Data option pricing method based on Stackelberg game

Abstract

The invention relates to the technical field of data pricing, and particularly provides a data option pricing method based on a Stackelberg game. The method comprises the following steps: determining the profit of a buyer, and measuring the profit of the buyer through two aspects of seller reputation and relative income; a Stackelberg game model is constructed, and a game model is constructed; performing equilibrium solution according to a Stackelberg game model to obtain a purchase strategy of the buyer and a pricing strategy of the seller; determining an option margin proportion according to a seller pricing strategy; according to the method, the benefits between the buyer and the seller are balanced, the method is suitable for the Internet data pricing direction, and in the existing research, the pricing method for the data in production is proposed for the first time.

Description

Technical Field

[0001] The present invention relates to the field of data pricing technology, and in particular to a data option pricing method based on Stackelberg game. Background Art

[0002] Currently, most research focuses on the differences between data commodities and traditional commodities, such as low marginal costs, data quality, and data privacy. Based on this, data trading and pricing mechanisms have been designed from various perspectives. To address the difficulty in quantifying data quality, industrial data markets often use experiments to help buyers assess data quality. However, this approach carries the risk of data leakage and arbitrage. On this basis, academics have proposed a data evaluation method based on functional encryption to help buyers evaluate and obtain high-quality data without sellers worrying about data leakage. Furthermore, research has proposed pricing methods based on model quality for trading machine learning models as data products. However, determining the quality of data during the production process is a challenge. Reputation mechanisms are often used to address this difficulty in assessing commodity quality. In data markets, establishing seller reputation from the buyer's perspective can effectively measure data quality.

[0003] Game theory is a common approach in the field of data pricing. The Stackelberg game is a classic two-stage perfect information game involving a leader and followers. The leader takes the first action, and the followers react and adjust their actions based on the leader's actions. In this game model, the leader has a greater advantage and is often used to study decision-making in monopoly markets. Summary of the Invention

[0004] In view of this, the present invention provides a data option pricing method based on Stackelberg game to balance the profits of data buyers and sellers, which is applicable to the Internet data pricing market.

[0005] In a first aspect, the present invention provides a data option pricing method based on Stackelberg game, the method comprising:

[0006] Step 1: Determine the seller's reputation and measure it through historical buyer ratings. The expression for measuring seller reputation is:

[0007]

[0008] Where k is the serial number of the seller's transaction, and K is the total number of the seller's historical transactions; Score the data corresponding to the transaction, is the weight of the transaction;

[0009] Step 2: Based on the seller’s reputation in step 1, construct a Stackelberg game model between the buyer and the seller;

[0010] Step 3: Solve the equilibrium based on the Stackelberg game model in step 2 to obtain the seller's pricing strategy and the buyer's purchasing strategy;

[0011] Step 4: Determine the option margin ratio based on the seller pricing strategy in step 3.

[0012] Optionally, step 1 includes: obtaining the data scoring weight through historical transaction volume, using Indicates the user's data score in the kth transaction, and Indicates the weight of the k-th transaction data score; x k Denotes the amount of data purchased in the kth transaction, and X K represents the total amount of sales data; the weight expression of the data score of the kth transaction is:

[0013]

[0014] Optionally, step 2 includes setting the seller to pay a transmission fee based on the amount of data purchased by the buyer. The seller pays the data transmission fee to the third-party transmission service provider for each data option transaction. The seller's profit π(p,q) is expressed as:

[0015] π(p,x)=(pc)x;

[0016] Among them, p represents the price of unit data option, the unit data transmission fee is c, and x represents the seller's data sales volume; the seller's profit maximization is expressed as:

[0017] π * (p * ,x)≥π(p,x);

[0018] stp>c>0;

[0019] where π * (p * ,x) means when the price is p * The seller obtains the maximum profit π * .

[0020] Assume that the buyer's utility is a monotonically increasing function of the data volume x and follows the marginal diminishing effect. The utility obtained by the user from the data volume c is u(x), which is expressed as:

[0021]

[0022] Among them, α1 and α2 represent the buyer’s data valuation parameters, represents the average data purchase amount of all other buyers from the seller;

[0023] The buyer's profit function is:

[0024] v(x,p)=u(x)-px;

[0025] The buyer maximizes profit, which can be expressed as:

[0026] v * (x * ,p)≥v(x,p);

[0027] stx>0;

[0028] Optionally, step 3 includes:

[0029] a. Buyer's purchasing strategy: Given a unit data option price, the buyer determines the amount of data x to purchase to obtain the best utility. The first-order derivative of the buyer's profit function v(x,p) is obtained, and its expression is:

[0030]

[0031] Obtain the second-order derivative of the buyer's utility function u(x,p), which is expressed as:

[0032]

[0033] Where v″(x,p) is a concave function; set v′(x,p)=0 to obtain the user’s optimal purchase data volume x * , whose expression is:

[0034]

[0035] b. Seller’s pricing strategy:

[0036] Based on the amount of optimal purchase data obtained x * , set the best price p * , the optimal purchase data volume x * Substitute into the seller's profit function π(p,x) to obtain the seller's optimal profit π * (p * ,x), its expression is:

[0037]

[0038] Comprehensively consider the values ​​of various parameters to obtain the seller's optimal pricing strategy p * , whose expression is:

[0039]

[0040] Among them, ε is a very small positive number, α1R+α2-ε is the upper bound of the price obtained under the constraint of x>0, is the function π * (p * ,x), c is the price lower bound constrained by p>c>0;

[0041] 5. The method according to claim 1, wherein step 4 comprises:

[0042] The buyer and seller agree on the data option margin ratio θ and the exercise date T. When purchasing data, the buyer prepays an option margin fee of θp for each unit of data purchased. On the exercise date T, the seller delivers the data to the buyer, and the buyer pays an option exercise fee of (1-θ)p for each unit of data purchased.

[0043] The technical solution provided by the present invention includes determining buyer utility, measuring buyer utility through two dimensions: seller reputation and relative benefits; constructing a Stackelberg game model; performing equilibrium solution based on the Stackelberg game model to obtain the buyer's purchasing strategy and the seller's pricing strategy; and determining the option margin ratio based on the seller's pricing strategy. This method balances the interests between buyers and sellers and is applicable to the Internet data market. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of a system model according to a specific embodiment of the present invention.

[0045] Figure 2 This is a flow chart of a data pricing method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0046] To further clarify the objectives, technical solutions, and advantages of the embodiments of the present invention, the technical solutions of the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. It should be understood that the described embodiments are only a portion of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments derived by persons of ordinary skill in the art without inventive effort are within the scope of protection of the present invention. It should be understood that the described embodiments are only a portion of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments derived by persons of ordinary skill in the art without inventive effort are within the scope of protection of the present invention. The terms used in the embodiments of the present invention are intended solely to describe specific embodiments and are not intended to limit the present invention. The singular forms "a," "the," and "the" used in the embodiments of the present invention are intended to include the plural forms, unless the context clearly indicates otherwise. It should be understood that the term "and / or" as used herein is merely a description of an association between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B simultaneously, or B alone. Furthermore, the character " / " as used herein generally indicates an "or" relationship between the associated objects. The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0047] In the data options market, sellers list data product options on the platform, including a price per unit of data and a delivery date. When the seller delivers the product to the buyer, they pay a per-unit data transmission fee to the third-party transmission service provider. The seller sets the price of the data product option based on the buyer's purchasing behavior, and the buyer determines the quantity of data product options to purchase based on the price.

[0048] Data option transactions generally involve both sellers and buyers, so the present invention designs the transaction as a Stackelberg game model involving both parties. In the game between the buyer and seller, the seller is the leader and the buyer is the follower.

[0049] Figure 2 The flowchart of the data option pricing method provided by the embodiment of the present invention is as follows: Figure 2 As shown, the method includes:

[0050] Step 1: Determine the seller's reputation and measure it through historical buyer ratings. The expression for measuring seller reputation is:

[0051]

[0052] Where k is the serial number of the seller's transaction, and K is the total number of the seller's historical transactions; Score the data corresponding to the transaction, is the weight of the transaction;

[0053] In the embodiment of the present invention, step 1 includes: obtaining the data scoring weight through the historical transaction volume, using Indicates the user's data score in the kth transaction, and Indicates the weight of the k-th transaction data score; x k Denotes the amount of data purchased in the kth transaction, and X K represents the total amount of sales data; the weight expression of the data score of the kth transaction is:

[0054]

[0055] Step 2: Based on the seller’s reputation in step 1, construct a Stackelberg game model between the buyer and the seller;

[0056] In an embodiment of the present invention, step 2 includes: setting the seller to pay the transmission fee based on the amount of data purchased by the buyer, and the seller pays the data transmission fee to the third-party transmission service provider for each data option transaction. The data has the characteristic of unlimited replication, and the same data can be sold to multiple buyers.

[0057] The seller's profit π(p,q) is expressed as:

[0058] π(p,x)=(pc)x;

[0059] Among them, p represents the price of unit data option, the unit data transmission fee is c, and x represents the seller's data sales volume;

[0060] The seller maximizes profit, which can be expressed as:

[0061] π * (p * ,x)≥π(p,x);

[0062] stp>c>0;

[0063] where π * (p * ,x) means when the price is p * The seller obtains the maximum profit π * .

[0064] Data has a wide range of uses, such as data analysis and model training. The accuracy of data analysis and model training is mainly determined by the amount and quality of data. Therefore, the buyer's utility is assumed to be a monotonically increasing function of the data volume x, and follows a diminishing marginal effect. The utility obtained by the user from the data volume c is u(x), which is expressed as:

[0065]

[0066] Among them, α1 and α2 represent the buyer’s data valuation parameters, represents the average data purchase amount of all other buyers from the seller;

[0067] The buyer's profit function is:

[0068] v(x,p)=u(x)-px;

[0069] The buyer maximizes profit, which can be expressed as:

[0070] v * (x * ,p)≥v(x,p);

[0071] stx>0;

[0072] Step 3: Solve the equilibrium based on the Stackelberg game model in step 2 to obtain the seller's pricing strategy and the buyer's purchasing strategy;

[0073] In this embodiment of the present invention, step 3 includes:

[0074] a. Buyer's purchasing strategy: Given a unit data option price, the buyer determines the amount of data x to purchase to obtain the best utility. The first-order derivative of the buyer's profit function v(x,p) is obtained, and its expression is:

[0075]

[0076] Obtain the second-order derivative of the buyer's utility function u(x,p), which is expressed as:

[0077]

[0078] Where v″(x,p) is a concave function; set v′(x,p)=0 to obtain the user’s optimal purchase data volume x * , whose expression is:

[0079]

[0080] b. Seller’s pricing strategy:

[0081] Based on the amount of optimal purchase data obtained x * , set the optimal price p* , the optimal purchase data volume x * Substitute into the seller's profit function π(p,x) to obtain the seller's optimal profit π * (p * ,x), its expression is:

[0082]

[0083] Comprehensively consider the values ​​of various parameters to obtain the seller's optimal pricing strategy p * , whose expression is:

[0084]

[0085] Among them, ε is a very small positive number, α1R+α2-ε is the upper bound of the price obtained under the constraint of x>0, is the function π * (p * ,x), c is the price lower bound constrained by p>c>0;

[0086] Step 4: Determine the option margin ratio based on the seller pricing strategy in step 3.

[0087] In the embodiment of the present invention, step 4 includes:

[0088] The buyer and seller agree on the data option margin ratio θ and the exercise date T. When purchasing data, the buyer prepays an option margin fee of θp for each unit of data purchased. On the exercise date T, the seller delivers the data to the buyer, and the buyer pays an option exercise fee of (1-θ)p for each unit of data purchased.

[0089] Compared with the prior art, the present invention has the following beneficial effects:

[0090] 1. Compared to other data pricing methods, this invention considers the quality of the data being produced. Data quality is measured through seller reputation, which better reflects the seller's actual average data quality. This invention also considers the impact of the number of buyers on buyer utility, incorporating the number of buyers as a parameter into the buyer's profit function.

[0091] 2. In other pricing models, the platform acts as a middleman between buyers and sellers, purchasing data from sellers and then reselling it to buyers. However, in this invention, the platform only provides the function of publishing data products, and buyers and sellers trade directly, which is beneficial to both parties.

[0092] 3. The present invention is suitable for the direction of Internet data pricing. In existing research, it is the first time to propose a method for pricing data that has not yet been completed. In the technical solution provided by the present invention, the method includes determining the buyer's utility, measuring the buyer's utility through the two dimensions of seller reputation and relative benefits; constructing a Stackelberg game model; performing equilibrium solution based on the Stackelberg game model to obtain the buyer's purchase strategy and the seller's pricing strategy; determining the option margin ratio based on the seller's pricing strategy; this method balances the interests between buyers and sellers and is applicable to the Internet data market. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here. The above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A data option pricing method based on Stackelberg game, characterized in that: The method comprises: Step 1: Determine the seller's reputation and measure it through historical buyer ratings. The expression for measuring seller reputation is: Where k is the serial number of the seller's transaction, and K is the total number of the seller's historical transactions; Score the data corresponding to the transaction, is the weight of the transaction; Step 2: Based on the seller’s reputation in step 1, construct a Stackelberg game model between the buyer and the seller; Step 3: Solve the equilibrium based on the Stackelberg game model in step 2 to obtain the seller's pricing strategy and the buyer's purchasing strategy; Step 4: Determine the option margin ratio based on the seller pricing strategy in step 3.

2. The method according to claim 1, characterized in that The step 1 includes: obtaining the data scoring weight through historical transaction volume, using Indicates the user's data score in the kth transaction, and Indicates the weight of the k-th transaction data score; x k Denotes the amount of data purchased in the kth transaction, and X K represents the total amount of sales data; the weight expression of the data score of the kth transaction is:

3. The method according to claim 1, characterized in that Step 2 includes: setting the seller to pay the transmission fee according to the amount of data purchased by the buyer. The seller pays the data transmission fee to the third-party transmission service provider for each data option transaction. The seller's profit π(p,q) is expressed as: π(p,x)=(pc)x; Among them, p represents the price of unit data option, the unit data transmission fee is c, and x represents the seller's data sales volume; The seller maximizes profit, which can be expressed as: π * ( p * ,x)≥π(p,x); stp>c>0; where π * (p * ,x) means when the price is p * The seller obtains the maximum profit π * ; Assume that the buyer's utility is a monotonically increasing function of the data volume x and follows the marginal diminishing effect; the utility obtained by the user from the data volume c is u(x), which is expressed as: Among them, α1 and α2 represent the buyer’s data valuation parameters, represents the average data purchase amount of all other buyers from the seller; The buyer's profit function is: v(x, p) = u(x) - px; The buyer maximizes profit, which can be expressed as: v * (x * ,p)≥v(x,p); stx>0.

4. The method according to claim 1, wherein The step 3 comprises: a. Buyer's purchasing strategy: Given a unit data option price, the buyer determines the amount of data x to purchase to obtain the best utility. The first-order derivative of the buyer's profit function v(x, p) is obtained, and its expression is: Obtain the second-order derivative of the buyer's utility function u(x, p), which is expressed as: Where v″(x, p) is a concave function; set v′(x, p) = 0 to obtain the user’s optimal purchase data volume x * , whose expression is: b. Seller’s pricing strategy: Based on the amount of optimal purchase data obtained x * , set the optimal price p * , the optimal purchase data volume x * Substitute into the seller's profit function π(p, x) to obtain the seller's optimal profit π * (p * , x), its expression is: Comprehensively consider the values ​​of various parameters to obtain the seller's optimal pricing strategy p * , whose expression is: Among them, ε is a very small positive number, α1R+α2-ε is the upper bound of the price obtained under the constraint of x>0, is the function π * (p * , the maximum point of x), c is the price lower bound constrained by p>c>0.

5. The method according to claim 1, wherein The step 4 comprises: The buyer and seller agree on the data option margin ratio θ and the exercise date T. When purchasing data, the buyer prepays an option margin fee of θp for each unit of data purchased. On the exercise date T, the seller delivers the data to the buyer, and the buyer pays an option exercise fee of (1-θ)p for each unit of data purchased.

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