Model game pricing method and system based on data utility and differential privacy

Abstract

The invention provides a model game pricing method and system based on data utility and differential privacy. The method comprises the following steps: constructing a game transaction model; the game transaction model is of a three-layer structure, the first layer is a model buyer, the second layer is a model broker, and the third layer is a data provider; respectively constructing profit functions of the model buyer, the model broker and the data provider; and modeling a Stackelberg game model, and solving to obtain an optimal pricing strategy meeting global optimum. According to the method, benefits of a data provider, a model broker and a model buyer are considered, and an optimal pricing strategy solving method with the maximum benefits of the three parties is provided and verified through experiments. The pricing based on the model is more efficient, more attention is paid to the value of the ML model derived from the data, finer pricing granularity is provided, and the demand for purchasing unnecessary data is eliminated. According to the invention, a more efficient and fair pricing mechanism is provided for the data market, and the development and innovation of the data market are promoted.

Description

Technical Field

[0001] The present invention belongs to the technical field of data processing, and specifically relates to a model game pricing method and system based on data utility and differential privacy. Background Art

[0002] Data is the core asset in the data-driven economic era, which has significantly promoted the rapid development of the data trading industry. Data pricing is to price data as an asset and ensure that data can be sold or purchased as a commodity in commercial and economic activities. The data market is a market where data is exchanged for income. A perfect data pricing system and a well-designed data market can widely promote data transactions.

[0003] In the process of data trading, the data value is different for different participants. Uncertain value index and neglect of interactivity will lead to information asymmetry in the transaction process. Therefore, it is necessary to establish a complete data pricing system to promote fair and efficient data trading.

[0004] For example, for a journalist or decision maker who is studying the relationship between demographics and economic indicators, he or she wants to test the predictive power of some demographic characteristics on average annual household income. Although there are data sets with this information online, they are expensive and far beyond the budget for writing reports or making economic decisions. Therefore, in this case, if the data sets are sold at a fixed price, individual buyers or small companies will not be able to obtain them, and the seller will not be able to earn income. However, if there is a data service model broker willing to sell an instance of a linear regression model with squared loss that can meet the above needs, and the price is affordable and willing to be paid by individual buyers or small companies, then the transaction will benefit all three parties. Therefore, how to make reasonable pricing so that buyers can charge according to the ML tasks they need and the expected accuracy of the model, buyers, sellers and model brokers can all benefit from it, which can greatly promote data sharing and the development of the data industry. Summary of the invention

[0005] In view of the defects of the prior art, the present invention provides a model game pricing method and system based on data utility and differential privacy, which can effectively solve the above problems.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The present invention provides a model game pricing method based on data utility and differential privacy, comprising the following steps:

[0008] Step S1, constructing a game transaction model; the game transaction model is a three-layer structure, the first layer is the model buyer, the second layer is the model broker, and the third layer is the data provider;

[0009] The number of data providers is n, denoted as data provider i, i = 1, 2, ..., n, and data provider i has original data z i ; Data provider i has access to original data z i Adopt Privacy Policyε i Perform privacy processing to obtain privacy protection data s i , and then sold to model brokers;

[0010] Model brokers follow the acquisition strategy price p s Purchase privacy-preserving data i , and privacy protection data i Perform feature engineering extraction, then train the data model to obtain a trained data model;

[0011] The model broker sells according to the selling strategy price p m Sell ​​the trained data model to the model buyer;

[0012] Step S2: construct the profit function Ψ of each data provider i i (p s ,ε i ), is about the acquisition strategy price p s and the privacy policy ε adopted by data provider i i The profit function of

[0013] Step S3, construct the profit function Ω(p m ,p s ,ε i ), is about the acquisition strategy price p s , selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of

[0014] Step S4, construct the model buyer's profit function Φ(p m ,ε i ), is about the selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of

[0015] Step S5, building a three-level Stackelberg game model:

[0016]

[0017]

[0018] in:

[0019] p m* Represents the selling strategy price adopted to maximize the model buyer's profit, which is the optimal selling strategy price;

[0020] p s * Represents the acquisition strategy price adopted to maximize the model broker's profit, which is the optimal acquisition strategy price;

[0021] ε i * It represents the privacy policy adopted when maximizing the benefits of data provider i while considering its privacy protection requirements, which is the optimal privacy policy;

[0022] Step S6, solving the Stackelberg game model to obtain the optimal pricing strategy that satisfies the global optimum <p m * ,p s * ,ε i * >, that is: when other participants do not change their pricing strategies, no single participant can increase its revenue by simply adjusting its optimal pricing strategy;

[0023] Through the optimal pricing strategy <p m * ,p s * ,ε i * >, pricing transactions between model buyers, model brokers, and data providers.

[0024] Preferably, in step S2, the profit function Ψ of data provider i is i (p s ,ε i )for:

[0025] Ψ i (p s ,ε i )=ξ i [ω(p s )]*p s *sv i *e i (ε i )-L i (ε i ) (1)

[0026] in:

[0027] Ψ i (p s ,ε i ): represents the adoption of privacy policy ε i and acquisition strategy price ps When , the profit of data provider i is the difference between the benefit obtained by data provider i from selling data and the cost caused to data provider i by data privacy leakage;

[0028] ξ i [ω(p s )]*p s *sv i *e i (ε i ) represents the benefits that data provider i obtains from selling data;

[0029] ω(p s ): represents the sensitivity of data provider i to changes in the acquisition strategy price. s The improvement of ω(p s ) continues to grow until it reaches a high critical value; as the acquisition strategy price p s The decrease of ω(p s ) continues to decrease until it reaches a lower critical value; ω(p s )=w i *p s , w i ≥0,w i is a parameter that adjusts the price sensitivity of data provider i;

[0030] ξ i [ω(p s )]: is the activation function, that is, a piecewise function of 0 and 1; when ω(p s ) reaches a high critical value, ξ i [ω(p s )]=1, indicating that data provider i is willing to sell its data; when ω(p s ) reaches a lower critical value, ξ i [ω(p s )] = 0, indicating that data provider i is unwilling to sell its data;

[0031] p s :Acquisition strategy price p s , meaning the data price per Shapley value;

[0032] sv i :Original data z i Shapley value of

[0033] e i (ε i ): indicates the adoption of privacy policy ε i When the original data z i The amount of added noise represents the level of privacy protection; 0≤ei (ε i )≤1;

[0034]

[0035] Where λ>0 represents the marginal growth rate of adjusting the sensitivity of data provider i to the privacy price, which is called the privacy sensitivity of data provider i; ρ i : represents the sensitivity of data provider i to privacy price, when 0≤ρ i When ρ < 1, it means that data provider i is not very sensitive to price changes; when ρ i When > 1, it means that data provider i is extremely sensitive to prices;

[0036] L i (ε i ): the loss function of the cost of data privacy leakage to data provider i;

[0037] L i (ε i )=θ i *ε i (3)

[0038] θ i Represents the coefficients of the loss function.

[0039] Preferably, in step S3, the profit function of the model broker Ω(p m ,p s ,ε i )for:

[0040] Ω(p m ,p s ,ε i )=p m *S sv -p s *S sv -T(S sv ) (4)

[0041] in:

[0042] p m *S sv Proceeds received from model buyers on behalf of model brokers;

[0043] p s *S sv represents the total amount paid to all data providers by the model broker;

[0044] T(S sv ) represents the cost required by the model broker to train the model;

[0045] S svRepresents the total Shapley value of data purchased from all data providers;

[0046] T(S sv )=α*S sv +β; where α is a variable in the system, α*S sv represents variable cost, and α>0; β is fixed cost, which is used to support the fixed expenses of model training process; T(S sv ) and S sv Positively correlated, when the Shapley value of the data added to the model increases, the model broker's training cost for the model also increases.

[0047] Preferably, in step S4, the model buyer's profit function Φ(p m ,ε i )for:

[0048] The model buyer's profit consists of the difference between the utility value estimate of the model after training with the acquired data and the fees paid to the intermediary and data provider:

[0049] Φ(p m ,ε i )=U(S sv )-p m *S sv (5)

[0050] in:

[0051] U(S sv ) represents the estimated expected utility of the model purchased by the model buyer, and is related to the total Shapley value S of the data sv Have a functional relationship;

[0052] p m *S sv Represents the total amount paid by the buyer of the model.

[0053] Preferably, U(S sv ) is calculated as:

[0054] U(S sv )=σln(1+S sv ) (6)

[0055] Among them: σ>1, is the system parameter;

[0056]

[0057] S sv About Privacy Policy i is an increasing function with decreasing marginal benefits; U(S sv ) With the total Shapley value S of the training data obtainedsv The corresponding growth will also increase with the improvement of the training data, but the speed of this growth decreases with the Shapley value S sv The accumulation of capital is slowed down and is defined as diminishing marginal utility.

[0058] Preferably, step S6 specifically comprises:

[0059] Step S6.1, determine the optimal privacy policy ε i * The expression is:

[0060] Profit function Ψ of data provider i i (p s ,ε i )=ξ i [ω(p s )]*p s *sv i *e i (ε i )-L i (ε i ) for ε i Perform the first-order derivative calculation. When the first-order derivative is 0, the solution is:

[0061]

[0062] Profit function Ψ i (p s ,ε i ) for ε i The second-order derivative is calculated and its second-order derivative is less than 0; this shows that the profit function Ψ i (p s ,ε i ) is a strictly convex function, and when the first-order derivative is 0, the unique optimal privacy policy ε is obtained i * ;

[0063] Step S6.2, determine the optimal acquisition strategy price p s * The expression is:

[0064] Replace ε in equation (19) i * Substituting into Ω(p m ,p s ,ε i )=p m *S sv -p s *S sv -T(S sv ) and converted to the following formula:

[0065]

[0066] Equation (20) for p s Calculate the first-order derivative:

[0067]

[0069] Where: Let the intermediate variable

[0070] make Solved

[0071] Equation (20) for p s Calculate the second-order derivative:

[0072]

[0073] It can be seen that Ω(p m ,p s ,ε i * ) is a strictly convex function and in The solution obtained is optimal and unique;

[0074] Step S6.3, determine the best selling strategy price p m * The expression is:

[0075] Will and Substituting into equation (7):

[0076]

[0077] S sv and ε i * Substitute Φ(p m ,ε i )=U(S sv )-p m *S sv middle:

[0078]

[0079] Let the intermediate variable Intermediate variables Then S sv =μ*p m -γ;

[0080] From equation (25), we get equation (26):

[0081] Φ(p m ,εi * )=σln(1+μ*p m -γ)-μ*p m 2 +γ*p m (26)

[0082] Let the intermediate variable but Therefore, solve the model buyer's optimal selling strategy price p m * The problem is transformed into the best strategy for solving Right now

[0083]

[0084] Formula (27) is Calculate the first-order derivative:

[0085]

[0086] Therefore, equation (27) is not a strictly convex function. We first need to determine monotonicity, and then find The intermediate variable that reaches the maximum value Therefore, let The solutions to the equation are all the solutions that satisfy the following equation:

[0087]

[0088] First determine whether the equation has a solution:

[0089] Calculate the difference Δ:

[0090] Δ=(2+γ) 2 -4*2*(γ-σ*μ)>(2-γ) 2 ≥0 (30)

[0091] Since Δ>0, equation (29) has two solutions;

[0092] When 2-γ≥0, the two roots and It is expressed as:

[0093]

[0094] When 2-γ<0, the two roots and It is expressed as:

[0095]

[0096] According to equations (31) to (34), it can be confirmed that Always holds true; therefore, according to the positive and negative characteristics of the derivative, the two roots and Substituting into equation (27), we can finally determine the monotonic interval of equation (26): It is monotonically increasing in the interval. Monotonically decreasing in the interval; It is monotonically increasing in the interval. Monotonically decreasing within the interval;

[0097] because so The best solution is That is: the best solution Therefore, according to The model buyer's optimal selling strategy price p m * for:

[0098]

[0099] Step S6.4, for data provider i, i=1,2,...,n, it has original data z i , determine the parameter ξ i [ω(p s )]、sv i ,λ,ρ i ,θ i , α, σ, so according to the model of equation (36), the buyer's optimal selling strategy price p m * The expression of the optimal selling strategy price p of the model buyer is obtained m * ;

[0100] The optimal selling strategy price p of the model buyer m * Substitute the value obtained in step S6.3 into The optimal acquisition strategy price p of the model broker is obtained s * ;

[0101] The optimal acquisition strategy price p of the model broker s * Substituting into equation (19) we can determine the optimal privacy policy ε for each data provider i i * The expression of ε is used to obtain the optimal privacy policy ε for each data provider i. i * ;

[0102] This achieves the optimal pricing strategy for data provider i, model brokers and model buyers.

[0103] The present invention also provides a system for the model game pricing method based on data utility and differential privacy, comprising:

[0104] The game trading model is a three-layer structure, the first layer is the model buyer, the second layer is the model broker, and the third layer is the data provider;

[0105] The number of data providers is n, denoted as data provider i, i = 1, 2, ..., n, and data provider i has original data z i ; Data provider i has access to original data z i Adopt Privacy Policyε i Perform privacy processing to obtain privacy protection data s i , and then sold to model brokers;

[0106] Model brokers follow the acquisition strategy price p s Purchase privacy-preserving data i , and privacy protection data i Perform feature engineering extraction, then train the data model to obtain a trained data model;

[0107] The model broker sells according to the selling strategy price p m Sell ​​the trained data model to the model buyer;

[0108] Profit function construction module, used to construct the profit function Ψ of each data provider i i (p s ,ε i ), is about the acquisition strategy price p s and the privacy policy ε adopted by data provider i i Profit function of the model broker; construct the profit function Ω(p m ,p s ,ε i ), is about the acquisition strategy price p s , selling strategy price p m and the privacy policy ε adopted by each data provider i i Profit function of the model; construct the buyer's profit function Φ(p m ,ε i ), is about the selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of

[0109] The Stackelberg game modeling module is used to model the Stackelberg game model including three levels:

[0110]

[0111]

[0112] in:

[0113] p m * Represents the selling strategy price adopted to maximize the model buyer's profit, which is the optimal selling strategy price;

[0114] p s * Represents the acquisition strategy price adopted to maximize the model broker's profit, which is the optimal acquisition strategy price;

[0115] ε i * It represents the privacy policy adopted when maximizing the benefits of data provider i while considering its privacy protection requirements, which is the optimal privacy policy;

[0116] A solution module is used to solve the Stackelberg game model to obtain the optimal pricing strategy that satisfies the global optimum. <p m * ,p s * ,ε i * >, that is: when other participants do not change their pricing strategies, no single participant can increase its revenue by simply adjusting its optimal pricing strategy;

[0117] Through the optimal pricing strategy <p m * ,p s * ,ε i * >, pricing transactions between model buyers, model brokers, and data providers.

[0118] The model game pricing method and system based on data utility and differential privacy provided by the present invention has the following advantages:

[0119] Based on the research on model pricing of data utility and privacy protection, the present invention constructs a model pricing framework based on Stackelberg game, takes into account the interests of data providers, model brokers and model buyers, proposes a solution method for the optimal pricing strategy with the maximum benefits for the three parties, and verifies it through experiments. The present invention promotes the expansion and innovation of the market, and is conducive to the realization of a fair and transparent data trading market. Compared with traditional data-based pricing methods, model-based pricing is more efficient, pays more attention to the value of ML models derived from data, provides finer pricing granularity, and eliminates the need to purchase unnecessary data. In short, the present invention provides a more efficient and fairer pricing mechanism for the data market, and promotes the development and innovation of the data market. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Figure 1 A schematic diagram of a game transaction model provided by the present invention;

[0121] Figure 2 The present invention provides Schematic diagram of the function graph of ;

[0122] Figure 3 A schematic diagram of the Shapley value of the diabetes data set provided by the present invention;

[0123] Figure 4 The ω(p s ) function diagram;

[0124] Figure 5 The ξ[ω(p s )] function diagram;

[0125] Figure 6 A schematic diagram of the model buyer's benefits provided by the present invention;

[0126] Figure 7 A schematic diagram of the model broker's earnings provided by the present invention;

[0127] Figure 8 A schematic diagram of the benefits provided by the data provided by the present invention;

[0128] Fig. 9 The present invention provides m and U(S sv ) relationship diagram;

[0129] Fig.10 A schematic diagram of the average Shapley value of the diabetes data set provided by the present invention at different levels of ε;

[0130] Fig.11A schematic diagram of the Shapley value of the 83rd data provided by the present invention at different levels of ε;

[0131] Fig.12 This is a relationship diagram between the total Shapley value of the data provided by the present invention and the model accuracy. DETAILED DESCRIPTION

[0132] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0133] As the market matures and the number of participants increases, there are higher requirements for fair and reasonable prices. This paper creates a comprehensive model that not only considers the maximization of model brokers' profits, but also the maximization of profits of data providers and model buyers, thus achieving a balance of interests among multiple parties in the market. By introducing advanced data quality measurement technology and dynamic data pricing models, a comprehensive pricing strategy that considers both differential privacy protection and data utility is proposed. Through simulation and numerical solution of public data sets, this paper not only theoretically proves the effectiveness of the method, but also provides a new pricing mechanism design idea for the data market.

[0134] Based on the research on model pricing of data utility and privacy protection, the present invention constructs a model pricing framework based on Stackelberg game, takes into account the interests of data providers, model brokers and model buyers, proposes a solution method for the optimal pricing strategy with the maximum benefits for the three parties, and verifies it through experiments. The present invention promotes the expansion and innovation of the market, and is conducive to the realization of a fair and transparent data trading market. Compared with traditional data-based pricing methods, model-based pricing is more efficient, pays more attention to the value of ML models derived from data, provides finer pricing granularity, and eliminates the need to purchase unnecessary data. In short, the present invention provides a more efficient and fairer pricing mechanism for the data market, and promotes the development and innovation of the data market.

[0135] The present invention provides a model game pricing method based on data utility and differential privacy, such as Figure 1 As shown, the following steps are included:

[0136] Step S1: constructing a game transaction model; the game transaction model is a three-layer structure, the first layer is the model buyer, the second layer is the model broker, and the third layer is the data provider;

[0137] The number of data providers is n, denoted as data provider i, i = 1, 2, ..., n, and data provider i has original data zi ; Data provider i has access to original data z i Adopt Privacy Policyε i Perform privacy processing to obtain privacy protection data s i , and then sold to model brokers;

[0138] Model brokers follow the acquisition strategy price p s Purchase privacy-preserving data i , and privacy protection data i Perform feature engineering extraction, then train the data model to obtain a trained data model;

[0139] The model broker sells according to the selling strategy price p m Sell ​​the trained data model to the model buyer;

[0140] Specifically, Figure 1 As shown in the figure, first, the data provider collects, stores and maintains the original data, selects a strategy for selling the data, obtains privacy-preserving data, and sells the privacy-preserving data to the model broker; secondly, the model broker purchases a certain unit size of privacy-preserving data from the data provider, then performs feature engineering, and trains the processed data according to the data utility and data privacy level to obtain a data model, and sells it to the model buyer; after that, the model buyer can choose to purchase data models with different data utilities, different data privacy levels, and different data sizes after being processed by the model broker according to their needs and purchasing strategies.

[0141] The present invention models the utility functions (profit functions) of the data provider, the model broker and the model buyer to construct a real and fair profit function.

[0142] Step S2, profit function of data provider

[0143] Construct the profit function Ψ for each data provider i i (p s ,ε i ), is about the acquisition strategy price p s and the privacy policy ε adopted by data provider i i The profit function of

[0144] The profit of data provider i comes from the difference between the income from selling data and the loss caused by its privacy leakage. It can be expressed as:

[0145] Ψ i (p s ,ε i )=ξ i [ω(p s )]*p s *svi *e i (ε i )-L i (ε i ) (1)

[0146] The first part represents the benefits that data provider i obtains by selling data, that is, the income that the data seller can obtain by selling data;

[0147] Ψ i (p s ,ε i ): represents the adoption of privacy policy ε i and acquisition strategy price p s When , the profit of data provider i is the difference between the benefit obtained by data provider i from selling data and the cost caused to data provider i by data privacy leakage;

[0148] ξ i [ω(p s )]*p s *sv i *e i (ε i ) represents the benefits that data provider i obtains from selling data;

[0149] ω(p s ): represents the sensitivity of data provider i to changes in the acquisition strategy price. s The improvement of ω(p s ) continues to grow until it reaches a high critical value, resulting in ξ(·) = 1; as the acquisition strategy price p s The decrease of ω(p s ) continues to decrease until it reaches a lower critical value; ω(p s )=w i *p s , w i ≥0,w i is a parameter that adjusts the price sensitivity of data provider i; it indicates the response of data provider i to price changes. s Next, ω(p s ) is larger, the greater the possibility that ξ(·)=1, and the higher w i This means a higher willingness to sell, which increases the likelihood of selling the data.

[0150] ξ i [ω(p s )]: is the activation function, that is, a piecewise function of 0 and 1; when ω(p s ) reaches a high critical value, ξ i [ω(p s)]=1, indicating that data provider i is willing to sell its data; when ω(p s ) reaches a lower critical value, ξ i [ω(p s )] = 0, indicating that data provider i is unwilling to sell its data;

[0151] p s :Acquisition strategy price p s , meaning the data price per Shapley value;

[0152] sv i :Original data z i Shapley value of

[0153] e i (ε i ): indicates the adoption of privacy policy ε i When the original data z i The amount of added noise represents the level of privacy protection; 0≤e i (ε i )≤1; specific, e i (ε i ) reflects the protection level of ε-differential privacy, where ε i (0≤ε i ≤1), a lower value means stronger privacy protection. i The smaller the value of , the more noise is added to the data, and thus the less compensation is paid to the data provider.

[0154] Due to e i (ε i ) has a value range of 0≤e i (ε)≤1, and sv i *e i (ε i ) means that the data z i The Shapley value that can be expressed after adding ε-differential privacy. i (ε i ) can directly reflect the amount of noise added to the data, that is, the level of privacy protection. i =1, e i (ε i ) must also satisfy e i (ε i )=1, which means no privacy protection is done for the data. i = 0, e i (ε i ) must also satisfy e i (ε i)=0, it means that a large amount of privacy protection has been added to the data, which will make the purchased data unable to provide effective accuracy contribution in model training, that is, it has no value.

[0155] When using differential privacy protection technology, the utility of the data may be lost to a certain extent, because the goal of differential privacy protection is to protect the privacy of individual data by adding noise or disturbance. The Shapley value can explain the utility and accuracy of the model trained under the differential privacy setting. The present invention uses the Laplace mechanism to add noise perturbations of different differential privacy protection levels to different data sets, and calculates the corresponding Shapley value. In the experiment, the present invention fits the functional relationship with the Shapley value in different scenarios. In the differential privacy model evaluation, by using the Shapley value to explain the prediction results of the model, we can understand the changes in the utility of the data after privacy protection, and help determine which data in the privacy protection model is critical to the model performance, so as to better balance the trade-off between privacy and practicality.

[0156] The inventor has studied that if more noise is injected into the training data, the Shapley value of the data will decrease nonlinearly, and the rate of decrease will become slower and slower. In view of this marginal decreasing feature, the present invention adopts the form of square root function to fit this trend, and i (ε i ) function uses the following expression:

[0157]

[0158] Where: λ>0, represents the marginal growth rate of adjusting the sensitivity of data provider i to the privacy price, called the privacy sensitivity of data provider i; ρ i : represents the sensitivity of data provider i to privacy price, when 0≤ρ i When ρ < 1, it means that data provider i is not very sensitive to price changes; when ρ i When > 1, it means that data provider i is extremely sensitive to prices;

[0159] The second part is the loss function L involving the cost of data privacy leakage to data provider i i (ε i ),

[0160] L i (ε i )=θ i *ε i (3)

[0161] Where L i (ε i ) is a random iA monotonically increasing, differentiable generalized convex function, that is, a linear function. θ i Represents the coefficient of the loss function, θ i ≥0, as ε i The growth of L i (ε i ) will also increase, and its growth rate will not change.

[0162] Step S3, profit function of model broker

[0163] Construct the model broker's profit function Ω(p m ,p s ,ε i ), is about the acquisition strategy price p s , selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of

[0164] The profit function of the model broker Ω(p m ,p s ,ε i )for:

[0165] Ω(p m ,p s ,ε i )=p m *S sv -p s *S sv -T(S sv ) (4)

[0166] The first part is the total revenue obtained by the model buyer, the second part is the total amount paid to the data provider, and the third part is the cost required by the model broker to train the model.

[0167] That is: p m *S sv Proceeds received from model buyers on behalf of model brokers;

[0168] p s *S sv represents the total amount paid to all data providers by the model broker;

[0169] T(S sv ) represents the cost required by the model broker to train the model;

[0170] S sv Represents the total Shapley value of data purchased from all data providers;

[0171] T(S sv )=α*S sv+β, where α is a variable in the system, α*S sv represents variable cost, and α>0. β is fixed cost, which is used to support the fixed expenses of model training process. As the middle layer of model Stackelberg game pricing, after the model broker purchases the data from the data provider, it cleans and analyzes the data. The cost of processing data of different quality is different. The higher the data quality requirement, the higher the cost. Therefore, T(S sv ) and S sv Positively correlated, when the Shapley value of the data added to the model increases, the model broker's training cost for the model also increases.

[0172] Step S4, model buyer's profit function

[0173] Construct the model buyer's profit function Φ(p m ,ε i ), is about the selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of the model buyer is composed of the difference between the utility value estimate of the model after training with the acquired data and the fees paid to the intermediary and data provider:

[0174] Φ(p m ,ε i )=U(S sv )-p m *S sv (5)

[0175] Part I U(S sv ) reflects the estimated value of the expected utility of the data model obtained by the model buyer through the purchased data training, which is consistent with the total Shapley value S of the data. sv There is a certain functional relationship. m *S sv is the total payment made by the buyer of the model.

[0176] Utility function U(S sv ) is a strictly concave function that is monotonically increasing and differentiable.

[0177] U(S sv )=σln(1+S sv ) (6)

[0178] Where σ>1 is a system parameter. In the above formula:

[0179]

[0180] S sv About Privacy Policy iis an increasing function with decreasing marginal benefits. sv ) With the total Shapley value S of the training data obtained sv The corresponding growth will also increase with the improvement of the training data, but the speed of this growth will vary with the Shapley value S of the training data. sv The accumulation of marginal utility is slowed down, a phenomenon defined as diminishing marginal utility.

[0181] Step S5: Modeling a three-level Stackelberg game model

[0182] It is crucial to determine the pricing mechanism between data providers, model brokers, and model buyers in the model market. This needs to take into account the maximization of the interests of all parties while ensuring the fairness and sustainability of the market. <p m * ,p s * ,ε i * >Modeled as a three-level Stackelberg game.

[0183] In this structure, the model buyer is at the top and plays a leading role, the model broker at the second level is both a subordinate of the model buyer and a leader of the data provider, obeying the model buyer and guiding the data provider, while the data provider at the bottom plays the role of a follower. The main purpose of each participant is to optimize its own income through strategy adjustment.

[0184] Model buyer at the first level:

[0185] Model Agent (8)

[0186] Model brokers at the second level:

[0187]

[0188] The third layer of data providers:

[0189]

[0190] p m * Represents the selling strategy price adopted to maximize the model buyer's profit, which is the optimal selling strategy price;

[0191] p s * Represents the acquisition strategy price adopted to maximize the model broker's profit, which is the optimal acquisition strategy price; ε i *It represents the privacy policy adopted when maximizing the benefits of data provider i while considering its privacy protection requirements, which is the optimal privacy policy;

[0192] In the game model, the goal is to find the best pricing strategy <p m * ,p s * ,ε i * >, and the strategy should satisfy global optimality, that is, when other participants do not change their pricing strategies, no single participant can increase its own benefits by simply adjusting its optimal pricing strategy. Global optimality can also be described as follows:

[0193]

[0194] Step S6, solving the optimal pricing strategy

[0195] Solve the Stackelberg game model to obtain the optimal pricing strategy that satisfies the global optimum <p m * ,p s * ,ε i * >, that is: when other participants do not change their pricing strategies, no single participant can increase its revenue by simply adjusting its optimal pricing strategy;

[0196] Through the optimal pricing strategy <p m * ,p s * ,ε i * >, pricing transactions between model buyers, model brokers, and data providers.

[0197] By giving the profit functions of the model buyer, model broker, and data provider, we then calculate the specific derivation process of the optimal pricing strategy for the unit data purchase price and model price, and analyze the optimality and uniqueness of the Stackelberg equilibrium solution.

[0198] In order to find the best pricing method for the set of equations, backward induction is used to derive the best pricing strategy <p m * ,p s * ,ε i * >. First, determine the purchase price p of data provider i at the third stage. s The optimal pricing scheme under i *Then, in the second stage, the model broker analyzes the purchase price p set by the model buyer. m The ideal incentive price p s * Finally, we go back to the first stage to calculate the ideal incentive price p for the model buyer. m * The detailed derivation process is as follows.

[0199] Step S6.1, determine the optimal privacy policy ε i * The expression is:

[0200] First, the profit function of data provider i is

[0201] Ψ i (p s ,ε i )=ξ i [ω(p s )]*p s *sv i *e i (ε i )-L i (ε i ) (14)

[0202] Rewritten as:

[0203]

[0204] Then, in equation (16), i Calculate the first-order derivative:

[0205]

[0206] and When

[0207] And the second-order derivative calculation:

[0208]

[0209] This shows that i (p s ,ε i ) is a strictly convex function and in The corresponding ε i Therefore, in the third stage, facing the price p arbitrarily proposed by the model broker, s In the case of , the optimal pricing for data provider i is:

[0210]

[0211] Step S6.2, determine the optimal acquisition strategy price p s * The expression is:

[0212] First, the ε obtained above is i * Substituting into the equation Ω(p m ,p s ,ε i )=p m *S sv -p s *S sv -T(S sv ) and convert it to:

[0213]

[0214] Next, in equation (20), s Calculate the first-order derivative:

[0215]

[0216] Let the intermediate variable

[0217] make Solved

[0218] And equation (20) for p s Calculate the second-order derivative:

[0219]

[0220] This means that Ω(p m ,p s ,ε i * ) is a strictly convex function and in The solution obtained is optimal and unique.

[0221] Therefore, in the second stage, facing any model buyer's purchase price p m Under the premise of s * for:

[0222]

[0223] Step S6.3, determine the best selling strategy price p m * The expression is:

[0224] In the first stage, the model buyer’s optimal pricing decision pm * for:

[0225]

[0226] Among them, the intermediate variable

[0227] The proof is as follows:

[0228] First, and Substituting into the following formula,

[0229]

[0230] Then S sv and ε i * Substituting into the following formula, we get

[0231]

[0232] To simplify the calculation, let the intermediate variable Intermediate variables Then S sv =μ*p m -γ

[0233] From equation (25), we get equation (26):

[0234] Φ(p m ,ε i * )=σln(1+μ*p m -γ)-μ*p m 2 +γ*p m (26)

[0235] Let the intermediate variable but Then solve the model buyer's optimal strategy p m * The problem is transformed into solving the best strategy Right now

[0236]

[0237] Formula (27) Calculate the first-order derivative:

[0238]

[0239] Equation (27) is not a strictly convex function, so we first need to determine monotonicity, and then find Reaching the maximum Then, let The solutions to the equation are all the solutions that satisfy the following equation:

[0240]

[0241] First determine whether the equation has a solution: calculate the difference formula Δ:

[0242] Δ=(2+γ) 2 -4*2*(γ-σ*μ)>(2-γ) 2 ≥0 (30)

[0243] Since Δ>0, equation (29) has two solutions.

[0244] When 2-γ≥0, the two roots and It can be expressed as:

[0245]

[0246] When 2-γ<0, the two roots and It can be expressed as:

[0247]

[0248]

[0249] According to equations (31) to (34), it can be confirmed that Therefore, according to the positive and negative characteristics of the derivative, the two roots and Substituting into equation (27), we can finally determine the monotonic interval of equation (26): It is monotonically increasing in the interval. It decreases monotonically in the interval. It is monotonically increasing in the interval. The interval is monotonically decreasing. Finally, we get Figure 2 About The function graph of .

[0250] because so The best solution is That is: the best solution Therefore, according to Based on the above analysis, the optimal pricing strategy for the model buyer can be determined as:

[0251]

[0252] For data provider i, i=1,2,...,n, it has original data z i , determine the parameter ξ i [ω(p s )]、sv i ,λ,ρ i ,θ i , α, σ, so according to the model of equation (36), the buyer's optimal selling strategy price p m * The expression of the optimal selling strategy price p of the model buyer is obtained m * ;

[0253] The optimal selling strategy price p of the model buyer m * Substitute the value obtained in step S6.3 into The optimal acquisition strategy price p of the model broker is obtained s * ;

[0254] The optimal acquisition strategy price p of the model broker s * Substituting into equation (19) we can determine the optimal privacy policy ε for each data provider i i * The expression of ε is used to obtain the optimal privacy policy ε for each data provider i. i * ;

[0255] This achieves the optimal pricing strategy for data provider i, model brokers and model buyers.

[0256] The present invention also provides a model game pricing system based on data utility and differential privacy, comprising:

[0257] The game trading model is a three-layer structure, the first layer is the model buyer, the second layer is the model broker, and the third layer is the data provider;

[0258] The number of data providers is n, denoted as data provider i, i = 1, 2, ..., n, and data provider i has original data z i ; Data provider i has access to original data z i Adopt Privacy Policyε i Perform privacy processing to obtain privacy protection data s i , and then sold to model brokers;

[0259] Model brokers follow the acquisition strategy price p s Purchase privacy-preserving data i , and privacy protection data iPerform feature engineering extraction, then train the data model to obtain a trained data model;

[0260] The model broker sells according to the selling strategy price p m Sell ​​the trained data model to the model buyer;

[0261] Profit function construction module, used to construct the profit function Ψ of each data provider i i (p s ,ε i ), is about the acquisition strategy price p s and the privacy policy ε adopted by data provider i i Profit function of the model broker; construct the profit function Ω(p m ,p s ,ε i ), is about the acquisition strategy price p s , selling strategy price p m and the privacy policy ε adopted by each data provider i i Profit function of the model; construct the buyer's profit function Φ(p m ,ε i ), is about the selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of

[0262] The Stackelberg game modeling module is used to model the Stackelberg game model including three levels:

[0263]

[0264] in:

[0265] p m * Represents the selling strategy price adopted to maximize the model buyer's profit, which is the optimal selling strategy price;

[0266] p s * Represents the acquisition strategy price adopted to maximize the model broker's profit, which is the optimal acquisition strategy price;

[0267] ε i * It represents the privacy policy adopted when maximizing the benefits of data provider i while considering its privacy protection requirements, which is the optimal privacy policy;

[0268] A solution module is used to solve the Stackelberg game model to obtain the optimal pricing strategy that satisfies the global optimum. <p m * ,ps * ,ε i * >, that is: when other participants do not change their pricing strategies, no single participant can increase its revenue by simply adjusting its optimal pricing strategy;

[0269] Through the optimal pricing strategy <p m * ,p s * ,ε i * >, pricing transactions between model buyers, model brokers, and data providers.

[0270] Experiment and analysis

[0271] This example experiment uses a real diabetes data set, with a total of 768 data, each with 8 features and 1 corresponding classification label. The data set contains 268 diabetic patient records and 500 non-diabetic patient records. The machine learning model trained is a support vector machine, and the scoring indicator V() uses the prediction accuracy.

[0272] First, the Shapley value of each training data is calculated using the fast Monte Carlo truncated sampling method. The results are as follows: Figure 3 .

[0273] In the experimental setup, ξ i [ω(p s )] is set to

[0274]

[0275] First, according to ω(p s )=w i *p s Calculate ω(p s ). In the experiment, we set w i is the coefficient of each data provider randomly selected from the interval [0,10]. For example, when w i is equal to 1, ω(p s )’s changing trend is as follows Figure 4 Then calculate the data provider's willingness to sell ξ i [ω(p s )]. According to the setting of formula (37), combined with Figure 5 It can be observed that the data provider is in ω(p s ) is not less than 1, and is willing to sell noisy data; otherwise, it is unwilling to provide. In addition, ρ i Set in the range [0,2]. The cost function parameter θ of the data provider iThe model broker's cost parameter α is between [0.1, 1.0], and the other cost parameter β and the parameter σ of the model buyer's profit function are both non-negative unbounded variables, with an interval of [0, ∞).

[0276] Figure 6 The relationship between the interests of the model buyer and the data privacy protection at different ε levels and the utility function parameter σ is revealed. m The diagram shows that, although ε i Under the specific condition that σ is 0, the model buyer's profit is zero, but as σ increases, the model buyer's interest also increases. Under the same utility function, the improvement of the privacy protection level of the data provider (the less noise added) will also increase the model buyer's profit.

[0277] Figure 7 Presents the purchase price of Shapley data in a specific unit p m Under different ε i Levels of privacy protection and different purchase prices s Impact on model broker income. Assume that the Shapley data purchase price of the model buyer is p m = 10, and assuming α = 0.1, β = 0. The figure shows that as p s As the privacy protection level remains unchanged, the model broker's profit will decrease. s When stable, the improvement in privacy level increases the utility of data and the income of model brokers also increases accordingly.

[0278] Figure 8 It shows how the revenue of data providers varies with p s When p s does not exceed a certain threshold p s 1 When ξ(·)=0, the data provider is unwilling to sell its data; when p s More than p s 1 When the data provider is willing to sell, and p s The higher the value, the less noisy the data. However, as the privacy protection level decreases, the loss caused by privacy leakage also increases. s Reach p s 2 When , the data provider's profit is maximized.

[0279] According to formula (23), Fig. 9 The Shapley data for the model buyer shows the purchase price p mThe relationship between the total Shapley value of purchasing all data at this price. The diagram shows that under the influence of the training cost of the model broker and the willingness function ξ(·) of the data provider, at p m Not exceeding a certain value p m 1 Under the condition of p, the total amount of data that the model buyer can purchase is zero. m The increase in sv will lead to a linear increase in the amount of data, because the slope of the straight line function is changed from sv i ,λ,ρ i ,θ i These fixed parameters determine the slope. Therefore, the slope does not change. m Increase to p m 2 When the model buyer can purchase training data U(S sv ) reaches its upper limit. On the other hand, a sufficiently high p m Make most of the data providers have ξ(·) = 1, and ε i =1, even if p is increased m No more useful data will be obtained.

[0280] Fig.10 This paper studies the relationship between different levels of ε and Shapley value after adding differential privacy protection to the entire diabetes dataset. ε=[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0] noise, where ε=1.0 means no noise is added, that is, the original dataset. The average Shapley value of the dataset is calculated after adding noise of different protection levels. Fig.11 Taking the 83rd data (the original data has a large Shapley value) as an example, when no noise is added to other data, the Shapley value of this data decreases after adding noise of different privacy protection levels to this data. This shows that as the noise increases, the data utility decreases, and the Shapley value also decreases accordingly.

[0281] Finally, the data utility of different data subsets, that is, the relationship between the total Shapley value and the model accuracy, is studied. Fig.12 The figure shows the relationship between the total Shapley value and the model accuracy when using a support vector machine for binary classification training model, using subsets with different total Shapley values ​​as training sets. In general, the higher the Shapley value, the better the model accuracy, but it is not monotonically increasing. This shows that model accuracy does not always improve with the increase in the amount of training data, but is also affected by diminishing marginal returns.

[0282] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be considered as the scope of protection of the present invention.

Claims

1. A model game pricing method based on data utility and differential privacy, characterized in that: The following steps are involved: Step S1, constructing a game transaction model; the game transaction model is a three-layer structure, the first layer is the model buyer, the second layer is the model broker, and the third layer is the data provider; The number of data providers is n, denoted as data provider i, i = 1, 2, ..., n, and data provider i has original data z i ; Data provider i has access to original data z i Adopt Privacy Policyε i Perform privacy processing to obtain privacy protection data s i , and then sold to model brokers; Model brokers follow the acquisition strategy price p s Purchase privacy-preserving data i , and privacy protection data i Perform feature engineering extraction, then train the data model to obtain a trained data model; The model broker sells according to the selling strategy price p m Sell ​​the trained data model to the model buyer; Step S2: construct the profit function Ψ of each data provider i i (p s ,ε i ), is about the acquisition strategy price p s and the privacy policy ε adopted by data provider i i The profit function of Step S3, construct the profit function Ω(p m ,p s ,ε i ), is about the acquisition strategy price p s , selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of Step S4, construct the model buyer's profit function Φ(p m ,ε i ), is about the selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of Step S5, building a three-level Stackelberg game model: in: p m * Represents the selling strategy price adopted to maximize the model buyer's profit, which is the optimal selling strategy price; p s * Represents the acquisition strategy price adopted to maximize the model broker's profit, which is the optimal acquisition strategy price; ε i * It represents the privacy policy adopted when maximizing the benefits of data provider i while considering its privacy protection requirements, which is the optimal privacy policy; Step S6, solving the Stackelberg game model to obtain the optimal pricing strategy that satisfies the global optimum <p m * ,p s * ,ε i * >, that is: when other participants do not change their pricing strategies, no single participant can increase its revenue by simply adjusting its optimal pricing strategy; Through the optimal pricing strategy <p m * ,p s * ,ε i * >, pricing transactions between model buyers, model brokers, and data providers.

2. A model game pricing method based on data utility and differential privacy according to claim 1, characterized in that: In step S2, the profit function Ψ of data provider i i (p s ,ε i )for: P i (p s ,he i )=ξ i [ω(p s )]*p s *sv i *e i (e i )-L i (e i ) (1) in: Ψ i (p s ,ε i ): represents the adoption of privacy policy ε i and acquisition strategy price p s When , the profit of data provider i is the difference between the benefit obtained by data provider i from selling data and the cost caused to data provider i by data privacy leakage; ξ i [ω(p s )]*p s *sv i *e i (ε i ) represents the benefits that data provider i obtains from selling data; ω(p s ): represents the sensitivity of data provider i to changes in the acquisition strategy price. s The improvement of ω(p s ) continues to grow until it reaches a high critical value; as the acquisition strategy price p s The decrease of ω(p s ) continues to decrease until it reaches a lower critical value; ω(p s )=w i *p s , w i ≥0,w i is a parameter that adjusts the price sensitivity of data provider i; ξ i [ω(p s )]: is the activation function, that is, a piecewise function of 0 and 1; when ω(p s ) reaches a high critical value, ξ i [ω(p s )]=1, indicating that data provider i is willing to sell its data; when ω(p s ) reaches a lower critical value, ξ i [ω(p s )] = 0, indicating that data provider i is unwilling to sell its data; p s :Acquisition strategy price p s , meaning the data price per Shapley value; sv i : Original data z i Shapley value of e i (ε i ): indicates the adoption of privacy policy ε i When the original data z i The amount of added noise represents the level of privacy protection; 0≤e i (ε i )≤1; Where λ>0 represents the marginal growth rate of adjusting the sensitivity of data provider i to the privacy price, which is called the privacy sensitivity of data provider i; ρ i : represents the sensitivity of data provider i to privacy price, when 0≤ρ i When ρ < 1, it means that data provider i is not very sensitive to price changes; when ρ i When > 1, it means that data provider i is extremely sensitive to prices; L i (ε i ): the loss function of the cost of data privacy leakage to data provider i; L i (e i )=θ i *e i (3) θ i Represents the coefficients of the loss function.

3. The model game pricing method based on data utility and differential privacy according to claim 1, characterized in that: In step S3, the profit function of the model broker Ω(p m ,p s ,ε i )for: Ω(p m ,p s ,ε i )=p m *S sv -p s *S sv -T(S sv ) (4) in: p m *S sv Proceeds received from model buyers on behalf of model brokers; p s *S sv represents the total amount paid to all data providers by the model broker; T(S sv ) represents the cost required by the model broker to train the model; S sv Represents the total Shapley value of data purchased from all data providers; T(S sv )=α*S sv +β; where α is a variable in the system, α*S sv represents variable cost, and α>0; β is fixed cost, which is used to support the fixed expenses of model training process; T(S sv ) and S sv Positively correlated, when the Shapley value of the data added to the model increases, the model broker's training cost for the model also increases.

4. The model game pricing method based on data utility and differential privacy according to claim 1, characterized in that: In step S4, the model buyer's profit function Φ(p m ,ε i )for: The model buyer's profit consists of the difference between the utility value estimate of the model after training with the acquired data and the fees paid to the intermediary and data provider: Φ(p m ,he i )=U(S sv )-p m *S sv (5) in: U(S sv ) represents the estimated expected utility of the model purchased by the model buyer, and is related to the total Shapley value S of the data sv Have a functional relationship; p m *S sv Represents the total amount paid by the buyer of the model.

5. A model game pricing method based on data utility and differential privacy according to claim 4, characterized in that: U(S sv ) is calculated as: U(S sv )=σln(1+S sv ) (6) Among them: σ>1, is the system parameter; S sv About Privacy Policy i is an increasing function with decreasing marginal benefits; U(S sv ) With the total Shapley value S of the obtained training data sv The corresponding growth will also increase with the improvement of the training data, but the speed of this growth decreases with the Shapley value S sv The accumulation of capital is slowed down and is defined as diminishing marginal utility.

6. A model game pricing method based on data utility and differential privacy according to claim 4, characterized in that: Step S6 is specifically as follows: Step S6.1, determine the optimal privacy policy ε i * The expression is: Profit function Ψ of data provider i i (p s ,ε i )=ξ i [ω(p s )]*p s *sv i *e i (ε i )-L i (ε i ) for ε i Perform the first-order derivative calculation. When the first-order derivative is 0, the solution is: Profit function Ψ i (p s ,ε i ) for ε i The second-order derivative is calculated and its second-order derivative is less than 0; this shows that the profit function Ψ i (p s ,ε i ) is a strictly convex function, and when the first-order derivative is 0, the unique optimal privacy policy ε is obtained i * ; Step S6.2, determine the optimal acquisition strategy price p s * The expression is: Replace ε in equation (19) i * Substituting into Ω(p m ,p s ,ε i )=p m *S sv -p s *S sv -T(S sv ) and converted to the following formula: Equation (20) for p s Calculate the first-order derivative: Where: Let the intermediate variable make Solved Equation (20) for p s Calculate the second-order derivative: It can be seen that Ω(p m ,p s ,ε i * ) is a strictly convex function and in The solution obtained is optimal and unique; Step S6.3, determine the best selling strategy price p m * The expression is: Will and Substituting into equation (7): S sv and ε i * Substitute Φ(p m ,ε i )=U(S sv )-p m *S sv middle: Let the intermediate variable Intermediate variables Then S sv =μ*p m -γ; From equation (25), we get equation (26): Φ(p m ,he i * )=σln(1+μ*p m -c)-μ*p m 2 +γ*p m (26) Let the intermediate variable but Therefore, solve the model buyer's optimal selling strategy price p m * The problem is transformed into the best strategy for solving Right now Formula (27) is Calculate the first-order derivative: Therefore, equation (27) is not a strictly convex function. We first need to determine monotonicity, and then find The intermediate variable that reaches the maximum value Therefore, let The solutions to the equation are all the solutions that satisfy the following equation: First determine whether the equation has a solution: Calculate the difference Δ: Δ=(2+γ) 2 -4*2*(γ-σ*μ)>(2-γ) 2 ≥0 (30) Since Δ>0, equation (29) has two solutions; When 2-γ≥0, the two roots and It is expressed as: When 2-γ<0, the two roots and It is expressed as: According to equations (31) to (34), it can be confirmed that Always holds true; therefore, according to the positive and negative characteristics of the derivative, the two roots and Substituting into equation (27), we can finally determine the monotonic interval of equation (26): It is monotonically increasing in the interval. Monotonically decreasing in the interval; It is monotonically increasing in the interval. Monotonically decreasing within the interval; because so The best solution is That is: the best solution Therefore, according to The model buyer's optimal selling strategy price p m * for: Step S6.4, for data provider i, i=1,2,...,n, it has original data z i , determine the parameter ξ i [ω(p s )]、sv i ,λ,ρ i ,θ i , α, σ, so according to the model of equation (36), the buyer's optimal selling strategy price p m * The expression of the optimal selling strategy price p of the model buyer is obtained m * ; The optimal selling strategy price p of the model buyer m * Substitute the value obtained in step S6.3 into The optimal acquisition strategy price p of the model broker is obtained s * ; The optimal acquisition strategy price p of the model broker s * Substituting into equation (19) we can determine the optimal privacy policy ε for each data provider i i * The expression of ε is used to obtain the optimal privacy policy ε for each data provider i. i * ; This achieves the optimal pricing strategy for data provider i, model brokers and model buyers.

7. A system for the model game pricing method based on data utility and differential privacy according to any one of claims 1 to 6, characterized in that: include: The game trading model is a three-layer structure, the first layer is the model buyer, the second layer is the model broker, and the third layer is the data provider; The number of data providers is n, denoted as data provider i, i = 1, 2, ..., n, and data provider i has original data z i ; Data provider i has access to original data z i Adopt Privacy Policyε i Perform privacy processing to obtain privacy protection data s i , and then sold to model brokers; Model brokers follow the acquisition strategy price p s Purchase privacy-preserving data i , and privacy protection data i Perform feature engineering extraction, then train the data model to obtain a trained data model; The model broker sells according to the selling strategy price p m Sell ​​the trained data model to the model buyer; Profit function construction module, used to construct the profit function Ψ of each data provider i i (p s ,ε i ), is about the acquisition strategy price p s and the privacy policy ε adopted by data provider i i Profit function of the model broker; construct the profit function Ω(p m ,p s ,ε i ), is about the acquisition strategy price p s , selling strategy price p m and the privacy policy ε adopted by each data provider i i Profit function of the model; construct the buyer's profit function Φ(p m ,ε i ), is about the selling strategy price p m and the privacy policy ε adopted by each data provider i i The profit function of The Stackelberg game modeling module is used to model the Stackelberg game model including three levels: in: p m * Represents the selling strategy price adopted to maximize the model buyer's profit, which is the optimal selling strategy price; p s * Represents the acquisition strategy price adopted to maximize the model broker's profit, which is the optimal acquisition strategy price; ε i * It represents the privacy policy adopted when maximizing the benefits of data provider i while considering its privacy protection requirements, which is the optimal privacy policy; A solution module is used to solve the Stackelberg game model to obtain the optimal pricing strategy that satisfies the global optimum. <p m * ,p s * ,ε i * >, that is: when other participants do not change their pricing strategies, no single participant can increase its revenue by simply adjusting its optimal pricing strategy; Through the optimal pricing strategy <p m * ,p s * ,ε i * >, pricing transactions between model buyers, model brokers, and data providers.

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