When leading manufacturers decide their own output, they will expect the impact of their own output on follower manufacturers [17] [18]. Therefore, the output determined by leading manufacturers is a profit maximization output constrained by following the manufacturer’s response function. With the continuous growth of the price of leading manufacturers, the price of follow-up manufacturers will also increase, and maintain a relative maximum price to achieve Nash equilibrium [19] [20].

Lloyd’s clustering algorithm is a classical clustering algorithm that can maintain scalability and efficiency when processing large data sets [21] [22]. Its execution process is as follows [23]:

1) Input points are divided into k groups, the center point of each group is calculated, and K initial points are randomly selected in the input point data set;

2) Calculate Voronoi diagram of K central points;

3) Integrate Voronoi diagram and calculate centroid;

4) Then move each center point to the centroid of the Voronoi diagram.

Repeat the above process until the center point does not change.

MCS of vehicular ad hoc networks means that in the Internet of vehicles, mobile vehicles use advanced sensor technology to collect and transmit perception data in real time. The MCS of the Internet of vehicles is often composed of the following parts [24] [25].

1) Trusted authority (TA)

In order to ensure the normal operation of the organizational structure of the Internet of vehicles, it is usually necessary to introduce a trusted certification authority named TA to store the identity information of all users in the corresponding area.

2) Service provider (SP)

SP pays a certain reward to the data collector, obtains data from the data collector, processes the data and sends it to the service consumer. The reward meets the following principles [14]: if the data validity is high, the payment reward is high; If the data schedule is high, the payment reward is high; The more similar data are provided, the lower the reward will be paid; If the collected data is more important for data coverage, the payment reward will be higher.

3) Data collector (DC)

DC is responsible for selecting an appropriate data collection strategy, collecting perceptual data, and providing the collected data to the SP. Vehicles in the Internet of vehicles have certain computing and storage capabilities [24], and can act as DC in the MCS of the Internet of vehicles.

4) Service consumer (SC)

Refers to some management departments (e.g. traffic management department, meteorological bureau) that generate demand for some data and want to extract valuable information (e.g. traffic conditions, accident conditions, weather conditions) from the existing perceived data. SC consider the optimal consumption strategy according to their own needs and choose the corresponding SP to provide services for themselves.

In order to avoid malicious data transmission by vehicles and ensure the availability of vehicle information data, the trusted organization generates time interval T α ∈ { T 1 , T 2 , ⋯ } , sets unique identification and initial reputation score for each vehicle, stores the information in the database, updates the vehicle reputation immediately according to the time interval, and sets the initial reputation score through Equation (1).

R M V i 0 = { 0.9   V i ∈ L E 0.5   V i ∈ P S 0.1   V i ∈ O T (1)

where LE is law enforcement vehicles, PS is public service vehicles and OT is other vehicles [26].

When SC requests information, it determines the task number TID, task content CM and the number of requested information N₀ according to the specific requirements of the perceived task, and then sends a request message Q t C i to SP through Equation (2).

Q t C i = ( T I D , C M , N 0 ) (2)

After receiving Q t C i , SP publishes the service information P m S i to SC through Equation (3).

P m S i = ( T I D , C M , A W S i ) (3)

where, A W S i is service pricing.

Then, SC selects the desired SP to send the demand message according to the service information Q m C i , as shown in Equation (4).

Q m C i = ( T I D , C M , N 0 , P c C i , T 0 ) (4)

where, P c C i is Compensation amount, T₀ is deadline.

After receiving the demand information, SP generates a request task Q t s i , such as Equation (5) to the vehicle V_i.

Q t s i = ( T I D , C M , T M , R M 2 0 , R M 1 0 ) (5)

where TM is expiration time, R M 1 0 and R M 2 0 ( 1 ≥ R M 1 0 ≥ R M 2 0 > 0 ) are the minimum reputation requirements of the two collection schemes described below, which are uniformly set by SP.

This paper provides two collection schemes: direct payment and cumulative compensation:

1) Direct payment: If V_i selects this scheme and the collected data passes the verification, a reward A W V i will be issued. Otherwise, the vehicle reputation feedback will be updated and the reward will be cancelled. For ease of illustration, the collection scheme is recorded as M 1 0 .

2) Cumulative compensation: If V_i selects this scheme and the collected data passes the verification, it will submit the vehicle reputation feedback and accumulate points for the vehicle. Otherwise, it will update the vehicle reputation feedback and cancel the reward. Calculate the cumulative integral by Equation (6).

S W ′ V i = S W V i n + A W V i (6)

where S W V i n is total points before vehicle accumulation, n means that the vehicle has participated in n times of integral accumulation.

In addition, when the vehicle’s points accumulate to a certain amount, you can get additional rewards. Specifically, calculate the total points S W ″ V i after additional rewards through Equation (7).

S W ″ V i = { ( 1 + σ ) S W ′ V i if   S W ′ V i ≥ S W 0 S W ′ V i otherwise (7)

where, σ ( 0 < σ < 1 ) is Incentive factor and S W 0 is extra bonus line by SP.

If n > n 0 , the vehicle can choose to extract points and convert the points owned into reward according to Equation (8). The collection scheme is recorded as M 2 0 .

A W V i = δ ⋅ S W V i ( n − n 0 ) (8)

where n 0 is extractable times threshold and δ is conversion scale factor by SP.

According to the above collection scheme, the follow-up operations are as follows:

After receiving the request task from SP, if V_i decides to participate in the collection task, select the corresponding collection scheme, generate the final feedback information R m V i , such as Equation (9), and feed back the results to SP.

R m V i = ( P s V i , M 1 , 2 0 , A W V i , T V i ) (9)

where P s V i is vehicle unique identification, M 1 , 2 0 ∈ { M 1 0 , M 2 0 } is collection method selected for the vehicle, A W V i is price, and T V i is current time.

Service provider collects the feedback information sent by the vehicle, and then sends a reputation query request, such as Equation (10), to TA.

Q s S i = ( T I D , P s V i ) (10)

Then, TA retrieves the reputation value according to the unique identification of the vehicle, generates a feedback message and sends it to SP as shown in Equation (11).

A s S i = ( T I D , R M V i ) (11)

After that, the collected information and data are processed. The main process is shown in Figure 2. The specific process is as follows:

Service provider judges whether the vehicle meets R M V i ≥ R M 1 , 2 0 ( R M 1 , 2 0 ∈ { R M 1 0 , R M 2 0 } ) according to the retrieved reputation value. If not, generate feedback on the current vehicle dishonesty. Otherwise, SP uses the following Lloyd’s clustering algorithm to cluster the information data.

Lloyd’s clustering algorithm are as follows:

Firstly, the vehicle is divided into several priorities according to the value ratio of ∂ = R M V i A W V i , and they are pressed into the corresponding priority queue. The

steps are as follows: first, SP input the number of priorities a to be divided, and randomly generate a random center point, expressed as { w 1 , w 2 , ⋯ , w a } . Secondly, SP assign each vehicle value ratio ∂ i ∈ { ∂ 1 , ∂ 2 , ⋯ , ∂ n } to the closest area according to the value of the center point. Integrate the Voronoi diagram of the center point in each region to calculate its centroid. Finally, SP move the center point to the centroid position and update the center point.

Repeat the above steps until the center point of the area does not change. Finally, output the values of a center points, and sort the values of the center points from large to small to obtain the final collection { w ′ 1 , w ′ 2 , ⋯ , w ′ a } .

Service provider can divide the received vehicle information data into a groups according to the ratio for priority judgment, and the groups with large values are given priority. Compared with random authentication, authentication according to clustering priority order can improve the total availability of data.

SP determines whether the data provided by each vehicle is null or inconsistent with the data required by the task and other invalid data according to the clustering priority order obtained from the above operations. If the above situation exists, reputation feedback R f V j = 0 is generated; Otherwise, reputation feedback R f V j = 1 is generated.

Then, service provider sends the feedback information, such as Equation (12), to the trusted institution for updating the vehicle reputation value.

A f V i = ( T I D , P s V i , R f V i ) (12)

Then, service provider sends the reliable data set after verification processing to SC and pays DC with reliable data.

At intervals T α , the trusted institution updates the reputation value of each vehicle according to the received vehicle reputation feedback. The set of n reputation feedback received by the vehicle in the current time period is F s V i = { R f V i 1 , R f V i 2 , ⋯ , R f V i n } , and the new reputation value Equation (13) is:

R M ′ V i = { ∑ F s V i n R M V i if F s V i = ϕ γ ⋅ R M V i otherwise (13)

In addition, at regular intervals T α , SC and DC will change their strategies under the influence of SP, and finally minimize costs and maximize profits [14]. Detailed proofs are proved in Varian’s Microeconomics [20].

In this section, corresponding experiments are designed to test the performance of the mechanism. All experiments run on the host configured with 1.8 GHz Intel processor, 8 GB memory and windows 10 operating system. This mechanism simulates and collects the data according to the pricing demand relationship and the Stackelberg optimization model [20], in which the pricing meets the normal distribution [27], the time period division is referred to [14], and the parameter values are shown in Table 1.

For 230 data of Nash equilibrium point, the reputation and pricing are sampled according to the normal distribution [26] [27] [28]. In this simulation experiment, the real numbers within the range of [0, 1] are randomly sampled for 7 times, and 230 data are randomly generated according to the normal distribution N ( μ , σ 2 ) . Since 99.7% of the value of normal distribution is within the range of three standard deviations around the average, let μ = 0.5 , σ = μ / 3 , so as to meet that most of the obtained data are within the range of [0, 1].

According to Lloyd’s clustering algorithm, the seven times of data can be divided into six clustering center points. After 2000 iterations, the center point image shown in Figure 3 can be obtained.

Among them, the higher the center point value, the higher the category priority. SP selects DC according to the priority.

Firstly, this paper analyzes the improvement of data collection by the mechanism, and compares it with the non incentive mechanism.

As shown in Figure 4, the initial data collection volume of this mechanism will be affected by comprehensive factors such as SP, SC and pricing, with certain randomness [14], while the data collection volume without incentive mechanism is only affected by stable factors such as pricing [20]. Through six experiments and the conclusion put forward by Kaoru et al. [14], the initial situation of incentive mechanism can be roughly divided into two types, which are recorded as situation a and situation B. In case a, the vehicle increases the collection

price to obtain a high initial data collection volume, but its profit is also relatively low; the vehicle in case B reduces the collection price, resulting in a low amount of initial data collection, but its profit is correspondingly high.

With the passage of time, the collection price of vehicles in case a will be reduced accordingly in order to improve the profit, so the number of vehicles collected will also be reduced accordingly; similarly, in case B, in order to increase the collection quantity, the collection price will be increased accordingly, so as to increase the collection quantity. Since the operation satisfies the Nash equilibrium, it will reach a corresponding equilibrium point after a period of time [20]. According to a certain proportion, the non incentive mechanism meets the normal distribution with the price fluctuation [25]. It can be seen from Figure 4 that the non incentive mechanism fluctuates greatly. According to the statistics in Table 2, compared with the non incentive mechanism of t ∈ { 1 , 3 , 5 , 7 } in different time periods, the average data collection of V-IMCS mechanism is significantly higher, and the collection in most time periods is higher than that of non incentive mechanism. Refer to [14] for time period division.

In conclusion, compared with no incentive mechanism, the mechanism proposed in this paper improves the amount of data collection.

Secondly, this paper analyzes the improvement of the amount of available data, and compares it with various incentive mechanisms.

According to [28], the pricing range and pricing constant benchmark can be defined, and the pricing constant can be adjusted according to demand. In this paper, 60% and 70% of the benchmark are taken as supplementary experimental data. According to the relevant parameter settings, Figure 5 is calculated. The demand curve of SC will intersect with the data supply curve under different pricing parameters, so as to obtain the data demand under different pricing parameters.

According to Figure 5, the demand is taken as 150, 130 and 120. Seven simulation experiments are carried out on each mechanism respectively to compare

the without incentive mechanism, QUOIN incentive mechanism and V-IMCS mechanism. For the data screening mechanism, refer to the reputation screening principle in [26].

When the amount of data is 150, the comparison of the amount of available data under different mechanisms is shown in Figure 6(a). Due to the use of clustering algorithm, the available data can be selected preferentially. Compared with no incentive mechanism and QUOIN incentive mechanism, the average amount of available data of V-IMCS incentive mechanism is more under 7 simulation experiments.

When the data volume is 130 and 120, the comparison of the available data volume under different mechanisms is shown in Figures 6(b)-(c). Compared with 150, the available data volume without incentive mechanism and QUOIN incentive mechanism is reduced, and the V-IMCS incentive mechanism is not greatly affected. Therefore, compared with no incentive mechanism and QUOIN incentive mechanism, the amount of available data obtained by V-IMCS incentive mechanism is not easily affected by the amount of data demand.

In addition, if the provided data is not used by the SP, the vehicle will not be paid accordingly. In order to obtain the reward, the vehicle needs to get a higher priority, which further encourages the vehicle to provide data honestly.

To sum up, in the MCS of the Internet of vehicles, while encouraging vehicles to honestly provide data, the amount of available data received is significantly higher than the existing QUOIN mechanism and without incentive mechanism, and is not easily affected by the amount of data demand.