Competition and Game of the Pre-Installed Market and Post-Installed Market of the Internet of Vehicles from the Perspective of Cooperation

Abstract

The Internet of Vehicles market is broadly divided into two parts—the pre-installed market and the post-installed market. Although they possibly have cooperative relationships, there is a competition game between them in terms of interests, and a healthy game relationship can promote the optimization of products and the overall improvement of the service level in the Internet of Vehicles market. Through the evolutionary game model, this article analyzes the dynamic game process between the pre-installed market and the post-installed market of the Internet of Vehicles, explores the various evolution trends of the Internet of Vehicles market from the perspective of cooperation, and combines the numerical simulation analysis to study the three possible evolutionary trends and corresponding steady states. The results show that, when the cooperation ratio is relatively high, both sides of the game are in the cyclical competition and game, which is the optimal competition state of the Internet of Vehicles market. On the contrary, any kind of “steady state” is unfavorable to the overall market. Therefore, all parties should be encouraged to establish a deeper level of cooperation and jointly promote the further prosperity of the Internet of Vehicles market in the process of cooperation and competition.

1. Introduction

Since the 1970s, the scale of vehicles has expanded rapidly, and vehicles have become the most important means of transportation in people’s daily lives [1]. However, with the rapid growth of vehicles, traffic congestion is also getting worse. An investigation report published by the Eno Center for Transportation revealed that the use of vehicular communication cooperation, autonomous driving, and other technologies will greatly ease urban traffic congestion [2]. Thus, the concept of the Internet of Vehicles (IoV) began to rise around the 1990s, which is conducive to reducing energy consumption and promoting sustainable development. With the promotion of governments and automobile manufacturers in some developed countries, the IoV industry has developed rapidly [3]. In 2007, six European automobile manufacturers (including BMW, DaimlerChrysler, AUDI, etc.) released the “CAR 2 CAR Communication Consortium Manifesto,” committed to actively promoting the establishment of an open European communication system standard [4]. In December 2009, the US Department of Transportation (DOT) released the “Intelligent Transportation System Standards Program Strategic Plan for 2011–2014” to provide strategic guidance for the development of the IoV in the United States and the construction of intelligent transportation systems [5]. With the vigorous promotion of all parties, according to data released by the Global System for Mobile Communications Association (GSMA), as of 2017, the market size of global IoV was approximately USD 52.5 billion, and it is expected to increase to $162.9 billion USD by 2022. The compound annual growth rate (CAGR) is 25.4%, and the penetration rate of IoV continues to increase.

According to the different providers of IoV equipment and services, most scholars divide the IoV industry chain into two sub-markets, the pre-installed market and the post-installed market [6]. Among them, the pre-installed market is mainly composed of automobile manufacturers and some on-vehicle equipment and service providers. Automobile manufacturers are closer to “cars” and focus on safety services. On-vehicle equipment and service providers are slowly infiltrating into the pre-installed market from the post-installed market [7], and have established cooperation with automobile manufacturers to promote automobile manufacturers to launch IoV systems, open up the IoV market, and gradually improve the installation rate of IoV equipment and provide services for consumers, such as GM’s Onstar, Ford’s SYNC, BMW’s iDrive, and Toyota’s G-BOOK. At the same time, the pre-installed market also reflects strong product closure. They often provide IoV equipment and services only for their own vehicles, and it is difficult to significantly increase equipment penetration. The post-installed market of IoV is mainly dominated by Telematics Service Providers (TSPs). They are a type of enterprise that was born under the users’ requirements of more intelligent, humane and professional, and are committed to improving the service level of IoV. From the perspective of market participation methods, TSPs are mainly divided into two modes: B2B and B2C. In the B2B mode, TSPs mainly provide IoV services to users by establishing a cooperative relationship with automobile manufacturers. Under the B2C mode, TSPs are directly facing users or relying on large 4S stores to promote the installation of IoV equipment. Compared with automobile manufacturers in the pre-installed market, TSPs are closer to users, can find user needs in time, and can often provide users with the in-car services that are more professional and meet user needs. Therefore, TSP have gradually occupied an important position in the IoV industry chain, playing the role of integrating various players in the industry chain [8].

In recent years, with the gradual saturation of the entire vehicle market and the decline in product sales profits, the overall efficiency of the automotive sales market is in a downward trend. The business model of the automotive industry is gradually changing from “selling products” to “serving customers,” and automobile manufacturers begin to attach importance to the profit model of obtaining profits by serving customers [9]. Therefore, although there may be cooperative relationships between the pre-installed market and the post-installed market, the two sub-markets have begun to generate more competition and games in the market share and benefit distribution of “IoV services.” Analyzing the competition between the pre-installed market and the post-installed market may ultimately lead to which kinds of market conditions, and exploring which condition is healthy competition and how to maintain healthy competition can provide a theoretical basis for promoting the healthy development of the IoV market. At the same time, it is also of great practical significance to solve automobile social problems and support the upgrading and transformation of the automobile industry.

2. Literature

In the current era of rapid development of information technology, the automotive industry and technology are gradually developing toward the direction of low-carbon emissions, information, and intelligence [10]. With the help of IoV and other technologies, vehicles have evolved from simple mechanical devices to intelligent sensors that can sense and record driving attributes and environmental conditions. As a result, vehicle safety and the experience of drivers and passengers have also been greatly improved [11,12]. In order to improve the construction of the IoV information service platform, some scholars [13,14,15] have optimized the platform and product performance in terms of technology based on the discussion of two communication technologies currently used in the IoV, C-V2X and DSRC, discussing the challenges and opportunities for resource allocations in modern vehicular network. Some scholars [16,17] have analyzed the V2V communication transmission between vehicles based on geographic location access (GLOC) from the technical aspect, optimized the vehicle networking platform and product performance, and provided technical support for the construction of IoV platform. Some scholars also researched from the perspective of the IoV information service platform architecture. Sun X. et al. [18] summarized the development status and existing problems of the IoV information service platform. The technical architecture, general functional architecture, and big data application framework are studied to build a new IoV information service platform in a big data environment. Duan Z. et al. [19] proposed a new type of traffic information coordination system based on the distributed mobile traffic information atomic service computing platform to improve the intelligence and personalization level of traffic information services and improve service quality.

With the development of related technologies and the gradual improvement of the platform architecture, IoV has been further promoted and popularized. A large number of automobile manufacturers have begun to develop IoV equipment and services [20], and scholars have also tried to study the development of IoV from the perspective of a business model. Thomas F. Golob and Amelia C. Regan [21] analyzed the information technology in the IoV information service system and found the opportunities and challenges of IoV in the field of personal travel and commercial vehicles. Baecke et al. [22] and Vaia et al. [23] used in-vehicle telematics data to assess customer risk profiles and help insurance companies customize corresponding products and services. Wang J. and Wu C. [24] proposed a routing protocol based on forwarding nodes. The protocol uses a dimensionless method to deal with factors such as distance between origin and destination, direction, speed vector, and traffic conditions; uses the eigenvector method to determine the impact factor weights; and uses weighted sum methods to combine them for better application in various practical VANET scenarios. Ge Y. et al. [25] developed a mobile recommendation system to recommend a series of pick-up points for taxi drivers or a series of potential parking spaces to improve efficiency. In addition, some scholars have analyzed the risks that may exist in the IoV information platform and constructed an evaluation system. Tian B. et al. [26] used network analysis to comprehensively consider the interconnections between various risk indicators, calculate their importance weights, and provide a reference for the risk identification and evaluation of automotive vehicle information platforms. Lin et al. [27] constructed a network relationship diagram between evaluation models containing 25 standards and used network analysis to determine the relative weights between standards, providing suggestions for TSP to improve existing functions and develop new functions. Catherine et al. [28] proposed an evaluation framework for the availability of in-vehicle information systems. The framework guides designers to select appropriate evaluation methods by defining usability standards, to improve the overall availability of the IoV information service system and enhance the driving experience.

With the further development of the IoV technology and applications, some scholars have conducted research on the composition of the IoV industry chain. Song et al. [29] compared the telematics industries in Korea and China and considered that the Korean IoV industry chain is a triangular structure composed of mobile communication providers, automobile manufacturers and navigation system providers. However, since the cost of telematics services is quite high, the actual Korean IoV industry only operates around the first two. While the Chinese IoV industry is mainly concentrated in terminal manufacturers, with the participation of automobile manufacturers and the three major telecommunications companies, the chain structure is quite complicated. At present, most scholars divide the IoV market into the pre-installed market and the post-installed market. The pre-installed market consists of automobile manufacturers, which mainly focus on providing vehicle testing and safety-related services. The post-installed market is consisted of mobile communication operators, which provide users a wide range of telematics services through the IoV equipment. Xiong J. et al. [6] conducted an in-depth analysis of the typical telematics application model and value chain composition, built the value chain of the pre-installed market and the post-installed market, and further explored the role positioning and business model of telecom operators. Li J. and Shen L. [7] found from the composition of the industrial chain that, in the pre-installed market, automobile manufacturers will strictly control the quality of various products and production links, the value chain is mainly dominated by automobile manufacturers, and the post-installed market has developed rapidly in recent years, with TSP leading the value chain.

With the increasingly mature IoV technology and services, automobiles have gradually become an information service platform. Users have begun to pay attention to the practicability and diversity of the IoV services, and cost-effectiveness of services (“service/price”) has become the basis for users to choose services from the pre-installed market and the post-installed market. Under this change, how the pre-installed market and the post-installed market will compete, and how the overall IoV market will develop, are worthy of scholars’ research. However, few existing studies involve the analysis of the competition of interests between the pre-installed market and the post-installed market. Based on the hypothesis that the scale of the IoV market is limited, this article uses an evolutionary game theory to theoretically discuss the dynamic game process between the pre-installed market and the post-installed market of the IoV market, analyzes the healthy competition status of the IoV market and the conditions of maintaining the healthy competition, and provides a theoretical basis for the healthy development of the IoV market. In view of the current research on the game process between the pre-installed market and the post-installed market, the literature draws on the techniques of Rand D. G. [30], Cao X. [31], etc. in the application of the evolutionary game method and refers to some other studies whose subjects are similar to the research problem in this paper [32,33,34,35,36].

3. Construction of the IoV Market Evolution Game Model and Stability Analysis

3.1. Subjects Analysis of the Evolutionary Game of the IoV Market

There are five main groups of participants in the IoV market—governments, customers, on-vehicle equipment and service providers, the pre-installed market, and the post-installed market. Among them, governments, customers, and on-vehicle equipment and service providers influence the development of the IoV market. The pre-installed market and the post-installed market are two sub-markets of the IoV industry that are segmented according to different terminal installing methods. Without considering government intervention, since customers and the on-vehicle equipment and service providers will choose according to their own interests, the multi-party IoV market is essentially a two-party game between the pre-installed market and the post-installed market. Thus, this article takes the two sub-markets as the two players in the evolutionary game. In the pre-installed market, automobile manufacturers dominate. They mainly sell vehicles to consumers. They can choose whether to install IoV terminal equipment during automobile manufacturing and provide services to customers after the entire vehicle leaves the factory. In the post-installed market, TSPs can modify the cars after they leave the factory and provide customers with IoV services, such as the installation and maintenance of On-Board Diagnostic (OBD). In addition, TSPs also provide users with a series of services such as financial services, car rental, insurance, advertising, decoration, maintenance, maintenance and maintenance, as well as driving schools, parking lots, car clubs, traffic information services and used cars. Overall, the pre-installed market and the post-installed market each have their own advantages. Because the pre-installed market is closer to “cars” and has a first-mover advantage over rear-installing in time, automakers can more actively choose whether to install the IoV equipment and bring immediate benefits and value to enterprises. Due to the large number of orders and large scale of automobile manufacturers, they can also reduce the cost of their equipment and services by establishing in-depth cooperation with on-vehicle equipment and service providers, thus having research and development advantages and cost advantages. However, TSPs in the post-installed market are more focused on improving the level of IoV services, and they are directly facing users. It is easy to comprehensively understand user needs and provide users with faster, more comprehensive, and more thoughtful personalized services, so users may be more inclined to choose products and services that are convenient and with a higher “service/price.”

With the continuous development of IoV technology and the pursuit of limited interests in the common market by companies such as automobile manufacturers, TSPs and 4S stores, the pre-installed market, and the post-installed market, there is therefore a dynamic game process between them. In the course of this game, companies in any market can establish cooperative relationships with companies in another market, and each learns from its strengths and jointly benefits. The two main players in the evolutionary game of the IoV market constructed in this article are the automobile manufacturers in the pre-installed market and all the TSP in the post-installed market. Among them, the strategy that manufacturers in the pre-installed market can choose is whether to install IoV equipment and provide services, and the strategy that TSP in the post-installed market can choose is whether to increase “service/price” through technology research and development. In the course of the game, due to the drive of consumer choice, automobile manufacturers, TSP, and 4S stores will weigh the gains and losses and choose the corresponding strategy. On the one hand, in the pre-installed market, in order to improve efficiency, enhance the brand’s impact on society, and enhance their own competitive advantages, car manufacturers will purchase IoV equipment from on-vehicle equipment and service providers and install them on their vehicles. If a car manufacturer chooses to install IoV equipment and provide services, the value of the vehicle will eventually increase, and the manufacturer will obtain higher economic benefits, but it will also need to bear the cost of equipment and services. On the other hand, in the post-installed market, when the “service/price” of the IoV car provided by TSP is high, consumers tend to choose the products and services provided by the post-installed market. That is to say, although the car manufacturers in the pre-installed market may choose a strategy to install IoV equipment and provide services, consumers will also choose the post-installed market and transfer the entire vehicle to the post-installed market for modification. At this time, post-installed market companies will receive additional economic benefits, the cost of which includes the vehicle costs paid to car manufacturers and the equipment costs paid to equipment suppliers. Meanwhile, the “service/price” of the post-installed market is high, which will inevitably squeeze the pre-installed market, and automobile manufacturers who choose pre-installed IoV equipment will bear certain economic losses. In addition, when companies in the two markets choose to cooperate, the party with the lower product and service will compensate the other party with certain cooperation costs, and the post-installed market company will not cause losses to the pre-installed market when the company chooses to cooperate. In the case of one party which choose to cooperate, the cooperating party will give the other party preferential or compensation according to the cooperation situation, but the non-cooperative party will not follow the established rules. In summary, the pre-installed market and the post-installed market are interrelated, and each party has different interests and choices of behavior. Different decision-making behaviors will affect the development of the entire market.

3.2. Hypotheses and Parameter Settings

3.2.1. Hypotheses

Hypothesis 1:

The market is a fully competitive market. During the entire dynamic game process of the IoV market between the pre-installed market and the post-installed market, the government does not take any action—that is, it does not interfere and does not have any impact on the evolution process. On-vehicle equipment and service providers do not discriminate against companies in the pre-installed market and post-installed companies.

Hypothesis 2:

Considering the system formed by the automobile manufacturers in the pre-installed market and the companies in the post-installed market as a complete two-party game system, it is assumed that all participants are bounded rational, and the information they hold is not completely symmetrical. In addition, it is assumed that both sides of the game in the evolutionary game model are in the initial stage of the game, and other subjects that may have an influence on the game process are not considered during the game.

Hypothesis 3:

The overall of the IoV market is limited. Automobile manufacturers in the pre-installed market and TSP in the post-installed market can only play a game in this limited market.

Hypothesis 4:

The game process between the pre-installed market and the post-installed market is due to the free choice of consumers, that is, consumers will choose the side that leads to a better consumer experience, that is, the one with the higher “service/price.”

Hypothesis 5:

The probability that the manufacturers in the pre-installed market choose to install on-vehicle equipment and provide services is $x$, and the probability that companies in the post-installed market will increase the “service/price” through technology research and development is$y$. $x, y\in \left[0, 1\right]$, and they are functions of time$t$.

3.2.2. Parameter Settings

Assuming that when the car manufacturer in the pre-installed market chooses to install on-vehicle equipment and provide services, the economic benefit is $R_1$, and the cost of the on-vehicle equipment and services is $\mathrm{c}$. At this time, the price of the vehicle supplied to the post-installed market is $P_1$. When the car manufacturer chooses not to install on-vehicle equipment and not to provide services, the economic benefit is $R_2$, and the vehicle price is $P_2$ at this time. In addition, when the “service/price” of the on-vehicle equipment and services provided by the post-installed market is high, consumers are more willing to choose the products and services provided by the post-installed market. This will cause a loss, which is assuming as $I$, to the pre-installed manufacturers who choose to install on-vehicle equipment.

Assuming that when the post-installed market company chooses to increase the “service/price” through technology research and development, the R&D cost that it needs to pay is $C$. At this time, when the consumer chooses the products and services of the post-installed market, the company will get additional economic benefits $r$, and the company will not only pay the cost of the entire vehicle to automobile manufacturer, but also pay the equipment and service costs to the on-vehicle equipment and service provider. If the “service/price” provided by the post-installed market company is low, the enterprise only needs to pay the entire vehicle cost to the automobile manufacturer. In addition, it is assumed that when the vehicle sold to consumers is finally assembled with the IoV equipment, the economic benefit of the post-installed market company is $R_3$. When the vehicle sold to consumers is not equipped with the IoV equipment, the economic benefit of the post-installed market company is $R_4$.

In addition, for the case of cooperation, it is assumed that the proportion of the pre-installed and post-installed companies that choose to cooperate is $\theta$ and $\phi$. And it is assumed that when the pre-installed market chooses to cooperate, the price of vehicle from manufacturer will be reduced, that is, the vehicle price will become $P_1^{*}$ and $P_2^{*}$, and the economic benefits of the pre-installed market will also become $R_1^{*}$ and $R_2^{*}$. Assuming that when the pre-installed market chooses to install on-vehicle equipment and the “service/price” of post-installed market is low, the cooperation cost for the pre-installed market is $\alpha$. When the pre-installed market chooses to not install on-vehicle equipment and the “service/price” of post-installed market is high, the cooperation cost for the post-installed market is $\beta$.

3.3. Construction of Evolution Game Model of the IoV Market

According to the above hypotheses and parameter settings, in the process of the game between the pre-installed market and the post-installed market, the payment matrix of automobile manufacturers in the pre-installed market and TSP in the post-installed is shown in

Table 1. Payment matrix for evolutionary games.

		Type	The Post-Installed Market
			high “service/price” ($y$)		low “service/price” ($1-y$)
Type			cooperate ($\phi$)	not cooperate ($1-\phi$)	cooperate ($\phi$)	not cooperate ($1-\phi$)
The pre-installed market	install equipment and provide service ($x$)	cooperate ($\theta$)	($R_1^{*}-c+0.3r$,$R_3+0.7r-P_1^{*}-C$)	($R_1^{*}-c-I$, $R_3+r-P_1^{*}-c-C$)	($R_1^{*}-c+\alpha$, $R_3-P_1^{*}-\alpha$)	($R_1^{*}-c$, $R_3-P_1^{*}$)
		not cooperate ($1-\theta$)	($R_1-c+0.3r$, $R_3+0.7r-P_1-c-C$)	($R_1-c-I$, $R_3+r-P_1-c-C$)	($R_1-c+\alpha$, $R_3-P_1-\alpha$)	($R_1-c$, $R_3-P_1$)
	not install equipment and not provide service ($1-x$)	cooperate ($\theta$)	($R_2^{*}+0.3r-\beta$, $R_3+0.7r-P_2^{*}-c-C+\beta$)	($R_2^{*}-\beta$, $R_3+r-P_2^{*}-c-C+\beta$)	($R_2$, $R_4-P_2$)	($R_2$, $R_4-P_2$)
		not cooperate ($1-\theta$)	($R_2+0.3r$, $R_3+0.7r-P_2-c-C$)	($R_2$, $R_3+r-P_2-c-C$)	($R_2$, $R_4-P_2$)	($R_2$, $R_4-P_2$)

.

The benefit for car manufacturer in the pre-installed market when it chooses to install equipment and provide services is the weighted sum of the corresponding earnings of the pre-installed market in each case in Table 1, that is

$$U_{\mathrm{M}1}=\theta \left(R_1{}^{*}-R_1\right)+\phi \left(y\cdot 0.3r+\alpha -y\alpha +yI\right)-yI+R_1-c.$$

(1)

The benefit for car manufacturer in the pre-installed market when it chooses to not install equipment and not provide services is the weighted sum of the corresponding earnings of the pre-installed market in each case in Table 1, that is

$$U_{\mathrm{M}2}=\theta \left(y{R}_2{}^{*}-y\beta -y{R}_2\right)+\phi \cdot y\cdot 0.3r+R_2.$$

(2)

The average benefit of car manufacturer in the pre-installed market is

$$U_M=x{U}_{M1}+\left(1-x\right)U_{M2}.$$

(3)

The replicator dynamics equation of car manufacturer in the pre-installed market is

$$\begin{gathered} dx/dt=x\left(U_{M1}-U_M\right) =x\left(1-x\right)[\theta \left(R_1{}^{*}-R_1-y{R}_2{}^{*}+y\beta +y{R}_2\right)+ \\ \phi \left(\alpha -y\alpha +yI\right)-yI+R_1-c-R_2]. \end{gathered}$$

(4)

The benefit of TSP with high “service/price” in the post-installed market is the weighted sum of the corresponding earnings of the post-installed market in each case in Table 1, that is

$$\begin{gathered} U_{E1}=\theta \left(-x{P}_1^{*}-P_2^{*}+\beta +x{P}_2^{*}-x\beta +x{P}_1+P_2-x{P}_2\right)-\phi ·0.3r-x{P}_1+R_3+ \\ r-P_2-c-C+x{P}_2. \end{gathered}$$

(5)

The benefit of TSP with low “service/price” in the post-installed market is the weighted sum of the corresponding earnings of the post-installed market in each case in Table 1, that is

$$U_{E2}=\theta \left(-x{P}_1{}^{*}+x{P}_1\right)-\phi \cdot x\alpha +x{R}_3-x{P}_1+R_4-P_2-x{R}_4+x{P}_2.$$

(6)

The average benefit of TSP in the post-installed market is

$$U_E=y{U}_{E1}+\left(1-y\right)U_{E2}.$$

(7)

The replicator dynamics equation of TSP in the post -installed market is

$$\begin{gathered} dy/dt=y\left(U_{E1}-U_E\right)=y\left(1-y\right)\left[\theta \left(-P_2{}^{*}+\beta +x{P}_2{}^{*}-x\beta +P_2-x{P}_2\right)+ \\ \phi \left(-0.3r+x\alpha \right)+R_3+r-c-C-x{R}_3-R_4+x{R}_4\right]. \end{gathered}$$

(8)

3.4. Stability Analysis of Evolution Game Model of the IoV Market

In order to find the stable point of the evolutionary game between automobile manufacturers in the pre-installed market and TSP in the post-installed market, define

$$\{\begin{array}{c}dx/dt=0\\ dy/dt=0\end{array}$$

(9)

In the $R=\left\{\left(x,y\right)|0\le x\le 1,0\le y\le 1\right\}$ plane, five stable points are acquired:

$$\left(0,0\right),\left(1, 0\right),\left(0, 1\right),\left(1, 1\right),\left(x^{*}, y^{*}\right).$$

$x^{*}=\frac{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \cdot 0.3r-R_3-r+c+C+R_4}{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4},y^{*}=\frac{-\theta R_1{}^{*}+\theta R_1-\phi \alpha -R_1+c+R_2}{-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I}$.

According to the replicator dynamics equations and the stable point analysis above, when $y^{*}=\frac{-\theta R_1{}^{*}+\theta R_1-\phi \alpha -R_1+c+R_2}{-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I}$ or $x=0, 1$, the proportion of automobile manufacturers who install equipment and provide services in the pre-installed market or do not install equipment and provide services is stable. When $x^{*}=\frac{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \cdot 0.3r-R_3-r+c+C+R_4}{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4}$ or $y=0, 1$, the proportion of TSP who improve “service/price” through technology research and development or with lower “service/price” is stable.

Using the local stability of the Jacobi matrix to analyze the stability of the stable point of the system, the Jacobi matrix of the system is

$$J=\left[\begin{array}{cc}\frac{\partial \left(\frac{dx}{dt}\right)}{\partial x}& \frac{\partial \left(\frac{dx}{dt}\right)}{\partial y}\\ \frac{\partial \left(\frac{dy}{dt}\right)}{\partial x}& \frac{\partial \left(\frac{dy}{dt}\right)}{\partial y}\end{array}\right],$$

(10)

and each first-order partial derivative is shown in the following formulae (11–14):

$$\frac{\partial \left(\frac{dx}{dt}\right)}{\partial x}=\left(1-2x\right)\left[\theta \left(R_1{}^{*}-R_1-y{R}_2{}^{*}+y\beta +y{R}_2\right)+\phi \left(\alpha -y\alpha +yI\right)-yI+R_1-c-R_2\right],$$

(11)

$$\frac{\partial \left(\frac{dx}{dt}\right)}{\partial y}=x\left(1-x\right)\left(-\theta R_2{}^{*}+\theta \beta +\theta R_2-\phi \alpha +\phi I-I\right),$$

(12)

$$\frac{\partial \left(\frac{dy}{dt}\right)}{\partial x}=y\left(1-y\right)\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3-R_4\right),$$

(13)

$$\frac{\partial \left(\frac{dy}{dt}\right)}{\partial y}=\left(1-2y\right)\left[\theta \left(-P_2{}^{*}+\beta +x{P}_2{}^{*}-x\beta +P_2-x{P}_2\right)+\phi \left(-0.3r+x\alpha \right)+R_3+r-c-C-x{R}_3-R_4+x{R}_4\right].$$

(14)

The determinant values and traces of the matrix J are:

$$Det J=\frac{\partial \left(\frac{dx}{dt}\right)}{\partial x}\times \frac{\partial \left(\frac{dy}{dt}\right)}{\partial y}-\frac{\partial \left(\frac{dx}{dt}\right)}{\partial y}\times \frac{\partial \left(\frac{dy}{dt}\right)}{\partial x}, Tr J=\frac{\partial \left(\frac{dx}{dt}\right)}{\partial x}+\frac{\partial \left(\frac{dy}{dt}\right)}{\partial y}.$$

(15)

Substituting the values of the five system stable points into the matrix J in turn. After finishing the calculation, the values of the matrix determinant $Det J$ and the values of the trace $Tr J$ are shown in

Table 2. Det J and Tr J of each stable point.

(x, y)	The Determinant and Trace Expressions of Matrix
O (0, 0)	$Det J=\left[\theta \left(R_1^{*}-R_1\right)+\phi \alpha +R_1-c-R_2\right]*\left[\theta \left(-P_2^{*}+\beta +P_2\right)-\phi ·0.3r+R_3+r-c-C-R_4\right]$ $Tr J=\left[\theta \left(R_1^{*}-R_1\right)+\phi \alpha +R_1-c-R_2\right]+\left[\theta \left(-P_2^{*}+\beta +P_2\right)-\phi ·0.3r+R_3+r-c-C-R_4\right]$
A (0, 1)	$Det J=-\left[\theta \left(R_1^{*}-R_1-R_2^{*}+\beta +R_2\right)+\phi I-I+R_1-c-R_2\right]*\left[\theta \left(-P_2^{*}+\beta +P_2\right)-\phi ·0.3r+R_3+r-c-C-R_4\right]$ $Tr J=\left[\theta \left(R_1^{*}-R_1-R_2^{*}+\beta +R_2\right)+\phi I-I+R_1-c-R_2\right]-\left[\theta \left(-P_2^{*}+\beta +P_2\right)-\phi ·0.3r+R_3+r-c-C-R_4\right]$
B (1, 0)	$Det J=\left[\theta \left(R_1^{*}-R_1\right)+\phi \alpha +R_1-c-R_2\right]*\left[\phi \left(-0.3r+\alpha \right)+r-c-C\right]$ $Det J=\left[\theta \left(R_1^{*}-R_1\right)+\phi \alpha +R_1-c-R_2\right]+\left[\phi \left(-0.3r+\alpha \right)+r-c-C\right]$
C (1, 1)	$Det J=-\left[\theta \left(R_1^{*}-R_1-R_2^{*}+\beta +R_2\right)+\phi I-I+R_1-c-R_2\right]*\left[\phi \left(-0.3r+\alpha \right)+r-c-C\right]$ $Tr J=-\left[\theta \left(R_1^{*}-R_1-R_2^{*}+\beta +R_2\right)+\phi I-I+R_1-c-R_2\right]+\left[\phi \left(-0.3r+\alpha \right)+r-c-C\right]$
D (x*, y*)	$Det J=-MN\ne 0$ $Tr J=0$

.

Annotation: (1) $M=\frac{\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \cdot 0.3r-R_3-r+c+C+R_4\right)\left(\phi \alpha -\phi \cdot 0.3r+r-c-C\right)\left(-\theta R_2+\theta \beta +\theta R_2-\phi \alpha +\phi I-I\right)}{{\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}^2}$

(2) $N=\frac{\left(-\theta R_1{}^{*}+\theta R_1-\phi \alpha -R_1+c+R_2\right)\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta +\phi I-I+\theta R_1{}^{*}-\theta R_1+R_1-c-R_2\right)\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}{{\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I\right)}^2}$

According to the evolutionary game theory, for the stable points in the system, if the conditions of Jacobi determinant and trace sign are met, then this point is the evolutionary stability strategy (ESS). The stable state of ESS in different situations is discussed and analyzed as follows:

Situation 1—When $-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I<0$ and $\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4<0$, that is, the overall loss of the pre-installed market and the overall loss of the post-installed market caused by the changing of the proportion of enterprises choosing to cooperate in the two markets are less than 0, as shown in

Table 3. Results of local stability analysis in Situation 1.

(x, y)	Det J	Tr J	Local Stability
O (0, 0)	+	+	not stable
A (0, 1)	+	−	ESS
B (1, 0)	+	−	ESS
C (1, 1)	+	+	not stable
D (x*, y*)	−	0	saddle point

and Figure 1, at this time, the system has two ESS stable states, which are (0, 1) and (1, 0). Among them, point (0, 1) indicates that the pre-installed market does not install equipment or provide services, and the post-installed market increases “service/price” through technology research and development to provide consumers with on-vehicle equipment and services, and point (1, 0) indicates that the pre-installed market install the on-vehicle equipment and provide services for consumers, and the post-installed market space is squeezed.

As shown in Figure 1, in this situation, regardless of the initial state, the pre-installed market and the post-installed market will undergo a long-term game. And finally the overall market will turn into two conditions, which are the post-installed market provide consumers with all on-vehicle equipment and services by increasing the “service/price,” or the pre-installed market provides consumers with all on-vehicle equipment and services and the space of post-installed market is squeezed. In this situation, when $S_{OACD}>S_{OBCD}$, it is more likely that the overall IoV market will eventually evolve into the condition that manufacturers will not install the on-vehicle equipment, and equipment and services will be provided by the post-installed market. When $S_{OACD}<S_{OBCD}$, it is more likely that the overall IoV market will eventually evolve into the condition that manufacturers in the pre-installed market will provide all on-vehicle equipment and services, and the space of post-installed market is squeezed. When $S_{OACD}=S_{OBCD}$, the probability of the system’s evolution to the two stable strategies is equal. By analyzing the factors that affect the two areas of $S_{OACD}$ and $S_{OBCD}$, they can be transformed into the factors that affect the evolution direction and the final strategy choice of the two players’ games. In the following, the area of $S_{OACD}$ is denoted as $S_1$, and the area of $S_{OBCD}$ is denoted as $S_2$, then

$$S_1=\frac{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \cdot 0.3r-R_3-r+c+C+R_4}{2\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}+\frac{-\theta R_2{}^{*}+\theta R_2+\theta \beta +\phi I-I+\theta R_1{}^{*}-\theta R_1+R_1-c-R_2}{2\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I\right)}.$$

(16)

$$S_2=\frac{-\theta R_1{}^{*}+\theta R_1-\phi \alpha -R_1+c+R_2}{2\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I\right)}+\frac{\phi \alpha -\phi \cdot 0.3r+r-c-C}{2\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}.$$

(17)

According to the area relationship of $S_1$ and $S_2$, the following conclusions can be drawn:

Conclusion 1—With the increase in R&D costs of “service/price” for the post-installed companies, the probability of the steady state evolution of the space of post-installed market is squeezed and manufacturers install on-vehicle equipment and provide services will get increased. The specific analysis is as follows:

Because $\frac{\partial S_1}{\partial C}=\frac{1}{2\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}<0$ and $\frac{\partial S_2}{\partial C}=-\frac{1}{2\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}>0$, $S_1$ is a monotonically decreasing function of $C$, and $S_2$ is a monotonically increasing function of $C$. If $C$ increases, the area of $S_1$ decreases and the area of $S_2$ increases, and the probability that the system evolves toward the point B (1, 0) increases. This shows that in this situation, the IoV market is developing with a higher probability to the condition that the pre-installed market install all the on-vehicle equipment and provide services to consumers, while the development space of the post-installed market is squeezed, and eventually the pre-installed market is dominant.

Conclusion 2—With the increase in the additional economic benefits of post-installed market companies, the probability of the steady state evolution of pre-installed market manufacturers not installing and the on-vehicle equipment and services provided by post-installed market will get increased. The specific analysis is as follows:

Because $\frac{\partial S_1}{\partial r}=\frac{0.3\phi -1}{2\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}>0$ and $\frac{\partial S_2}{\partial r}=\frac{1-0.3\phi }{2\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}<0$, $S_1$ is a monotonically increasing function of $r$, and $S_2$ is a monotonically decreasing function of $r$. If $r$ increases, the area of $S_1$ increases and the area of $S_2$ decreases, and the probability that the system evolves toward the point A (0, 1) increases. This shows that in this situation, the IoV market is developing with a higher probability to the condition that the pre-installed market is compressed, the development prospects of the post-installed market are better, and the post-installed market is finally dominant.

Conclusion 3—When the loss in the pre-installed market due to the change in the proportion of companies that choose to cooperate is greater than the loss in the post-installed market, with the increase in the cost of on-vehicle equipment provided by equipment suppliers, the probability of the steady state evolution of pre-installed market manufacturers not installing and the on-vehicle equipment and services provided by post-installed market will increase. On the contrary, when the loss in the pre-installed market due to the change in the proportion of companies that choose to cooperate is less than the loss in the post-installed market, with the increase in the cost of on-vehicle equipment provided by equipment suppliers, the probability of the steady state evolution of pre-installed manufacturers installing on-vehicle equipment and providing services and the space of post-installed market is squeezed will increase. The specific analysis is as follows:

Because $\frac{\partial S_1}{\partial c}=\frac{\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I\right)-\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}{2\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I\right)}$ and $\frac{\partial S_1}{\partial c}=\frac{\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)-\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I\right)}{2\left(-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I\right)\left(\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4\right)}$, when the loss in the pre-installed market due to the change in the proportion of companies that choose to cooperate is greater than the loss in the post-installed market, $\frac{\partial S_1}{\partial c}>0$ and $\frac{\partial S_2}{\partial c}<0$. So, $S_1$ is a monotonically increasing function of $c$, $S_2$ is a monotonically decreasing function of $c$. If $c$ increases, the area of $S_1$ increases and the area of $S_2$ decreases, and the probability that the system evolves toward the point A (0, 1) increases. This shows that in this situation, the IoV market is developing with a higher probability to the condition that the pre-installed market is compressed, the development prospects of the post-installed market are better, and the post-installed market is finally dominant. On the contrary, when the loss in the pre-installed market due to the change in the proportion of companies that choose to cooperate is less than the loss in the post-installed market, then $\frac{\partial S_1}{\partial c}<0$ and $\frac{\partial S_2}{\partial c}>0$. So, $S_1$ is a monotonically decreasing function of $c$, $S_2$ is a monotonically increasing function of $c$. If $c$ increases, the area of $S_1$ decreases and the area of $S_2$ increases, and the probability that the system evolves toward the point B (1, 0) increases. This shows that in this situation, the IoV market is developing with a higher probability to the condition that the pre-installed market install all the on-vehicle equipment and provide services to consumers, while the development space of the post-installed market is squeezed, and eventually the pre-installed market is dominant.

However, under the conditions of Situation 1, because the IoV market is a dynamic balanced market, the two parties in the game often adjust their strategies when their interests are lost, and gain more market share by changing “service/price,” etc. to guarantee their own interests. Besides, any party of the IoV market which bears the entire content of on-vehicle services, which may damage the interests of consumers. Therefore, both evolutionary stable states will be detrimental to the overall market. Instead, the pre-installed market and the post-installed market will jointly promote the development of the overall IoV market and improve on-vehicle service levels in the process of continuously adjusting their strategic choices and competing with each other.

Situation 2—When $-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I>0$ and $\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4<0$, as shown in

Table 4. Results of the local stability analysis in Situation 2 and Situation 3.

(x, y)	Situation 2			Situation 3
	Det J	Tr J	Local Stability	Det J	Tr J	Local Stability
O (0, 0)	−	uncertain	saddle point	−	uncertain	saddle point
A (0, 1)	−	uncertain	saddle point	−	uncertain	saddle point
B (1, 0)	−	uncertain	saddle point	−	uncertain	saddle point
C (1, 1)	−	uncertain	saddle point	−	uncertain	saddle point
D (x*, y*)	+	0	saddle point	+	0	saddle point

and Figure 2, all stable points are saddle points, and the system does not have ESS stable states at this time.

Situation 3—When $-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I<0$ and $\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4>0$, as shown in Table 4 and Figure 2, all stable points are saddle points, and the system does not have ESS stable states at this time.

In the above two situations, the difference in losses suffered by the pre-installed market and the post-installed market due to the change in the proportion of companies choosing to cooperate indicates that the overall benefits of the IoV market are limited. At this time, the competition between the two players in the game is the most intense, and it will show a cyclical process, that is, when one party’s strategy changes, the other party can also protect itself from loss by changing its own strategy choices. In other words, the pre-installed market and the post-installed market will constantly change their strategic choices during the game and increase their competitive advantages and gain market share by providing value-added services and increasing “service/price.” Therefore, under the two conditions of Situation 2 and Situation 3, the two parties in the game will continue to promote the overall product quality and service level of the IoV market in a cyclical competition, which is the most benign state of competition.

Situation 4—When $-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I>0$ and $\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4>0$, that is, the overall loss of the pre-installed market and the overall loss of the post-installed market caused by the changing of the proportion of enterprises choosing to cooperate in the two markets are greater than 0, as shown in

Table 5. Results of local stability analysis in Situation 4.

(x, y)	Det J	Tr J	Local Stability
O (0, 0)	+	−	ESS
A (0, 1)	+	+	not stable
B (1, 0)	+	+	not stable
C (1, 1)	+	+	not stable
D (x*, y*)	−	0	saddle point

and Figure 3. At this time, the ESS stable state of the system is (0, 0), that is, the car manufacturers in the pre-installed market do not install on-vehicle equipment and provide services, and the post-installed market does not increase “service/price” through technological research and development. This is because in this case, installing on-vehicle equipment and providing services to users is not profitable for both players and may even cause losses. This situation is also the most unfavorable stable state for the development of the IoV market. Therefore, we should avoid this situation as much as possible.

4. Numerical Simulation Analysis of the IoV Market Evolution Game

In order to better explore the evolutionary game process of the IoV market and further demonstrate the validity of the model and its results, this article will fit the relevant parameters of the game process and analyze the strategic choices of the two sub-markets under different parameter settings. Low-range vehicle users are usually more price-sensitive, the possibility of choosing the IoV products and services is relatively low, and the proportion of high-range vehicle users is relatively small. Therefore, in this article, it selects the price of mid-range vehicles as an example for numerical simulation. The simulation results are universal.

Defining ${\delta }_1=-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I$ and ${\delta }_2=\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4$, because of the price difference between the car with and without on-vehicle is generally larger, that is, ${\delta }_2<0$, so this article does not perform simulation analysis on Situation 3 and Situation 4. In addition, in order to analyze the influence of the proportion of the cooperative companies on the competition and game in the IoV market, this article chooses three values as $\theta$ and $\phi$, 20%, 50%, and 80%, to explore the evolutionary trend. And assumes that, when the proportion of cooperative companies is 20%, due to the low degree of cooperation, the price difference between the car with and without the on-vehicle equipment is greater when the car is finally sold to customers, which is RMB¥20,000; when the proportion of cooperative companies is 50%, the price difference is RMB¥15,000; when the proportion of cooperative companies is 80%, the price difference is RMB¥10,000 The following are other parameter settings:

Assuming that when the proportion of cooperative companies is 20%, the final selling price of vehicles equipped with on-vehicle equipment is RMB¥200,000, and the final selling price of vehicles without on-vehicle equipment is RMB¥180,000. So, the economic profits of the post-installed market ($R_3$ and $R_4$) are RMB¥200,000 and RMB¥180,000. According to the data, the overall tax burden of the automobile industry will not be higher than 20%. This article calculates the tax burden of automobile manufacturers with its maximum upper limit of 20%, and the tax is RMB¥40,000. Assuming that the price of the car with on-vehicle equipment sold to the post-installed market by the automobile manufacturers in the pre-installed market ($P_1$) is RMB¥170,000, so the economic benefits of the pre-installed market ($R_1$) is RMB¥130,000. And assuming that the price of the car without on-vehicle equipment ($P_2$) is RMB¥150,000, so the economic benefits of the pre-installed market ($R_2$) is RMB¥110,000. According to the actual prices of various equipment and services related to the IoV, such as electric tailgates is about RMB¥2000–4000, OBD is about RMB¥100–150, navigation is about RMB¥800, digital combination instrument is about RMB¥2000–3000, and intelligent rear view cloud mirror is about RMB¥1000–2000, driving recorder is about RMB¥500–1000, etc. It is assumed that the on-vehicle equipment and service cost paid to the on-vehicle equipment and service provider ($c$) is 0.9 million. According to the data of the post-installed market profit of about 7%, etc. in the relevant data, it is assumed that the cost of the post-installed market company to increase “service/price” ($C$) is RMB¥10,000, the company’s additional economic income ($r$) is RMB¥14,000, the loss of the pre-installed market when the “service/price” of the post-installed market is high ($I$) is RMB¥16,000, and the cooperation cost ($\alpha$ and $\beta$) is RMB¥3,000. In addition, it is assumed that when the pre-installed market chooses to cooperate, it will reduce the price of the vehicles by RMB¥5,000, that is, $P_1^{*}=\mathrm{165,000}$ (RMB¥) and $P_2^{*}=\mathrm{145,000}$ (RMB¥), and the economic benefits of the pre-installed market will also decrease, that is, $R_1^{*}=\mathrm{125,000}$ (RMB¥) and $R_2^{*}=\mathrm{105,000}$ (RMB¥). Similarly, the parameter values of other cooperative enterprises can be obtained. The specific parameter values are shown in

Table 6. Parameter values of simulation process.

	Parameter	${\mathit{R}}_1$	${\mathit{R}}_2$	${\mathit{R}}_3$	${\mathit{R}}_4$	${\mathit{R}}_1^{*}$	${\mathit{R}}_2^{*}$	${\mathit{P}}_1$	${\mathit{P}}_2$	${\mathit{P}}_1^{*}$	${\mathit{P}}_2^{*}$	$\mathit{c}$	$\mathit{C}$	$\mathit{I}$	$\mathit{r}$	$\mathit{\alpha }$	$\mathit{\beta }$
$\mathit{\theta }\left(\mathit{\phi }\right)$
0.2		13	11	20	18	12.5	10.5	17	15	16.5	14.5	0.9	1	1.6	1.4	0.3	0.3
0.5		13	11.5	20	18.5	12.5	11	17	15.5	16.5	15	0.9	1	1.6	1.4	0.3	0.3
0.8		13	12	20	19	12.5	11.5	17	16	16.5	15.5	0.9	1	1.6	1.4	0.3	0.3

. Since most of the above parameters are calculated proportionately, the replacement of the vehicle price range only changes the proportion, and the calculation process is consistent, so the results are credible and universal.

4.1. Example Analysis when θ = φ = 0.2

When $\theta =0.2$ and $\phi =0.2$, according to the parameter settings, we can know that ${\delta }_1<0$. At this time, the system satisfies the Situation 1. According to the formula $x^{*}=\frac{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \cdot 0.3r-R_3-r+c+C+R_4}{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4}$ and $y^{*}=\frac{-\theta R_1{}^{*}+\theta R_1-\phi \alpha -R_1+c+R_2}{-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I}$, the saddle point of the evolutionary game is $\left(x^{*}, y^{*}\right)\approx \left(0.750, 0.898\right)$. According to Formulas (4) and (8), the game simulation of the hypothetical related parameters is carried out, and the evolution path of the game of the pre-installed market and the post-installed market of IoV market is shown in Figure 4. The horizontal axis is the value range of $x$, and the vertical axis is the value range of $y$.

As shown in Figure 4, when the point (x, y), which is formed by the initial proportion x of the pre-installed market choosing to install on-vehicle equipment and provide services and the initial proportion y of the post-installed market to increase the "service/price,” is at the upper left of the graph, the IoV market will eventually evolve to (0, 1), that is, the pre-installed market does not install equipment or provide services, and the post-installed market increases “service/price” through technology research and development to provide consumers with on-vehicle equipment and services; when the point (x, y) is at the bottom right of the graph, the IoV market will eventually evolve to (1, 0), that is, the pre-installed market install the on-vehicle equipment and provide services for consumers, and the post-installed market space is squeezed. Because the areas of the two quadrilaterals are similar, under the current parameter value conditions, the probability gap between the two stable states is not obvious, and both stable states may be final evolution results. In order to further illustrate the evolutionary trend of the two players under the current parameter settings, $dx/dt-t$ image and $dy/dt-t$ image are obtained through simulation, as shown in Figure 5, which is the evolution trend of the strategy of the pre-installed market and post-installed market. Because the data in the simulation process is simulated data, the unit of the horizontal axis time $t$ is not specifically set, but refers to general time units (such as year, month, etc.).

Figure 5 can further illustrate that under the current parameter settings, the probability that x eventually becomes 0 or 1 is similar, and so is y. The proportion of the two strategies that the pre-installed market evolves to install and provide services or not to install or provide services is basically equal, and the proportion of the two strategies that the post-installed market evolves to increase “service/price” or not increase “service/price” is also basically equal. The preference for game evolution in the IoV market is not obvious. At this time, automobile manufacturers in the pre-installed market, TSP and 4S stores in the post-installed market should improve their competitive advantage by improving technology, improving service quality, reducing R&D costs, and establishing deeper partnerships with equipment suppliers, and gradually improve their own dominant position and expand the market in the continuous game.

4.2. Example Analysis when θ = φ = 0.5

When $\theta =0.5$ and $\phi =0.5$, according to the parameter settings, we can know that ${\delta }_1<0$. At this time, the system also satisfies the Situation 1. According to the formula $x^{*}=\frac{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \cdot 0.3r-R_3-r+c+C+R_4}{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4}$ and $y^{*}=\frac{-\theta R_1{}^{*}+\theta R_1-\phi \alpha -R_1+c+R_2}{-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I}$, the saddle point of the evolutionary game is $\left(x^{*}, y^{*}\right)\approx \left(0.680, 0.909\right)$. According to Formula (4) and Formula (8), the game simulation of the hypothetical related parameters is carried out, and the evolution path of the game of the pre-installed market and the post-installed market of IoV market is shown in Figure 6. The horizontal axis is the value range of $x$, and the vertical axis is the value range of $y$.

It can be seen from Figure 6 that under the conditions of the current parameter values, the game between the pre-installed market and the post-installed market of the IoV market will also tend to evolve in two directions, which are manufacturers in the pre-installed not install on-vehicle equipment and TSP in the post-installed market provide all the equipment and services (0, 1), or manufacturers install on-vehicle equipment and provide services and the post-installed market space is squeezed(1, 0). The probability of evolution to (1, 0) is greater than the previous case (Figure 4). The $dx/dt-t$ image and $dy/dt-t$ image can be obtained through simulation, as shown in Figure 7.

As shown in Figure 7, under the current parameter settings, although the probability of the stable states that the pre-installed market installs all the on-vehicle equipment and provide services is slightly greater, the difference is also not obvious. At this time, car manufacturers in the pre-installed market, TSP and 4S stores in the post-installed market also should improve their competitive advantage by improving technology, improving service quality, reducing R&D costs, and establishing deeper partnerships with equipment suppliers, and gradually improve their own dominant position and expand the market in the continuous game. In addition, comparing Figure 5 and Figure 7, although the unit of time t on the horizontal axis is not specifically set, it can also be found that the evolution rate of the IoV market at this time is slower than that in Figure 5, and it takes longer for the market to stabilize (one side dominates).

4.3. Example Analysis when θ = φ = 0.8

When $\theta =0.8$ and $\phi =0.8$, according to the parameter settings, we can know that ${\delta }_1>0$. At this time, the system also satisfies the Situation 2. According to the formula $x^{*}=\frac{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \cdot 0.3r-R_3-r+c+C+R_4}{\theta P_2{}^{*}-\theta \beta -\theta P_2+\phi \alpha -R_3+R_4}$ and $y^{*}=\frac{-\theta R_1{}^{*}+\theta R_1-\phi \alpha -R_1+c+R_2}{-\theta R_2{}^{*}+\theta R_2+\theta \beta -\phi \alpha +\phi I-I}$, the saddle point of the evolutionary game is $\left(x^{*}, y^{*}\right)\approx \left(0.574, 0.768\right)$. According to Formula (4) and Formula (8), the game simulation of the hypothetical related parameters is carried out, and the evolution path of the game of the pre-installed market and the post-installed market of IoV market is shown in Figure 8. The horizontal axis is the value range of $x$, and the vertical axis is the value range of $y$.

It can be seen from Figure 8 that, under the current parameter values, the system will form a cyclic process regardless of the value of the initial ratio (x, y). In the process, the value of (x, y) continuously changes between (0, 1). That is to say, when one of the strategies changes, the other will change its own strategy choice to protect itself from loss. In other words, there is no stable state in the game of the pre-installed market and the post-installed market. Instead, during the cyclic competition, car manufacturers in the pre-installed market and TSP in the post-installed market will continuously change their strategy choices according to market trends. The pre-installed market and the post-installed market continue to compete to jointly promote the development of the overall IoV market. The $dx/dt-t$ image and $dy/dt-t$ image can be obtained through simulation (as shown in Figure 9).

It can be further seen from Figure 9 that the proportion x of the pre-installed market choosing to install on-vehicle equipment and provide services and the proportion y of the post-installed market increasing the "service/price" will fluctuate continuously between (0, 1) and will not form a stable state. The pre-installed market and the post-installed market compete cyclically. As the IoV market is composed of the pre-installed market and the post-installed market, absolute dominance of either party will adversely affect the overall market. If the pre-installed market is too strong, it will squeeze the survival space of the post-installed market, resulting in the decrease of the overall level of service in the IoV market and the decrease of customer satisfaction. Conversely, if the post-installed market is too strong, it will adversely affect the pre-installed market and affect the economic benefits of automobile manufacturers, thus affecting the entire market. Therefore, when the cooperative enterprise ratio reaches 0.8, it will not cause any party to monopolize the market, and the two parties in the game will compete cyclically, which is the most benign state of market competition. At the same time, in the course of this cycle, the product quality and service level of the IoV industry will improve constantly.

5. Conclusions, Limitations, and Future Research

5.1. Conclusions

This article analyzes the dynamic game process between the pre-installed market and the post-installed market of the IoV market under the condition of the limited rationality. At the same time, it introduces parameters such as the proportion of cooperative enterprises to explore the evolution trend of the IoV market from a cooperative perspective to make the model more realistic. The study found that in the case of cooperation, due to the uncertainty of the proportion of companies choosing to cooperate, there may be three evolutionary trends in the IoV market: (1) When the overall market interest is high, the market has two stable states—that is, all on-vehicle equipment and services are provided by the pre-installed market or the post-installed market, and the state in which the market is ultimately stable depends on the proportion of the companies that choose each strategy. (2) When the overall market interest is limited, the IoV market has no stable state, and the strategies selection of the two players is a cyclical process. (3) When the overall market is not profitable, the IoV market has only one stable state—that is, neither the pre-installed market nor the post-installed market provide on-vehicle equipment and services. Among them, the second type of evolutionary trend is the benign competition of the IoV market. In this state, the pre-installed market and the post-installed market are constantly changing their chosen strategies to jointly promote the overall product quality and service level of the IoV market. On the contrary, under the first and third evolutionary trends, neither the pre-installed market nor the post-installed market can provide customers with on-vehicle equipment and services that are satisfactory to consumers, and the interests of consumers are impaired, which is detrimental to the overall IoV market and even the automotive industry. Finally, through the analysis of simulation, this article finds that when the proportion of cooperative enterprises is 0.2 and 0.5, the system meets the first evolutionary trend. When the proportion of cooperative enterprises reaches 0.8, the system meets the second evolutionary trend, which is the optimal competitive state.

This article gives the following recommendations for reference:

First, although there are competitions and games in the service of IoV between the pre-installed market and the post-installed market, the two sides should also be encouraged to establish cooperative relationships and increase the proportion of cooperative enterprises, so that the IoV market is in a state of optimal competition in a cyclical cycle. In this cyclic “dynamic balance,” the two players compete in cooperation and continuously adjust their strategic choices to improve their own competitive advantages and influence the evolutionary trend of the IoV market to ensure that their own interests are not damaged. At the same time, in the process of continuous competition and dynamic games, it will also promote the development of the IoV market, and promote the further prosperity of the IoV market and even the automobile market.

Second, by analyzing the monotonicity of the area function in the first evolutionary trend, this article explores the factors that influence the competitive advantage of the pre-installed market and the post-installed market. The results show that the R&D costs of the post-installed market, the additional economic benefits of the post-installed market by installing on-vehicle equipment and providing services to users, and the cost of equipment and services provided by on-vehicle equipment and service providers will affect the competitive advantage and competitive position of the two markets, which in turn affects the evolution direction and stability of the IoV market. Therefore, the pre-installed market and the post-installed market should seek to establish deeper cooperation with on-vehicle equipment and service providers to reduce costs. The post-installed market can also provide professional and personalized services on the basis of controlling “service/price” to expand the market space and obtain higher additional economic benefits. Through the above methods, the two markets can continuously strengthen their competitive advantages and enhance their competitive position on the basis of cooperation.

Finally, the analysis process and related conclusions of this article are based on the consistent cost of equipment and services provided by on-vehicle equipment and service providers to the pre-installed market and the post-installed market. In fact, automobile manufacturers in the pre-installed market may have a deeper level of cooperation with on-vehicle equipment and service providers. If the cost of on-vehicle equipment and services provided by the on-vehicle equipment and service providers to the pre-installed market is lower than it to the post-installed market, the pre-installed market will have a price advantage to a certain extent, and it will be easier to expand the market, while the post-installed market should strive to establish deeper cooperation with on-vehicle equipment and service providers and strive for lower equipment and service costs.

5.2. Limitations and Future Research

Although the hypotheses of this article are reasonable and more in line with the conditions of equal and free competition, if the government and other relevant entities participate in the competition and game process of the IoV market, they will affect the evolution of the IoV market and lead to different results. Therefore, future research can consider the competition of the IoV market in which multiple parties participate, analyze what choices the government and other entities will make during the competition, what impact it will have on the evolution of the IoV market, and investigate the conditions result in optimal competition in the IoV market.