradable parking permit schemes are effective; environmental consciousness boosts their effectiveness | |
| Parking space sharing behaviour | Zhang et al. [11] | CART models | Owners' self-use behaviour etc. influences sharing willingness |
| Lai et al. [26] | New model and stable exchange scheme | Trade network theory optimizes welfare in shared parking | |
| Yan et al. [29] | Multinomial logit model including cumulative prospect | Sociodemographic characteristics, context variables, revenues and psychological concerns are all important factors |
Brief description of the literature.
| Field | Research paper | Method | Result |
|---|---|---|---|
| Parking demand and supply matching | Ma and Zhang [13] | Traffic flow analysis | Dynamic parking and ridesharing fees improve traffic flow and system performance |
| Tang et al. [28] | Lagrangian relaxation algorithm | High computational efficiency and accuracy in addressing the shared parking problem | |
| Radvand et al. [20] | System of ordinary differential equations | Dynamic time-based tolling and parking provision optimize parking management for automated vehicles | |
| Parking management methods and policies | Kim et al. [22] | Alternating direction method of multipliers (ADMM) | ADMM excels in balancing parking demand and reducing parking expenses |
| Han et al. [23] | Joint model design and simulation | Shared parking increases utilization and profits | |
| Bao and Ng [25] | Online experiments | Tradable parking permit schemes are effective; environmental consciousness boosts their effectiveness | |
| Parking space sharing behaviour | Zhang et al. [11] | CART models | Owners' self-use behaviour etc. influences sharing willingness |
| Lai et al. [26] | New model and stable exchange scheme | Trade network theory optimizes welfare in shared parking | |
| Yan et al. [29] | Multinomial logit model including cumulative prospect | Sociodemographic characteristics, context variables, revenues and psychological concerns are all important factors |
| Field | Research paper | Method | Result |
|---|---|---|---|
| Parking demand and supply matching | Ma and Zhang [13] | Traffic flow analysis | Dynamic parking and ridesharing fees improve traffic flow and system performance |
| Tang et al. [28] | Lagrangian relaxation algorithm | High computational efficiency and accuracy in addressing the shared parking problem | |
| Radvand et al. [20] | System of ordinary differential equations | Dynamic time-based tolling and parking provision optimize parking management for automated vehicles | |
| Parking management methods and policies | Kim et al. [22] | Alternating direction method of multipliers (ADMM) | ADMM excels in balancing parking demand and reducing parking expenses |
| Han et al. [23] | Joint model design and simulation | Shared parking increases utilization and profits | |
| Bao and Ng [25] | Online experiments | Tradable parking permit schemes are effective; environmental consciousness boosts their effectiveness | |
| Parking space sharing behaviour | Zhang et al. [11] | CART models | Owners' self-use behaviour etc. influences sharing willingness |
| Lai et al. [26] | New model and stable exchange scheme | Trade network theory optimizes welfare in shared parking | |
| Yan et al. [29] | Multinomial logit model including cumulative prospect | Sociodemographic characteristics, context variables, revenues and psychological concerns are all important factors |
2.2. Parking demand and supply matching
Owing to the disparity between parking demand and supply, parking issues can be improved through demand management and technological innovation [13]. Research has indicated that parking demand fluctuates over time, demonstrating different states across various temporal and spatial scales. Specifically, its variability exhibits daily cyclical and seasonal changes and notable spatio-temporal heterogeneity [14]. Therefore, a dynamic or differentiated management method is essential for adjusting parking supply and demand.
To reduce parking users’ travel time in searching for a parking space and achieve more effective systematic optimization of urban shared parking resource allocation, the intelligent parking reservation mechanism is a plausible method for adjusting parking demand. Parking reservation systems not only influence users’ travel behaviour but also reduce exhaust emissions [15,16]. Shared parking services need to optimally allocate capacities for reserved and temporary users, and parking space reservation policies can curtail the excess time spent by parking users within the system [17,18]. However, early arrival and late driver departure may lead to service failure of the reservation system. The uncertain parking time can be transformed into a reservation model with a given parking arrival/departure time distribution, which can maximize the parking utilization rate and align more closely with the actual demand [3]. With the rapid advancement in autonomous vehicles, urban traffic and parking are poised for a revolution [19]. Shared self-driving cars can alleviate the high parking demand, with flexibility in parking location selection despite their low market penetration rate [20].
Most of the research primarily matches parking resources from the perspective of parking space users. The scarce literature has been devoted to considering the uncertainty in shared parking supply, and there is a lack of extensive examination of the reasons behind the small scale of private parking supply, specifically the influence of complex neighbourhood relations on owners’ willingness to share.
2.3. Parking management methods and policies
Sustainable transport typically requires a broad spectrum of policy measures, and the sharing travel economy contributes significantly to social, environmental and economic impacts. Therefore, parking management policies can optimize the alignment of limited parking resources with supply and demand [21]. The alternating direction method of multipliers (ADMM) can concurrently minimize the user's parking cost and balance parking demand across multiple private and public parking lots [22]. Different management strategies cater to diverse parking objectives. By considering the fragmented time availability of parking spaces in residential areas, a shared parking decision model can enhance both the utilization rate of parking facilities and the profits of sharing platforms [23].
It is necessary to consider the balance between social equity and interests in the implementation of parking policies [24]. For instance, in high-density cities with parking constraints, parking permits can ease the friction between the supply and demand for parking spaces. When shared transportation modes are restricted, tradable parking permit schemes emerge as an effective transportation demand management strategy [25].
Different parking management strategies vary in their objectives. Existing parking policies literature focuses on the balance of supply and demand and fairness in parking, hardly discussing the adverse effects of property owners sharing parking spaces with other non-sharing owners.
2.4. Parking space sharing behaviour
Current parking management policies predominantly focus on enhancing the utilization rate of parking spaces by optimizing allocation mechanisms. Few studies have focused on maximizing the use of idle parking spaces to increase parking supply. Private residential parking spaces offer considerable potential, yet shared parking requires the approval of residents and the cooperation of property management agencies [26]. Therefore, finding the main factors influencing parking space owners’ willingness to share is critical to increasing the availability of shared parking spaces. The results obtained from the willingness of private residential parking space owners to be analysed by two classification and regression trees (CART) show that the parking demand, the physical characteristics of the location and the previous month's rent significantly influenced their willingness to share [11]. Furthermore, the family environment and intra-family interactions such as age, leadership personality, family structure and financial management all influence the decision to share parking spaces [27].
Parking management policies influence residents’ willingness to share. Thus, policymakers must understand the acceptance level of shared parking by owners, the uncertainty of demand and income, and the perceived psychological value of diverse users.
2.5. Research gap and contributions
Most previous research has empirically studied the willingness of parking supply and demand parties to participate in shared parking projects [6,10], but none of them have considered that the community owner relationship can also affect owners' willingness to share private parking spaces [3,5]. Moreover, most complex networks use the Fermi updating rule to update the participant strategy, without considering that the participants are individuals with learning abilities. Finally, parking management policies can alleviate the contradiction between parking supply and demand, but mostly consider parking allocation management, increasing emerging travelling modes and fairness; there is a lack of research related to alleviating the negative impacts of public opinion from the perspectives of management.
In light of the aforementioned research gaps, this study makes new contributions are as follows:
The complex network representing the dynamic social interactions among community owners is delineated. We study the impact of owners’ relations and network topology characteristics on their propensity to share parking spaces.
The sway of non-shared parking space owners’ public opinion on shared parking space owners is considered, as well as the influence of management measures on the shared parking willingness of all community owners. The government subsidize all owners and provides subsidizes to non-sharing owners to reduce neighbour-avoidance conflicts.
The EWA algorithm considers the owner's experience and learning, which can better simulate individuals updating their strategies in a community network and promoting cooperative behaviour.
3. Evolutionary game model for community owners
3.1. Model assumption
In the context of the supply being far less than the demand, the more available parking resources, the better. Community owners can be divided into two groups: shared owners and non-shared owners. Assume that the owners in the community are homogeneous, that is, each owner has the same perceived value for rent. Besides, each owner corresponds to one parking space for one household. Therefore, the strategic sets of owners are shared parking and non-shared parking. The notations for the models are listed in Table 2. The following hypotheses regarding owner revenues are proposed:
H1: When a community owner decides to share private parking space, the rent paid by the shared parking platform to the owners is p hourly, and the platform rental time is h hours. To stimulate the growth of the shared parking market, government departments grant S subsidies to shared owners.
H2: Parking users must make reservations in advance via the platform to use shared spaces. It is assumed that the utility of the shared parking spaces used by owners is B, the rejection rate of parking requests is |$\varphi $| and the range of rejection rate is |$\varphi \in [0,1)$|. It is noted that owners of shared parking spaces enjoy priority in arranging parking requests on the shared platform; that is, the platform gives priority to the parking reservation requests of the shared-space owners, so in this situation, φ = 0. When parking demand exceeds the number of available spaces, the parking requests of non-shared parking owners may be rejected, incurring a disappointment cost represented by R.
H3: The inclusion of outsiders introduces security risks into the community, resulting in security costs imposed on the owners. Considering that shared parking spaces can potentially generate negative externalities, the endeavour to maintain a secure environment exclusive to owners’ mobility may result in public opinion pressure from non-sharing owners. This pressure could lead to distress and neighbour-avoidance conflict costs labelled |${\hat{\delta }}_{\rm{r}}$| for shared parking owners. To boost the growth of the shared parking market and alleviate potential concerns and burdens on shared parking platforms, the government proactively assumes responsibility for compensating for non-shared owners’ losses. This compensation is delivered at the subsidy rate of θ, which is within the range of θ∈[0,1]; non-shared owners receive compensation θS.
H4: Individuals utilizing parking spaces face the risk of exceeding the reservation time, and parking overtime probability is assumed to be β. Furthermore, when the parking time exceeds the reservation time, the time window conflict cost caused by overtime is ρr. Generally, parking users overtime could necessitate shared parking owners to occupy the parking spaces of other owners or resort to public parking areas, causing inconvenience to other non-shared parking owners, and the cost of overtime inconvenience is denoted as ρe.
Notation of the model.
| Parameter | Description | Unit |
|---|---|---|
| p | Rent paid by the platform | CNY/h |
| h | Platform rental time | h |
| B | Utility of using shared parking spaces | CNY |
| φ | Rejection rate of parking requests, |$\varphi \in [0,1]$| | |
| R | Disappointment cost | CNY |
| θ | Rate subsidies given to non-shared owners, |$\theta \in [0,1]$| | |
| S | Government subsidies to community owners | CNY |
| |${\hat{\delta }}_{\rm{e}}$|, |${\delta }_{\rm{e}}$| | Security risks cost of evolutionary game and complex network evolutionary game | CNY |
| |${\hat{\delta }}_{\rm{r}}$|, |${\delta }_{\rm{r}}$| | Neighbour-avoidance conflict cost in evolutionary game and complex network evolutionary game | CNY |
| ρr | Time window conflict cost | CNY |
| ρe | Overtime inconvenience cost | CNY |
| ω | Public opinion adjustment coefficient, |$\omega \in [0,1]$| | |
| β | Overtime probability, |$\beta \in [0,1]$| | |
| α | Initial proportion shared owners in complex network evolutionary game, |$\alpha \in [0,1]$| | |
| x | Proportion of owners in group A willing to share in evolutionary game, |$x \in [0,1]$| | |
| |$y$| | Proportion of owners in group B willing to share in evolutionary game, |$y \in [0,1]$| |
| Parameter | Description | Unit |
|---|---|---|
| p | Rent paid by the platform | CNY/h |
| h | Platform rental time | h |
| B | Utility of using shared parking spaces | CNY |
| φ | Rejection rate of parking requests, |$\varphi \in [0,1]$| | |
| R | Disappointment cost | CNY |
| θ | Rate subsidies given to non-shared owners, |$\theta \in [0,1]$| | |
| S | Government subsidies to community owners | CNY |
| |${\hat{\delta }}_{\rm{e}}$|, |${\delta }_{\rm{e}}$| | Security risks cost of evolutionary game and complex network evolutionary game | CNY |
| |${\hat{\delta }}_{\rm{r}}$|, |${\delta }_{\rm{r}}$| | Neighbour-avoidance conflict cost in evolutionary game and complex network evolutionary game | CNY |
| ρr | Time window conflict cost | CNY |
| ρe | Overtime inconvenience cost | CNY |
| ω | Public opinion adjustment coefficient, |$\omega \in [0,1]$| | |
| β | Overtime probability, |$\beta \in [0,1]$| | |
| α | Initial proportion shared owners in complex network evolutionary game, |$\alpha \in [0,1]$| | |
| x | Proportion of owners in group A willing to share in evolutionary game, |$x \in [0,1]$| | |
| |$y$| | Proportion of owners in group B willing to share in evolutionary game, |$y \in [0,1]$| |
Notation of the model.
| Parameter | Description | Unit |
|---|---|---|
| p | Rent paid by the platform | CNY/h |
| h | Platform rental time | h |
| B | Utility of using shared parking spaces | CNY |
| φ | Rejection rate of parking requests, |$\varphi \in [0,1]$| | |
| R | Disappointment cost | CNY |
| θ | Rate subsidies given to non-shared owners, |$\theta \in [0,1]$| | |
| S | Government subsidies to community owners | CNY |
| |${\hat{\delta }}_{\rm{e}}$|, |${\delta }_{\rm{e}}$| | Security risks cost of evolutionary game and complex network evolutionary game | CNY |
| |${\hat{\delta }}_{\rm{r}}$|, |${\delta }_{\rm{r}}$| | Neighbour-avoidance conflict cost in evolutionary game and complex network evolutionary game | CNY |
| ρr | Time window conflict cost | CNY |
| ρe | Overtime inconvenience cost | CNY |
| ω | Public opinion adjustment coefficient, |$\omega \in [0,1]$| | |
| β | Overtime probability, |$\beta \in [0,1]$| | |
| α | Initial proportion shared owners in complex network evolutionary game, |$\alpha \in [0,1]$| | |
| x | Proportion of owners in group A willing to share in evolutionary game, |$x \in [0,1]$| | |
| |$y$| | Proportion of owners in group B willing to share in evolutionary game, |$y \in [0,1]$| |
| Parameter | Description | Unit |
|---|---|---|
| p | Rent paid by the platform | CNY/h |
| h | Platform rental time | h |
| B | Utility of using shared parking spaces | CNY |
| φ | Rejection rate of parking requests, |$\varphi \in [0,1]$| | |
| R | Disappointment cost | CNY |
| θ | Rate subsidies given to non-shared owners, |$\theta \in [0,1]$| | |
| S | Government subsidies to community owners | CNY |
| |${\hat{\delta }}_{\rm{e}}$|, |${\delta }_{\rm{e}}$| | Security risks cost of evolutionary game and complex network evolutionary game | CNY |
| |${\hat{\delta }}_{\rm{r}}$|, |${\delta }_{\rm{r}}$| | Neighbour-avoidance conflict cost in evolutionary game and complex network evolutionary game | CNY |
| ρr | Time window conflict cost | CNY |
| ρe | Overtime inconvenience cost | CNY |
| ω | Public opinion adjustment coefficient, |$\omega \in [0,1]$| | |
| β | Overtime probability, |$\beta \in [0,1]$| | |
| α | Initial proportion shared owners in complex network evolutionary game, |$\alpha \in [0,1]$| | |
| x | Proportion of owners in group A willing to share in evolutionary game, |$x \in [0,1]$| | |
| |$y$| | Proportion of owners in group B willing to share in evolutionary game, |$y \in [0,1]$| |
The evolutionary mechanism of community owner parking space sharing is illustrated in Fig. 3.
Evolution mechanism of community owners' sharing parking under government subsidy.
Table 3 presents the payoff matrix for owners sharing parking spaces, where |${V}_{\rm{e}} = (1 - \varphi )B - \varphi R$|.
Sharing parking payoff matrix.
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|, |${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S$|, |${V}_{\rm{e}} + \theta S$|) |
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|, |${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S$|, |${V}_{\rm{e}} + \theta S$|) |
Sharing parking payoff matrix.
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|, |${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S$|, |${V}_{\rm{e}} + \theta S$|) |
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|, |${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \theta S - \beta {\rho }_{\rm{e}} - {\hat{\delta }}_{\rm{e}}$|, |$B + ph + S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S$|, |${V}_{\rm{e}} + \theta S$|) |
3.2. Replication of dynamic equations
Referring to the game payoff matrix presented in Table 3, the expected payoffs when owners choose shared and non-shared strategies, respectively, are as follows:
Given |${G}_{\rm{u}} = B + ph + (1 - \theta )S - \beta {\rho }_{\rm{r}} - {\hat{\delta }}_{\rm{r}} - {V}_{\rm{e}}$|. Hence, the expected payoff for owner A when choosing to share parking spaces or not with probabilities |$x$| and |$1 - x$|, respectively, is as follows:
Similarly, the expected payoff corresponding to owner B’s strategic decisions are as follows:
The expected payoff for owner B under the two strategies described above is:
The stability of an owner's decision is examined using a replicator dynamics equation, which denotes the rate of change in the probability of owner A adopting a sharing strategy. Then the replicator dynamics equations for owners A and B when they opt for a sharing strategy are as follows:
3.3. Stability analysis of the evolutionary game model
Setting |$\frac{{{\rm{d}}x}}{{{\rm{d}}t}} = 0$|, |$\frac{{{\rm{d}}y}}{{{\rm{d}}t}} = 0$| to yields |$x_1^* = 0$|, |$x_2^* = 1$|, |${y}^* = \frac{{ - {G}_u}}{{{{\hat{\delta }}}_{\rm{r}} + \beta {\rho }_{\rm{e}} + {{\hat{\delta }}}_{\rm{e}}}}$|; |$y_1^* = 0$|, |$y_2^* = 1$|, |${x}^* = \frac{{ - {G}_u}}{{{{\hat{\delta }}}_{\rm{r}} + \beta {\rho }_{\rm{e}} + {{\hat{\delta }}}_{\rm{e}}}}$|, five partial equilibrium points are expressed as: (0,0), (0,1), (1,0), (1,1) and (x*, y*), respectively.
The Jacobian matrix of the system [30], derived from dynamic Equations (7) and (8), is given as follows:
To analyse the local stability of the system's equilibrium point, the determinant of the matrix (10) and trace (11) of the matrix can be derived from the Jacobian matrix (9), are as follows:
The local stability of the equilibrium points can be assessed using a Jacobian matrix, where an equilibrium point is deemed an evolutionarily stable strategy (ESS) of the system if and only if the conditions of |${\rm{Det}}{\boldsymbol{J}} > 0$| and trJ < 0 are satisfied [31]. Therefore, upon substituting the five partial equilibrium points into Equations (10) and (11), it is revealed that the equilibrium points (0,1) and (1,0) correspond to trJ > 0, and (x*, y*) yield DetJ = 0. Consequently, the equilibrium points (0,1), (1,0) and (x*, y*) are unstable solutions within the interval. By evaluating the classification of the logical relationships among the model variables, two different scenarios were obtained:
Scenario 1: In the shared parking market, when the difference between the aggregate of parking utility expectation, total rent and government subsidies received by the shared parking owner and the time window conflict cost expectation and neighbourhood conflict cost is smaller than the difference between the compensation amount of the owners of non-shared spaces and the disappointment cost expectation of not using shared spaces, that is, |$\varphi B + ph + S - {\hat{\delta }}_{\rm{r}} - \beta {\rho }_{\rm{r}} > \theta S - \varphi R$|, the system's stable solution is (0,0).
Scenario 2: In contrast to Scenario 1, the stable solution is (1,1) when |$\varphi B + ph + S - {\hat{\delta }}_{\rm{r}} - \beta {\rho }_{\rm{r}} < \theta S - \varphi R$|.
Consequently, the difference between the total revenues of shared and non-shared owners determines the evolutionarily stable strategy of the system. The preceding ‘owner-owner’ evolutionary game model within the community illuminates the decision-making process related to sharing from the owners’ perspective but cannot account for subject variability. Nevertheless, the relationships among community owners have pronounced topological statistical characteristics, and shared parking behaviour is a game subject to inter-individual synergy and interaction. Therefore, this study revisits the evolutionary game model to explore these relationships better and address the limitations of the game's evolutionary processes. It considers the potential influence of interindividual interactions on participants and introduces complex networks to better represent the interaction law among game subjects, thereby refining the evolution law of the strategies of both game stakeholders.
4. Complex network evolutionary game model for community owners
4.1. Community ‘owner-owner’ network structure
In this study, the connections between owners show a small-world feature [32]. We use a complex network evolutionary game model to analyse the decision-making process related to sharing among owners. A social network composed of community owners is represented by G = (V, E), where |$V = \{ {v}_1,\ {v}_2,\ \cdot \cdot \cdot ,\ {v}_N\} $| representing the set of all nodes in the network. Each node corresponds to an owner, and |$E = \{ {e}_1,\ {e}_2,\ \cdot \cdot \cdot ,\ {e}_m\} $| represents the set of edges between all nodes, i.e. the direct connections among owners. It is assumed that all network connections are undirected. If a connection exists between owner i and owner j, then |$({v}_i,{v}_j) = 1$| applies, otherwise |$({v}_i,{v}_j) = 0$|. The total number of an owner i’s edges in the network is referred to as the degree of the owner, and the degree of owner vi is symbolized as di.
4.2. Community network game model
In a complex network evolutionary game, two entities are involved: community owners and other community owners. Based on the foregoing analysis, the following hypotheses are proposed:
H5: This cost escalates with an increasing number of non-shared parking space owners, and the unit cost of neighbour-avoidance conflict that non-shared parking imposes on shared parking owners is represented by δr. Moreover, parking spaces shared by community owners can detrimentally affect community traffic and the environment, manifested as waiting in queues to exit garages or random parking spaces. The safety risk cost brought about by space sharing for non-parking individuals is δe.
H6: Given the strong negative externality of parking space sharing, public opinion pressure from non-sharing parking space owners influences decision-making processes. To alleviate this pressure, government departments provide compensation to non-shared owners. The public opinion adjustment coefficient |$\omega $| correlates government compensation with public opinion pressure.
Table 3 only considers the strategy evolution of fixed neighbour-avoidance conflict costs between owner groups, but the neighbour-avoidance conflict costs between owners are related to the number of owners who do not want to participate in sharing, which establishes the game matrix as shown in Table 4, where |${V}_{\rm{r}} = (1 - \omega \theta S)(1 - \alpha )N{\delta }_{\rm{r}}$|.
Sharing parking payoff matrix.
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}},\ {V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S,\ {V}_{\rm{e}} + \theta S$|) |
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}},\ {V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S,\ {V}_{\rm{e}} + \theta S$|) |
Sharing parking payoff matrix.
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}},\ {V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S,\ {V}_{\rm{e}} + \theta S$|) |
| Owner A | Owner B | |
|---|---|---|
| Shared space | Non-shared space | |
| Shared space | (|$B + ph + S - \beta {\rho }_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}}$|) | (|$B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}},\ {V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}}$|) |
| Non-shared space | (|${V}_{\rm{e}} + \omega \theta S - \beta {\rho }_{\rm{e}} - \alpha N{\delta }_{\rm{e}} + {V}_{\rm{r}},\ B + ph + S - \beta {\rho }_{\rm{r}} - {V}_{\rm{r}}$|) | (|${V}_{\rm{e}} + \theta S,\ {V}_{\rm{e}} + \theta S$|) |
4.3. The strategy updating rules
At each evolutionary step, the cumulative sum of the individual game payoffs of any given owner engages in a game with all neighbouring owners within its game radius r, represented as follows:
where Ui represents the total revenue of owner i in the current round of the game, xi refers to the strategy vectors |${(0,1)}^ {\rm{T}}$| and |${(1,0)}^ {\rm{T}}$|, |${x}_i = {(1,0)}^{\rm{T}}$| represents owner i opting for the shared parking space strategy and |${{\boldsymbol{x}}}_i = {(0,1)}^{\rm{T}}$| denotes the choice of the non-shared parking space strategy. The owner's payoff matrix M is represented as indicated in Table 4. The set of owner i’s neighbours is denoted by Ni, and j ∈ Ni indicates that an owner j is a neighbour of owner i.
4.3.1. Empirically weighted attraction learning algorithm
With the ability to adapt and learn, owners can adjust their strategies based on strategies and revenues from past games. Therefore, the owner strategy updating rule is computed using an experience-weighted attraction (EWA) learning algorithm that considers past experiences and information learning [33].
The probability of choosing a strategy w in the EWA algorithm depends on the attraction index |$A_i^w$|. The updated equation of strategy w to owner i in period t is defined as:
where ψ symbolizes the discount factor for the attraction index from the preceding period. As the value of ψ increases, the influence of the prior period's attraction index on the current period intensifies. The parameter ϕ, with the range of ϕ ∈ [0,1], signifies the subjective weight assigned by the learner to the revenue of the unchosen strategy. |${U}_i(s_i^w)$| corresponds to the cumulative revenue acquired from the t-th round of the game involving owner i and all neighbouring owners. I(·) stands for the indicator function, and N(t) represents the experience weight at the t-th round. The expressions for the experience weight and the indicator function are presented as follows:
where |$\mu$| signifies the discount factor applied to the experience weights. When the strategy w is chosen by owner i during the period t, that is, |$s_i^w = {s}_i(t)$|, the strategy is reinforced and the payoff value is assigned a weight of 1. Conversely, if w failed to be selected, i.e. |$s_i^w \ne {s}_i(t)$|, the allocated weight at this juncture would be 0.
Ultimately, the attractiveness of the strategy is transformed into the probability of it being chosen by the owner in the next period using a Logit function, where λ represents the sensitivity to the strategy attraction value and m indicates the count of viable strategies [33,34].
4.3.2. Fermi dynamic updating rule
The updating rules of the owners’ strategies may affect the simulation results [35]. If the community publishes sharing information through imperfect channels or lags in updating information, it may prevent owners from effectively observing the historical choices of all the owners in the network. Thus, we comparatively analysed the Fermi updating rule and EWA algorithm. Initially, each owner adheres to a distinct strategy, and the proportion of owners within the network that adopt a shared parking strategy is denoted by α. During the t period, the owner i updates the strategy according to Fermi dynamics by observing the strategy and income of the owner and their neighbours during the t−1 period:
where Ui represents the revenue of owner i adopting strategy si, while Uj denotes the revenue of neighbour j adopting strategy sj. The parameter k measures the intensity of individual irrational strategies. Additionally, k stands for system noise (k > 0), and if k approaches infinity it signifies that the impact of environmental disturbances on the strategy update of network subjects is significantly severe. Conversely, when k approaches zero, the impact of environmental disturbances on the strategy update of network subjects is rather minimal.
5. Model testing and simulation analysis
5.1. Parameter initialization setting
The mutual influence of owners’ strategic behaviours and the resulting stable state of the network are examined. Parameter values in the EWA algorithm are ψ = 0.5, ϕ = 0.5, |$\mu$|= 0.5 and λ = 0.5 [36]. The detailed parameters are illustrated in Table 5. To ensure the robustness of the simulation results, the simulation was repeated 300 times and then averaged. In addition, after 300 evolution rounds, some data points were averaged by taking 80−100 times of results.
Moel parameter value.
| Variable | Mean | Value | Source |
|---|---|---|---|
| α | Initial proportion of shared owners | 0.2 | [7] |
| N | Network size | 500 | [3] |
| h | Platform rental time | 7 | [37] |
| p | Rent | 2 | [38] |
| B | Parking utility | 6 | |
| R | Disappointment cost | 3 | |
| φ | Rejection rate | 0.2 | [37] |
| ω | Public opinion adjustment coefficient | 0.1 | |
| δr | Neighbour-avoidance conflict cost | 0.043 | |
| δe | Security risks cost | 0.02 | |
| β | Overtime probability | 0.2 | [39] |
| ρr | Time window conflict cost | 8 | [40] |
| ρe | Overtime inconvenience cost | 6 | |
| S | Subsidy | 2 | |
| θ | Subsidy compensation ratio | 0.5 |
| Variable | Mean | Value | Source |
|---|---|---|---|
| α | Initial proportion of shared owners | 0.2 | [7] |
| N | Network size | 500 | [3] |
| h | Platform rental time | 7 | [37] |
| p | Rent | 2 | [38] |
| B | Parking utility | 6 | |
| R | Disappointment cost | 3 | |
| φ | Rejection rate | 0.2 | [37] |
| ω | Public opinion adjustment coefficient | 0.1 | |
| δr | Neighbour-avoidance conflict cost | 0.043 | |
| δe | Security risks cost | 0.02 | |
| β | Overtime probability | 0.2 | [39] |
| ρr | Time window conflict cost | 8 | [40] |
| ρe | Overtime inconvenience cost | 6 | |
| S | Subsidy | 2 | |
| θ | Subsidy compensation ratio | 0.5 |
Moel parameter value.
| Variable | Mean | Value | Source |
|---|---|---|---|
| α | Initial proportion of shared owners | 0.2 | [7] |
| N | Network size | 500 | [3] |
| h | Platform rental time | 7 | [37] |
| p | Rent | 2 | [38] |
| B | Parking utility | 6 | |
| R | Disappointment cost | 3 | |
| φ | Rejection rate | 0.2 | [37] |
| ω | Public opinion adjustment coefficient | 0.1 | |
| δr | Neighbour-avoidance conflict cost | 0.043 | |
| δe | Security risks cost | 0.02 | |
| β | Overtime probability | 0.2 | [39] |
| ρr | Time window conflict cost | 8 | [40] |
| ρe | Overtime inconvenience cost | 6 | |
| S | Subsidy | 2 | |
| θ | Subsidy compensation ratio | 0.5 |
| Variable | Mean | Value | Source |
|---|---|---|---|
| α | Initial proportion of shared owners | 0.2 | [7] |
| N | Network size | 500 | [3] |
| h | Platform rental time | 7 | [37] |
| p | Rent | 2 | [38] |
| B | Parking utility | 6 | |
| R | Disappointment cost | 3 | |
| φ | Rejection rate | 0.2 | [37] |
| ω | Public opinion adjustment coefficient | 0.1 | |
| δr | Neighbour-avoidance conflict cost | 0.043 | |
| δe | Security risks cost | 0.02 | |
| β | Overtime probability | 0.2 | [39] |
| ρr | Time window conflict cost | 8 | [40] |
| ρe | Overtime inconvenience cost | 6 | |
| S | Subsidy | 2 | |
| θ | Subsidy compensation ratio | 0.5 |
5.2. Numerical simulation analysis
5.2.1. Comparison of EWA algorithm and Fermi updating rules
Fig. 4 depicts the comparison results of the superiority of the EWA algorithm and the Fermi updating rule when the network size is 100, 500 and 1000, respectively. The superiority of the EWA algorithm was not discernible when the network size was small. However, as the network size increased, the diffusion depth of the EWA algorithm increased, suggesting that the EWA algorithm, which concentrates on experience learning and adaptive capability, is more efficient than the Fermi updating rule, which solely emphasizes the cumulative revenue of the current period. A comparison of the EWA algorithm and the Fermi updating rule shows that the EWA algorithm is more conducive to owner cooperation. Therefore, the subsequent contents use the EWA algorithm to update the owner's strategy.
Comparison of EWA and Fermi on different network sizes.
5.2.2. Impact of community network characteristics on the level of cooperation
As demonstrated in Fig. 5, the level of community owners cooperation diminishes as the network size increases, and smaller average degree differences have a negligible impact on the level of owner cooperation, where the level of owner cooperation represents the proportion of owners who choose to share in the whole community. Within the same range of neighbour-avoidance conflict costs, the level of community owners cooperation progressively declined from 1 to 0 with the expansion of the network size. For instance, when the number of owners is 1000, no owners are willingness to share private parking spaces. Conversely, when the number of owners was 100, all owners were willing to share. This is attributable to the neighbour-avoidance conflict costs that shared parking owners must bear, which correlate with the number of non-shared parking owners. When the network size was 1000, no one was willing to share, even if the average degree was large. This is because as the size of the network increases, the number of non-shared parking owners increases, resulting in a significant increase in the overall neighbour-avoidance conflict costs and a decrease in the revenue of the shared parking owners, which impedes the proliferation of the community shared parking market.
Effect of network size |$N$| and average degree |$K$| on cooperation rate.
It can be observed that the average degree of owners has a minor influence on the level of community owner cooperation when the degree is small or the cost of neighbour-avoidance conflict is high. However, when the neighbour-avoidance conflict cost is low, a larger average degree can encourage owner cooperation. For instance, when the average degree K was 100, owners communicated more frequently via social media, fostering a greater willingness to share than those with a lower average degree. This is because increasing the average degree of node connectivity results in a more efficient information transfer and greater owner unity.
5.2.3. Impact of shared parking platform operation methods on the level of cooperation
1) Impact of overtime probability on the evolution of owner cooperation level
Fig. 6 shows the influence of both time window conflict cost and overtime inconvenience cost on the degree of owner cooperation under varying overtime probabilities. The horizontal axis represents the number of evolutions, whereas the vertical axis corresponds to the time window conflict cost and overtime inconvenience cost. The colour spectrum represents the strategies adopted by the owners: dark red signifies unanimous owner cooperation, dark purple indicates that all owners opt not to cooperate and the remaining colours denote a blend of strategies employed by community owners.
Effect of overtime probability |$\beta $| on cooperation rate: (a) overtime probability β = 0.2; (b) overtime probability β = 0.25; (c) overtime probability β = 0.3; (d) overtime probability β = 0.2; (e) overtime probability β = 0.25; (f) overtime probability β = 0.3.
Considering Figs. 6(d)–(f), it is surprising that the level of owner cooperation increases and accelerates the speed of cooperation evolution as the overtime inconvenience cost increases. Owners select the shared parking strategy to mitigate their losses. As evidenced by Fig. 7 and Fig. 8, an increase in overtime inconvenience cost yields a decrease in revenue for non-shared parking space owners but concurrently amplifies the revenue for shared parking space owners. Consequently, with the intensification of overtime inconvenience costs, owners prefer to opt for shared parking spaces to increase their revenue.
Effect of overtime probability |$\beta $| on non-sharing owner revenue evolution results: (a) overtime probability β = 0.2; (b) overtime probability β = 0.25; (c) overtime probability β = 0.3.
Effect of overtime probability |$\beta $| on sharing owner revenue evolution results: (a) overtime probability β = 0.2; (b) overtime probability β = 0.25; (c) overtime probability β = 0.3.
Fig. 7 and Fig. 8 illustrate that the revenue of non-shared parking owners increases with an increase in overtime probability, but the revenues for shared parking owners correspondingly decrease. For non-shared parking owners, an increase in the probability of overtime results in a decline in owner cooperation, which leads to fewer owners participating in shared parking. This reduces the likelihood of inconvenience over time, subsequently elevating the expected revenue for non-shared owners. Conversely, the aggregate inconvenience cost that shared parking owners must bear increases, thereby diminishing the revenues to community parking owners.
Fig. 7 and Fig. 8 reveal that the overtime inconvenience cost increases, with the revenue for non-shared parking owners gradually diminishing and the revenue for shared parking owners generally increasing. According to the payoff matrix, the revenue of non-shared owners exhibits an inverse relationship with the overtime inconvenience cost; that is, the higher the overtime inconvenience cost, the lower the revenues to non-shared owners. For shared parking owners, a surge in the overtime inconvenience cost results in an increase in the number of shared parking owners and a decrease in the number of non-shared owners. Consequently, the aggregate cost for shared parking owners to neighbourhood conflicts decreases, which subsequently enhances the revenues of shared parking owners.
2) Impact of shared parking platform rejection rate on the evolution of the owner cooperation level
Fig. 9 illustrates the correlation between the shared platform's rejection rate and the level of cooperation, asserting that the rejection rate can effectively promote cooperative network behaviour. As the rejection rate increases, the density of cooperators increases from 0 to 1, reaching a cooperative equilibrium state more swiftly at higher rejection rates. This is because the shared parking requests of non-shared owners are not always accommodated by the increase in rejection rates, leading to dissatisfaction for shared parking users. Establishing a priority system for satisfying parking requests can amplify the perceived parking utility of owners, thereby incentivizing them to favour shared parking.
Effect of rejection rate |$\varphi $| on cooperation rate.
When the rejection rate was zero, the cooperation level among community owners in shared parking spaces remained zero after 100 games. As the rejection rate increased, there was a corresponding increase in cooperation among community owners. The influence on shared parking is displayed until the rejection rate reaches 0.2, indicating that the shared parking platform's rejection rate can impact community owners’ strategic choices. More specifically, a lower rejection rate can undermine community owners’ willingness to share parking, causing the cooperation level to decrease to zero. However, as the rejection rate increased to 0.4, the cooperation level approached 1, prompting owners to opt for shared parking spaces.
3) Impact of platform rental parking space length on the evolution of the owner cooperation level
Fig. 10 shows the influence of varying rental and rental time on community owner cooperation levels. As indicated in Fig. 10, both the rental amount offered to owners by the shared parking platform and the rental time influence the community owners’ decision on whether to share their spaces. Therefore, longer rentals and rental time correlate, which will contribute to higher levels of cooperation.
Effect of owners' sharing parking time |$h$| on cooperation rate.
A comparison of the impacts of rentals and rental time indicates that rentals significantly influence community owners’ willingness to share. Specifically, higher rentals improve the level of community owner cooperation, bring more revenues and thus exhibit an increased willingness to share private parking spaces. However, when rentals are low, owners only see a significant increase in revenues when the platform rents private parking spaces for extended periods, the attraction of the shared space project is enhanced and the level of cooperation is improved. Similarly, as rentals increased, the rental duration that community owners willingness tended to decrease.
5.2.4. Impact of government policies on the level of cooperation
1) Impact of government subsidies on the evolution of the owner cooperation level
Fig. 11 clearly illustrates that the level of community owner cooperation correspondingly diminishes as the neighbour-avoidance conflict cost increases, converging from one to zero. Conversely, the level of cooperation among community owners gradually increases as the amount of subsidies increases.
Effect of subsidies |$S$| on cooperation rate.
At the same level of cooperation, subsidies increase responses to a decrease in the cost of neighbour-avoidance conflict, suggesting that governmental subsidies can mitigate neighbourhood conflicts among community owners, reduce public opinion pressure on non-shared parking spaces and curb the negative attitude of other owners towards shared parking spaces.
2) Impact of the public opinion adjustment coefficient on the evolution of the owner cooperation level
The impact of the interplay between neighbour-avoidance conflict cost and the public opinion adjustment coefficient on the cooperation level among community owners is shown in Fig. 12. Notably, at a given neighbour-avoidance conflict cost, a larger public opinion adjustment coefficient correlates with a higher level of cooperation among community owners.
Effect of weight coefficient |$\omega $| on cooperation rate.
As the neighbour-avoidance conflict cost increases, the cooperation level among community owners decreases correspondingly. However, the public opinion adjustment coefficient slowly decrease cooperation rate because government departments mitigate public opinion pressure by compensating non-shared owners. Additionally, a larger public opinion adjustment coefficient translates into more compensation and lower public opinion pressure for non-shared owners, thus enhancing the cooperation level among community owners.
3) Relationship between the subsidy ratio and public opinion adjustment coefficient on the cooperation level
The results in Fig. 13(a) demonstrate a positive correlation among the subsidy ratio, subsidy amount and level of cooperation among owners. As either the subsidy ratio or subsidy amount increases, the owners’ cooperation levels correspondingly increase. Once the subsidy amount exceeds 2.1 or the subsidy ratio surpasses 0.7, the cooperation level stably evolves to 1, indicating that owners are more inclined to share.
Effect of the relationship between subsidy ratio |$\theta $| and subsidies |$S$| (a) and the relationship between public opinion adjustment coefficient |$\omega $| and subsidies |$S$| (b) on the cooperation rate.
Keeping the other parameters unchanged, Fig. 13(b) presents the results of the cooperation rates of community owners under different public opinion adjustment coefficients and subsidy levels. It can be observed that the cooperation rate among owners also increases until it gradually stabilizes at 1 as the subsidy amount and public opinion adjustment coefficients increase.
Furthermore, as shown in Fig. 13(b), when the public opinion adjustment coefficient is small, the level of community owner cooperation in shared parking decreases and falls below the initial cooperation rate. In this case, the compensation provided to non-shared parking owners fails to effectively motivate them to share their parking spaces, even undermining their initial willingness to do so, leading to a decrease in network cooperation. However, as subsidy amount increased, cooperation rate began to increase. This is because an increase in the public opinion adjustment coefficient raises the compensation for non-shared parking owners, which in turn alleviates public opinion pressure. Consequently, this increases the revenue of shared parking owners and enhances their willingness to share.
When the public opinion adjustment coefficient was set to 0.13, and the government subsidy amount was 2.125, community owners generally are willing to share their parking spaces. As the subsidy amount increased, the level of cooperation among community owners approached 1 and remained stable. Hence, the willingness of community owners to share parking spaces can be improved through approaches that provide subsidies to shared parking owners and compensation for non-shared parking owners by government departments. Specifically, when the public opinion adjustment coefficient, subsidy ratio and subsidy amount are 0.13, 0.07 and 2.215, respectively, community owners demonstrate a willingness to share private parking spaces and sustain them.
6. Conclusions
6.1. Research conclusions
This study conducted a comprehensive analysis of the motivating factors that influence owners in the shared parking market, explored their underlying micro-level mechanisms and explored the interactions among community owners to select appropriate strategies through an evolutionary game model and a complex network evolutionary game model. The following conclusions are drawn:
1) Compared with the Fermi dynamic updating rules, the EWA learning strategy that focuses on experiential learning and adaptability can better promote sharing among owners. The larger network sizes are not conducive to promoting the sharing of parking spaces, whereas a higher average degree within the network positively impacts owners’ willingness to share.
2) Prioritizing parking requests from sharing owners can increase owners' willingness to share. Meanwhile, the total rent provided by the platform and the overtime inconvenience cost are positively proportional to the shared owners’ revenue, while the overtime probability and the time window conflict cost decrease shared owners’ revenue, but too high overtime inconvenience cost is detrimental to owners sharing private parking spaces long-term.
3) The government improves the public opinion adjustment coefficient, increasing the subsidy ratio and subsidy amount to increase revenues of shared owners and contribute to improving the cooperation rate. These efforts are favourable for the expansion and proliferation of the shared parking market.
6.2. Policy implications
Based on these findings, governments and platforms can take measures to mitigate owners’ negative interactions, which can lessen adverse effects and enhance support for sharing parking projects.
The property management department should immediately update and disclose the number of shared parking and non-shared parking owners within the community. Additionally, it is necessary to enhance the transparency and real-time updates of community parking sharing information, which allows the owners to stay abreast of the developments in community shared parking and adjust their strategies appropriately.
The rejection rate by the platform can impact the satisfaction of parking users, adversely affecting the shared parking platform operation and potentially leading to enduring losses. Therefore, shared parking platforms should reasonably establish rejection rates under the dual objectives of maximizing profits and optimizing the use of idle parking spaces. This not only encourages community owners to share but also reduces the loss of revenue caused by refusing parking requests. Furthermore, owing to the parking inconvenience caused by parking demand overstay in shared parking spaces, one approach to mitigate this issue is the platforms that employ reliability mechanisms or designate specific areas for overtime parking to control the risk of users exceeding their reservation time.
The government can subsidize different amounts according to owners’ willingness to increase the supply of parking spaces. Owing to its financial, human and material constraints, the government cannot persist in subsidizing shared parking projects for a long period. Therefore, the platform should undertake more tasks to develop the long-term development of the shared parking market and solve the inconvenience problems resulting from sharing by mitigating the conflict of sharing in the neighbouring relationship, parking rejection rate and overtime probability.
However, there are limitations to the complex network evolution game model that should be addressed in future research. First, this study aimed to study the willingness of community owners to participate. The dynamic change of parking demand also has an important impact on parking supply, and further research can be conducted to study the interactions between supply and demand on both sides as well as the development of the shared parking market. Second, this study focused on network games among owners, and future research should consider exploring the interactions among different roles within multilayer networks. Third, this study investigated the dynamic relationship between the network topology and owner decision-making regarding parking sharing. It failed to portray real relationships between owners. Therefore, future research could construct realistic relationships to establish a real topological network that would facilitate a more comprehensive analysis of the owners’ shared willingness. Fourth, using the questionnaire or actual case analysis to verify the model is more in line with the actual situation but also more able to highlight the effectiveness and superiority of the model.
Acknowledgements
The authors are grateful for the financial support from fundings and the Humanities and Social Science Research Foundation of China's Ministry of Education (Grant No. 20YJC630156), the Natural Science Foundation of Chongqing (Grant No. cstc2021jcyj-msxmX0482) and the Humanities and Social Science Foundation of Chongqing Education Commission (Grant Nos. 20SKGH080 and 21SKGH083).
Conflict of interest statement
The authors declare that there is no conflict of interest.
