A railway monitoring data sharing incentive scheme based on reputation value and smart contracts

Reputation modeling

This model utilizes a Beta distribution-based approach to calculate the reputation value of a data sharer (Chidawa & Mambo, 2021). Intuitively, the reputation value rep of a data sharing party is the credibility value credentials of a data sharing party in the process of railway disaster prevention and monitoring data sharing; the higher the Reputation Value, the more likely the data sharer is to engage in honest railway disaster prevention and monitoring data sharing, and at the same time, the benefit of a successful data sharing session will be higher for a reputable railway disaster prevention and monitoring data sharing party. Meanwhile, the number of ratings in each rating class reflects the reliability and certainty of the behavior of the bidder represented by that rating class. In this article, the Beta probability density function is used to dynamically assess the credibility of users.

(1) $$f(x_i)=\{\begin{array}{cc}{\displaystyle \frac{1}{\mathrm{B}(\alpha ,\beta )}{x}_i^{\alpha -1}{(1-x_i)}^{\beta -1}}\hfill & 0<x_i<1\hfill \\ 0\hfill & \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.\hfill \end{array}$$

When $B\mathbf{(}a,b\mathbf{)}={\displaystyle \frac{\mathrm{\Gamma }(a)\cdot \mathrm{\Gamma }(a)}{\mathrm{\Gamma }(a+b)}}$, the parameters and Beta are set according to the ratings, assuming the reputation vector $R\mathrm{e}{p}_A(a,b)$ of the data sharing party, which indicates that user A has conducted a+b times of data sharing before the current data sharing, including a times of honest data sharing, and b times of non-honest data sharing due to their reasons. According to the Bayesian formula and the nature of Beta, it is easy to see that the distribution after the inclusion of the reputation vector also satisfies the Beta distribution, and the parameters a and b contain the updates of a, b in the current reputation vector, respectively, so that every time the data sharer has a new data sharing transaction completed, it will be updated for the new transaction that has just been observed. Since the reputation $R\mathrm{e}p(A)$ of user A is a prediction of the probability P that the user is a trusted sharer, the expected value of P is denoted as $Rep(A)=E(P)={\displaystyle \frac{\alpha }{\alpha +b}}$: In the initial state, user A has not performed any data sharing transaction yet, then both a and b take the initial value of 1. At this time, the reputation value of user $R\mathrm{e}p(A)$ is 0.5, which indicates that the probability that user A is the one who performs honest data sharing and dishonest data sharing is the same. When the user has ended a data sharing process, the values of a and b will be updated to obtain a dynamic assessment of the user’s reputation value.

Figure 2A shows the Beta probability density functions when a user submits five trustworthy data shares and two dishonest data shares (a = 5, b = 2) and when a user submits five trustworthy data shares and three dishonest data shares (a = 5, b = 3). Based on the Beta distribution calculations, the corresponding user credibility scores are 0.71 and 0.625, respectively. These credibility scores indicate that while it is impossible to determine whether the user is trustworthy, it is at least possible to assess the user’s past credibility based on their previous seven or eight data shares, with scores of 0.71 and 0.625, respectively. Similarly, Fig. 2B shows the Beta probability density function after the user has performed two trustworthy data shares and five dishonest data shares (a = 2, b = 5) and after the user has performed three trustworthy data shares and five dishonest data shares (a = 3, b = 5). The user’s credibility values are 0.287 and 0.375, respectively. It can be seen that the user’s credibility value decreases dynamically after performing dishonest data shares. The Beta-based reputation mechanism can dynamically update the reputation value Rep for each data sharing transaction performed by the user.

Three-party evolutionary game modeling

Based on the tripartite evolutionary game method, the gains and optimal choices between rail-road disaster prevention and monitoring data sharing party A, railway regulators and railway disaster prevention and monitoring data sharing party B. Disaster prevention and monitoring data sharing parties A and B usually consist of data centers of each railway bureau station section or directly under the agency, for relevant parameter settings, see Table 2.

The regulator’s policy set is {strict regulation, normal regulation}. Assume the probability that the regulator chooses strict regulation is $x$, and the probability of choosing normal regulation is $1-x$. Data sharing parties A and B have a strategy set {honest sharing, dishonest sharing}. The probability that parties A and B engage in honest data sharing are $y$ and $z$, and the probability of dishonest sharing are $1-y$ and $1-z$. Here, x, y, z are all functions of time t.

The logical relationship between the benefits and costs for each party in this model is as follows (see Table 1 for detailed definitions):

Data sharing parties (A and B): The revenue of sharing parties primarily consists of three components: base revenue, additional rewards, and illegal gains. The base benefit $sE$ is positively correlated with the size $s$ of the shared data and its complementarity $E$. To incentivize honest behavior, when both parties share honestly, the platform provides an additional reward $P_1$ based on their reputation value $k$. If a party chooses dishonest sharing, they gain illicit benefits $N$. The costs for sharing parties include fixed costs, losses, and penalties. All sharing parties must pay the platform’s basic maintenance cost $C_1$ upon participation. If one party chooses dishonest sharing, the honest sharing party incurs a loss $C$. The dishonest sharing party also bears concealment costs $aN$, which are negatively correlated with reputation value $\mathrm{Re}p$—meaning lower reputation results in higher concealment costs (penalty coefficient). Additionally, under “strict regulation,” dishonest sharing parties face harsher penalties $M$.

Railway regulatory platform: The platform’s benefits and costs depend on its regulatory strategy. The platform’s fixed baseline benefit is $B$. When the platform adopts “strict regulation” and facilitates honest sharing, it gains an additional benefit $D$. Its costs include baseline maintenance cost $C_2$ and the additional cost $C_3$ under the “strict regulation” strategy. If dishonest transactions cause losses to the platform, the loss is recorded as $p$. The evolutionary game payoff matrix is shown in Table 3.

Earnings and expected earnings

The railway regulator, monitoring data sharer A, and monitoring data sharer B all choose the best strategy based on their actual gains and losses. Setting the expected gains of the railway regulator using strict and ordinary regulation as $U_{11}$ and $U_{12}$, and the average gain as $\overline{U_1}$, it can be obtained:

(2) $$\begin{array}{rl}{U}_{11}=& \mathrm{y}\mathrm{z}\mathbf{(}B+D-C_2-C_3\mathbf{)}+\mathrm{y}\mathbf{(}1-z\mathbf{)}\mathbf{(}B+D-C_2-C_3-p\mathbf{)}\\ & +\mathbf{(}1-y\mathbf{)}z\mathbf{(}B+D-C_2-C_3-\mathrm{p}\mathbf{)}+\mathbf{(}1-y\mathbf{)}\mathbf{(}1-z\mathbf{)}\mathbf{(}B+D-C_2-C_3-p\mathbf{)}\end{array}$$

(3) $$\begin{array}{rl}{U}_{12}=& yz\mathbf{(}B-C_2\mathbf{)}+\mathrm{y}\mathbf{(}1-z\mathbf{)}\mathbf{(}B-C_2-p\mathbf{)}\\ & +\mathbf{(}1-y\mathbf{)}z\mathbf{(}B-C_2-\mathrm{p}\mathbf{)}+\mathbf{(}1-y\mathbf{)}\mathbf{(}1-z\mathbf{)}\mathbf{(}B-C_2-\mathrm{p}\mathbf{)}\end{array}$$

(4) $$\overline{U_1}=\mathrm{x}{U}_{11}+\mathbf{(}1-x\mathbf{)}{U}_{12}.$$Similarly, monitoring the expected payoffs of data sharing party A for choosing honest data sharing and fraudulent trading in the data sharing game as $U_{21}$ and $U_{22}$, respectively, with an average payoff of $\overline{U_2}$, it can be obtained:

(5) $$\begin{array}{rl}{U}_{21}=& \mathrm{x}\mathrm{z}\mathbf{(}sE+k_1{P}_1-C_1\mathbf{)}+\mathrm{x}\mathbf{(}1-z\mathbf{)}\mathbf{(}sE-C_1-C\mathbf{)}\\ & +\mathbf{(}1-x\mathbf{)}z\mathbf{(}sE+k_1{P}_1-C_1\mathbf{)}+\mathbf{(}1-x\mathbf{)}\mathbf{(}1-z\mathbf{)}\mathbf{(}sE-C_1-C\mathbf{)}\end{array}$$

(6) $$\begin{array}{rl}{U}_{22}=& \mathrm{x}\mathrm{z}\mathbf{(}sE+N-C_1-aN-M\mathbf{)}+x\mathbf{(}1-z\mathbf{)}\mathbf{(}sE+N-C_1-aN-M\mathbf{)}\\ & +\mathbf{(}1-x\mathbf{)}z\mathbf{(}sE+N-C_1-aN\mathbf{)}+\mathbf{(}1-x\mathbf{)}\mathbf{(}1-z\mathbf{)}\mathbf{(}sE+N-C_1-aN\mathbf{)}\end{array}$$

(7) $$\overline{U_2}=y{U}_{21}+\mathbf{(}1-y\mathbf{)}{U}_{22}.$$Similarly, monitoring the expected payoffs of data sharing party A for choosing honest data sharing and fraudulent trading in the data sharing game as $U_{31}$ and $U_{32}$, respectively, with an average payoff of $\overline{U_3}$, it can be obtained:

(8) $$\begin{array}{rl}{U}_{31}=& \mathrm{x}\mathrm{y}(sE+k_2{P}_1-C_1\mathbf{)}+\mathrm{x}\mathbf{(}1-y\mathbf{)}\mathbf{(}sE-C_1-C\mathbf{)}\\ & +\mathbf{(}1-\mathrm{x}\mathbf{)}\mathrm{y}\mathbf{(}sE+k_2{P}_1-C_1\mathbf{)}+\mathbf{(}1-x\mathbf{)}\mathbf{(}1-y\mathbf{)}\mathbf{(}sE-C_1-C\mathbf{)}\end{array}$$

(9) $$\begin{array}{rl}{U}_{32}=& \mathrm{x}\mathrm{y}\mathbf{(}sE+N-C_1-aN-M\mathbf{)}+x\mathbf{(}1-y\mathbf{)}\mathbf{(}sE+N-C_1-aN-M\mathbf{)}\\ & +\mathbf{(}1-\mathrm{x}\mathbf{)}y\mathbf{(}sE+N-C_1-aN\mathbf{)}+\mathbf{(}1-\mathrm{x}\mathbf{)}\mathbf{(}1-y\mathbf{)}\mathbf{(}sE+N-C_1-aN\mathbf{)}\end{array}$$

(10) $$\overline{U_3}=\mathrm{z}{U}_{31}+\mathbf{(}1-\mathrm{z}\mathbf{)}{U}_{32}.$$

Revenue and evolutionary direction analysis

Analysis of the evolutionary direction of the railway regulator

Based on the above analysis, the replication dynamic equation for the application strategy of the railway regulator is:

(11) $$F\mathbf{(}\mathrm{x}\mathbf{)}={\displaystyle \frac{\mathrm{d}\mathbf{(}x\mathbf{)}}{d\mathbf{(}t\mathbf{)}}=x\mathbf{(}{U}_{11}-\overline{U_1}\mathbf{)}=x\mathbf{(}1-x\mathbf{)}\mathbf{(}{C}_{2}Dyz+D-Dyz-C_3+C_2\mathrm{z}\mathrm{y}\mathbf{)}.}$$

The first-order derivatives of x is respectively:

(12) $${\displaystyle \frac{d\mathbf{(}F\mathbf{(}x\mathbf{)}\mathbf{)}}{dx}=\mathbf{(}1-2\mathrm{x}\mathbf{)}\mathbf{[}\mathrm{d}-C_3-dyz+C_{2}dyz+C_{2}yz\mathbf{]}.}$$

The phase diagram of the strategy evolution of the railway regulatory platform is shown in Fig. 3A. The upper half of the curve indicates that the railway regulatory platform tends to be strictly regulated, and the lower half of the curve indicates that the railway regulatory platform tends to be non-strictly regulated. See the Supplementary file Appendix A for a detailed analysis process.

Monitoring data sharing party B evolutionary path analysis

Based on the above analysis, the replication dynamic equation for monitoring the sharing strategy of data sharer B is:

(15) $$F\mathbf{(}\mathrm{z}\mathbf{)}={\displaystyle \frac{\mathrm{d}\mathbf{(}\mathrm{z}\mathbf{)}}{d\mathbf{(}t\mathbf{)}}=z\mathbf{(}{U}_{31}-\overline{U_3}\mathbf{)}=z\mathbf{(}1-z\mathbf{)}\mathbf{(}an+cy+mx+k_2{p}_{1}y-n-c\mathbf{)}.}$$

The first-order derivatives of z and is respectively:

(16) $${\displaystyle \frac{d\mathbf{(}F\mathbf{(}z\mathbf{)}\mathbf{)}}{dz}=\mathbf{(}1-2\mathrm{z}\mathbf{)}\mathbf{[}\mathrm{a}\mathrm{n}+\mathrm{c}\mathrm{y}+mx-k_2{p}_1\mathrm{y}-\mathrm{n}-\mathrm{c}\mathbf{]}.}$$

The phase diagram of the strategy evolution of the intended transferee can be obtained, as shown in Fig. 4. In the region of the first half of the surface, z tends to 1, monitoring that data sharing party B tends to share honestly; when in the second half of the surface, z tends to 0, monitoring that data sharing party B tends to share dishonestly. See the Supplementary file Appendix C for a detailed analysis process.

Stability analysis of equilibrium points in evolutionary games

The equilibrium points of the three-party evolutionary game system can be obtained from $F\mathbf{(}x\mathbf{)}=0,F\mathbf{(}\mathrm{y}\mathbf{)}=0,F\mathbf{(}z\mathbf{)}=0:E_1(0,0,0),E_2(0,0,1),$ $E_3(0,1,0),E_4(0,1,1),E_5(1,0,0),E_6\mathbf{(}1,0,1\mathbf{)},E_7\mathbf{(}1,1,0\mathbf{)},E_8\mathbf{(}1,1,1\mathbf{)}$. Based on the theory of evolutionary game, when the eigenvalues of the Jacobi matrix are all negative, the corresponding local equilibrium point is the Evolutionary Stability Point (ESS). Calculate the eigenvalues of the Jacobi matrix corresponding to each equilibrium point, and analyze the sign and stability of the eigenvalues to get the Jacobi matrix of the three-party evolutionary game, and the analysis based on the Jacobi eigenvalues is shown in Table 4. Please see the Supplementary file Appendix D for the Jacobi Matrix.

The ESSs requiring conditions in Table 4 are: condition 1: $\mathrm{D}-C_3<0$, $an-\mathrm{n}-\mathrm{C}<0$; condition 2: $n-an-k_1{p}_1<0$, $C_2-C_3+C_2\ast d<0$ and $n-an-k_2{p}_1<0$; condition 3: $m-C-n+an<0$ and $C_3<D$; condition 4: $n-an-\mathrm{m}-k_1{p}_1<0$, $C_3-C_2-C_2\ast \mathrm{D}<0$ and $\mathrm{n}-\mathrm{m}+\mathrm{a}\mathrm{n}-k_2{p}_1<0$. The ESS of the equilibrium point is analyzed point E₁(0, 0, 0), E₄(0, 1, 1), E₅(1, 0, 0), E₈(1, 1, 1) matrix eigenvalues can be transformed into the ESS evolutionary stability point under certain conditions, the four points are discussed, and the analysis of the three-party game of the evolution of the railway disaster prevention and monitoring data is carried out in four cases. When the parameters satisfy the condition one, the cost C₃ of the regulating department to carry out strict regulation is higher than the benefit D of the platform after strict regulation. cost C₃ is higher than the benefit D after strict regulation by the platform, the railway disaster prevention and monitoring data sharing parties A, B will tend to choose the strategy of non-honest sharing, and the three parties of the game will evolve in the direction of {non-strict regulation, non-honest sharing, and non-honest sharing} choices, i.e., the direction of point E₁(0, 0, 0). When the parameters satisfy condition two, the three parties of the game will evolve towards the choice of {non-strict regulation, honest sharing, honest sharing} i.e., point E₄(0, 1, 1). When the parameters satisfy condition three, the three parties of the game will evolve towards the choice of {strict regulation, non-honest sharing, non-honest sharing} i.e., point E₅(1, 0, 0). When the parameter condition IV. The three parties of the game will evolve towards the choice of {Strict Regulation, Honest Sharing, Honest Sharing}, i.e., the direction of point E₈(1, 1, 1).

Analysis of the direction of the tripartite evolution of railway monitoring data

The initial parameter assignments are shown in Table 5. In this section, the model of the evolutionary game is set to four groups, corresponding to the four cases of condition 1, condition 2, condition 3, and condition 4, respectively, and for each case, the simulation of the evolutionary game is carried out for 20 times, and the results of the evolutionary simulation are shown in Fig. 5.

Figure 5A shows through the assignment of parameters, when the conditions of $\mathrm{d}-C_3<\mathbf{0}$, $an-\mathrm{n}-\mathrm{C}<0$ are satisfied, the evolution direction of x, y, z is x tends to 0, y tends to 0, z tends to 0, respectively, and the evolution direction is consistent with the analysis results in Condition 1. In the case of satisfying the condition of Condition 1, the system will evolve in the direction of the point $E_1\mathbf{(}0,0,0\mathbf{)}$ and tends to be stabilized, i.e., the current evolutionary stabilization strategy is {non-strict regulation, honest sharing, honest sharing}, Fig. 5B shows when the conditions of $n-an-k_1{p}_1<0$, $C_2-C_3+C_2\ast d<0$ and $n-an-k_2{p}_1<0$ are satisfied, the evolution direction of x, y, and z is that x tends to 0, y tends to 1, and z tends to 1, respectively, and the evolution direction is consistent with the analysis results in Condition 2, and in the condition of Condition 2 is satisfied, the system will evolve in the direction of the point $E_4\mathbf{(}0,1,1\mathbf{)}$ and tends to be stabilized, i.e., the current evolution stabilization strategy is {non-strictly regulated, honestly sharing, honest sharing}.

Figure 5C through the assignment of parameters, when the conditions of $m-C-n+an<0$, $C_3<d$ are satisfied, the evolution direction of x, y, and z is x tends to 1, y tends to 0, and z tends to 0, respectively, and the evolution direction is in line with the analysis results in Condition 3, in the case of satisfying Condition 3, the system will evolve towards the point $E_5\mathbf{(}1,0,0\mathbf{)}$ and tend to be stabilized, i.e., the current evolutionary stabilization strategy is {strict regulation, non-honest sharing, non-honest sharing}. Figure 5D shows when the parameters satisfy $n-an-\mathrm{m}-k_1{p}_1<0$, $\mathrm{n}-\mathrm{m}+\mathrm{a}\mathrm{n}-k_2{p}_1<0$ and $C_3-C_2-C_2\ast \mathrm{d}<0$, the evolution direction of x, y and z is x tends to 1, y tends to 1 and z tends to 1, respectively, and the evolution direction is consistent with the analysis of condition 4, and in the case of satisfying condition 4, the system will evolve and stabilize towards the point $E_8\mathbf{(}1,1,1\mathbf{)}$, i.e., the current evolution stabilization strategy is {Strict Regulation, Honest Sharing, Honest Sharing}.

Figure 5 illustrate the evolutionary simulation results of the initial parameter settings to verify the validity of the blockchain-based tripartite evolutionary game stability analysis of railway disaster prevention and monitoring data sharing proposed in this article, where the system can dynamically regulate the parameters through the smart contract and the numerical relationship of the variables affects the evolutionary stability strategy of the railway disaster prevention and monitoring data sharing, which carries out the honest and active participation of railway disaster prevention and monitoring platforms in the data sharing process.

Analysis of parameters related to railway monitoring data sharers A and B

This section focuses on exploring the impact of different parameters on the specific incentive process of sharing railway disaster prevention and monitoring data. For the railway disaster prevention data sharing parties A and B, it mainly explores the impact of the parameters k related to the credibility value, as well as the masking cost N on the evolutionary game process. For the regulator, it mainly explores the impact of the cost C3 of strict supervision by the platform and the benefit D of strict supervision by the platform on the evolutionary game process.

Analysis of parameters related to creditworthiness

For the railway monitoring data platform, this section focuses on exploring the parameter $k$ of the reputation value Rep off, and the impact of illegal gains $N$ and cover-up cost $aN$ on the evolutionary game process with the railway disaster prevention data monitoring platforms A, B. The experimental parameters in this section are set as ${\mathrm{k}}_1=0.8$, $C_2=50,$ $D=60,$ $C_3=50$. ${\mathrm{p}}_1=100,$ $C=40,$ $\mathrm{m}=50,$ $\mathrm{a}=0.6,$ $\mathrm{N}=80,$ ${\mathrm{k}}_2=1.$ Keeping other parameters unchanged, changing the value of $k_1$, and observing the influence of the change of reputation value on the evolution process of railway monitoring data platform A. The experiments on $k_1$ in this section are divided into three parts, and the value intervals of $k_1$ are {0.8, 1, 1.2}, {1, 1.2, 1.6}, {0.4, 0.6, 0.8} in the simulation process of this section. Explore the effect of these three cases on the evolutionary game process, and set the parameters in such a way that both the three values in the credibility value Rep below 0.5, the three values above 0.5, and the three values above and below 0.5 are taken, set up the three control groups, and combine the three-dimensional and two-dimensional evolutionary processes, to make the simulation of the $k_1$ more adequate and more comprehensive.

It can be obtained from Fig. 6A that in the case where $k_1$ takes the value of {0.8, 1, 1.2}, which corresponds to the Rep reputation value of {0.4, 0.5, 0.6}, and from Fig. 6A, it can be obtained that in the case where the ${\mathrm{k}}_1$ value equals to 1 and 1.2, which corresponds to the scenarios where Rep reputation values are 0.5 and 0.6, the nodes with high reputation value tends to be in the evolutionarily stable state of {1, 0, 0} when the reputation value is larger than 0.5, the because the current situation has low masking cost and high cost of strict regulation by the platform, nodes with high reputation value tend to be tightly regulated by the system, while they may increase their revenue through dishonest behaviors. In Fig. 6B the node with ${\mathrm{k}}_1$ value of 0.8 tends to {1, 1, 1} evolutionary stable state, the current system honest sharing transaction gain is high, low reputation node tends to continue to carry out honest sharing to improve their reputation value, so as to maximize their revenue. The system nodes can dynamically adjust the relevant system parameters at this time, such as continuing to increase the honest sharing gains, increase the cost of masking and so on to continue to promote the nodes to carry out honest data sharing. Through the right diagram of Fig. 6B, it can be obtained that in the case of k₁ taking the value of {1, 1.2, 1.6}, corresponding to the Rep reputation value of {0.5, 0.6, 0.8}, at this time, all the nodes involved in the evolution of the nodes with high reputation value, due to their evolutionary incentives for the gain has been sufficient, and the masking cost is low, the nodes are inclined to {strict regulation, non-honest sharing, non-honest sharing} of the evolution of the stable state, and the higher the value of k₁ the tendency to {1, 0, 0} is stronger.

As can be seen from Fig. 6C, when k₁ takes the value of {0.4, 0.6, 0.8}, corresponding to the Rep reputation value of {0.2, 0.3, 0.4}, due to the current situation of carrying out honest data sharing based on the higher gains, for the nodes with low reputation value due to the lower reputation value, the additional gains based on honest data sharing is lower, the nodes tend to improve their reputation by carrying out honest sharing value, to obtain more honest sharing gains, so the nodes tend to {strict regulation, honest sharing, honest sharing} evolutionary stable state, and the lower the value of k₁, the tendency to {1, 1, 1} is stronger, the system at this time can carry out a positive intervention, prompting these low-reputation-value nodes to participate in the honest data sharing many times, to improve their gains and improve the node’s reputation value.

Analysis of parameters related to dishonest gains and masking costs

For the railway disaster prevention data monitoring platform, this section focuses on exploring the impact of the illicit gains N from dishonest sharing conducted by the disaster prevention data monitoring platform on the evolutionary game process, as N involves the masking cost of the nodes to conduct dishonest sharing. The experiments in this section set up two groups with different parameter settings as a control, and the base parameters of the two groups are: k₁ = 1, C2 = 50, D = 60, C3 = 50, p1 = 200, C = 40, m = 100, a = 0.5, n = 50, k₂ = 1; Keeping the other parameters constant and varying the value of N, the effect of the parameters of the illegal gains of the nodes on the evolutionary process. This section of the experiment is divided into two groups, the first group of parameter settings only satisfies condition four, the second group of parameter settings meets the conditions of condition three and condition four, to explore in the evolutionary direction tends to {1, 1, 1} and {1, 0, 0} direction of the process of the three values of N on the process of the evolutionary game, the first group of N value setting interval are {50, 70, 100}, the second group of N value setting interval are {100, 150, 200} setting three control groups.

As can be seen from Fig. 7, under the condition of satisfying condition four, i.e., the direction of the evolutionary game tends to {1, 1, 1}, and the evolutionary strategy is {strict regulation, honest sharing, honest sharing}, no matter the value of N is taken to be any one of the values of {50, 70, 100}, the direction of the system’s evolution tends to be {1, 1, 1}, and as can be seen in Fig. 7, the bigger the value of N is, the less the nodes tend to evolve in the direction of {1, 1, 1}, this is because the larger the value of N, the node’s gain from dishonest sharing increases, all other things being equal, nodes with larger values of N may tend to share dishonestly, while nodes with smaller values of N may tend to share honestly because the gain from dishonest sharing is relatively low, and at the same time, they have to pay the corresponding penalties.

When the set of parameters is set with different N values in satisfying condition four that is the direction of the evolutionary game tends to {1, 1, 1}, in satisfying condition three the direction of the evolutionary game tends to {1, 0, 0}, at N = 100 and 150 and and is consistent with the analytical results of Fig. 7 and N = 150 tends to be more slowly evolved than N = 100, which also agrees with the analytical process of Fig. 7. When N = 200, the direction of evolutionary game tends to {1, 0, 0}, which is because the node’s gain from performing dishonest sharing is large enough that it has exceeded the sum of the cover-up cost and the loss of the other party performing dishonest sharing, so the node tends to perform dishonest sharing to maximize the node’s gain. However, if the node carries out dishonest sharing for a long time, on the one hand, it is detrimental to its reputation value, and in the long run, it is also harmful to the revenue of the whole system. At this time, the system must modify the parameters, which can be adjusted to adjust the value of N or adjust the extra revenue of the node based on its reputation value to incentivize nodes to carry out honest data sharing, and to achieve the maximization of the nodes and the whole data-sharing incentive system.

Parametric analysis of regulatory sector-related benefits

For the railway regulator, this section focuses on exploring the impact of the gains D from strict regulation by the platform on the evolutionary game process. Two sets of experiments with different parameter settings are set up as controls in this section. the first set of parameters are: k₁ = 1, C₂ = 50, D = 50, C₃ = 20, p₁ = 200, C = 40, m = 50, a = 0.5, n = 80, k₂ = 1. The second set of experiments are set up with the following parameters: k₁ = 1, C₂ = 30, D = 50, C₃= 20, p₁ = 200, c = 40, m = 50, a = 0.5, n = 80, k₂ = 1; keep the other parameters unchanged, change the value of d, and observe the effect of the platform’s revenue parameters on the evolutionary process after strict regulation. The experiments in this section are divided into two groups, the parameter settings of the first group only satisfy condition three, and the parameter settings of the second group satisfy condition two and condition three, to explore the influence of three values of d on the evolutionary game process in the process of the evolutionary direction converging to the direction of {1, 1, 1} and {1, 0, 0}, and the d values of the two groups are set in the interval of {50, 100, 150}, and three control groups are set up to combine with the three-dimensional evolutionary diagrams, so as to make the simulation of d simulation more fully and comprehensively.

It can be seen that under the condition of satisfying condition three from Fig. 8A, i.e., the direction of the evolutionary game tends to {1, 1, 1}, and the evolutionary strategy is {Strict Regulation, Honest Sharing, Honest Sharing}, no matter the value of D is taken to be any one of the values of {50, 100, 150}, the direction of the system’s evolution is tending to {1, 1, 1}, and as the value of D increases, the nodes in the evolutionary game tend to {1, 1, 1} The trend is stronger, while the difference in the speed of convergence to {1, 1, 1} is not very obvious when D increases to a certain degree, which can be shown that the system can prompt the platform to carry out strict supervision by adjusting the platform’s revenue D after the platform is strictly supervised, thus prompting honest data sharing between railway monitoring platforms, while D can be adjusted to a certain value and then does not need to be increased, because in Fig. 8A The trend of evolution is close to the same when D is taken as 100, 150, and the convergence speed is obviously faster compared to D = 50, i.e., the system can reach a certain threshold by increasing D to prompt the platform to carry out strict supervision, and the nodes in the system will also converge towards the evolution direction of the ESS quickly, so as to provide more adequate theoretical support for the system to dynamically regulate the parameters.

It can be known from Fig. 8B, the group of parameter settings with different D values in the satisfaction of condition three that is, the direction of the evolutionary game tends to {1, 1, 1}, in the satisfaction of condition two, the direction of the evolutionary game tends to {1, 0, 0}, in the D = 100 and 150 time and with the results of the second group of analysis are consistent with the second group of results are similar convergence of the speed of evolution, tends to {1, 0, 0}, the evolutionary strategy for the {strict regulation, honesty sharing, honest sharing}. When D = 50, the parameter setting satisfies condition two, i.e., the evolution direction tends to {1, 0, 0}, and the evolution strategy is {strict regulation, non-honest sharing, non-honest sharing}, which indicates that the nodes of the evolutionary game tend to non-honest sharing when the platform’s gain from strict regulation is very low. The second set of results illustrates that changing the value of D can change the node selection strategy within the evolutionary game system, and the system can be changed by changing the platform’s strictly regulated revenue D dynamically regulates the stable direction of evolution. If the nodes within the platform maintain the evolutionary direction in the figure for a long time, the strategy combination is not beneficial either to the system as a whole or to the gains of the nodes of the railway disaster prevention and monitoring, at this time, the system is required to modify the parameters, to dynamically regulate the strategy and direction of the evolution, and to motivate the nodes to carry out honest data sharing, to achieve the maximization of the gains of the whole and the nodes of the two parts of the system.