A rumor propagation prediction method based on antagonistic behavior and evolutionary game

Abstract

The application belongs to the technical field of Internet application, and relates to a rumor propagation prediction method based on confrontation behavior and evolutionary game, comprising the following steps: obtaining data of users and messages in a social network, constructing real-time preference degrees of users to rumor messages and rumor-busting messages according to the data of users and messages; calculating driving forces of users to forward rumor messages and rumor-busting messages according to the real-time preference degrees by using evolutionary game theory; calculating coexistence and confrontation coefficients of rumor messages and rumor-busting messages according to the willingness driving forces by using a Rosenzweig-MacArthur model; and constructing a rumor propagation dynamics model SIPOR to predict rumor propagation situations according to the willingness driving forces; in the rumor propagation process, the state of a user is divided into an ordinary infection state, a rumor state and a rumor-busting state, and a propagation dynamics model SIPOR more in line with the fact of rumor propagation is constructed by considering the interaction between users in different states, so that the accuracy of rumor propagation prediction is improved.

Description

Technical Field

[0001] This invention belongs to the field of Internet application technology and relates to a method for predicting the spread of rumors based on adversarial behavior and evolutionary game theory. Background Technology

[0002] Online rumors refer to false information spread through online media that carries intentional and offensive intent. Such rumors severely mislead public judgment and cause extremely negative social impacts. Due to the lowered threshold for rumor dissemination, the spread of online rumors has become a phenomenon that cannot be ignored. Therefore, research into the mechanisms of online rumor dissemination and the control of its spread are crucial.

[0003] Currently, research on rumors on social networks can be broadly categorized into three main types: disease transmission models, mathematical models, and machine learning algorithm models. In the field of disease transmission models, infectious disease models are widely used in the study of rumor propagation dynamics. These models categorize users into different behavioral states during the propagation process and analyze the propagation mechanism of rumors using constructed state transition equations. In the field of mathematical models, many scholars have constructed various classic rumor propagation dynamic models based on infectious disease models using mathematical methods. In the field of machine learning algorithm models, scholars utilize algorithmic models to extract features from social network information, detect and study the prevalence of rumors, and then analyze and predict the spread of rumors.

[0004] As research on social networks has deepened, scholars have realized that relying solely on user awareness or the topic of rumors can no longer be effective in influencing the spread of rumors. Xiao et al. (Y. Xiao, W. He, T. Yang and Q. Li, "A Dynamic Information Dissemination Model Based on User Awareness and Evolutionary Games," in IEEE Transactions on Computational Social Systems, vol. 10, no. 5, pp. 2837-2846, Oct. 2023) proposed a dynamic information dissemination model based on user perception and evolutionary game theory. This model categorizes users into low-awareness and high-awareness states, and then analyzes the interactions between users with different cognitive levels through evolutionary game theory mechanisms, thereby analyzing the dynamic information dissemination model. This paper demonstrates that classifying users and then exploring their interactions can effectively analyze the dynamics of information dissemination.

[0005] Inspired by this paper, this invention employs a rumor propagation prediction method based on adversarial behavior and evolutionary game theory. It introduces intentional rumor states and intentional debunking states, and by analyzing the adversarial behavior between the two groups, it addresses the problems of existing technologies that do not fully consider the comprehensive impact of the topic (i.e., the rumor message) itself and its derived information (i.e. the debunking message) on the spread of the topic, and cannot analyze the coexistence and adversarial situation of the rumor message and the debunking message, as well as the important factors affecting the spread of rumors. Summary of the Invention

[0006] To address the aforementioned problems in the prior art, this invention employs a rumor propagation prediction method based on adversarial behavior and evolutionary game theory, comprising:

[0007] S1. Obtain user and message data from social networks, including rumor messages and debunking messages; calculate users' real-time preference for rumor messages and debunking messages using a multiple linear regression model based on the user and message data.

[0008] S2. Calculate the driving force of users' willingness to forward rumors and debunking messages based on users' real-time preference for rumors and debunking messages using an evolutionary game model; calculate the coexistence and antagonism coefficients of rumors and debunking messages based on users' willingness to forward rumors and debunking messages using the Rosenzweig-MacArthur model.

[0009] S3. Based on users' willingness to forward rumors and debunking information, construct the rumor propagation dynamics model SIPOR to predict the spread of rumors.

[0010] Calculating users' real-time preference for messages includes: calculating user factors based on user data, and calculating topic factors based on data from rumor messages and debunking messages; analyzing the weights of user factors and topic factors using a multiple linear regression model; and weighting and combining user factors and topic factors according to their weights to obtain users' real-time preference for rumor messages and debunking messages.

[0011] The evolutionary game model includes two game decisions: forwarding rumors and forwarding debunking messages. Calculating the driving force behind a user's willingness to forward rumors and debunking messages involves: calculating the user's behavioral payoff function for the two game decisions based on the user's real-time preference for rumors and debunking messages; and calculating the user's willingness to forward the two game decisions based on the behavioral payoff function.

[0012] Users include: ordinary infected users, rumor-mongering users, and rumor-debunking users; the payoff function for each user's behavioral decision includes: calculating the proportion of users who "forward rumor messages" among their neighbors x i The ratio of "forwarding debunking messages" to "1-x" iLet i∈{I,P,O}, and obtain the purpose-driven gain factor ε when rumor users and debunking users forward rumor messages. i The purpose-driven gain factor ω when forwarding debunking messages i Among them, I, P, and O represent ordinary infected users, rumor-mongering users, and debunking users, respectively.

[0013] If the user is a regular infected user, then according to the ratio x I 1-x I Calculate the behavioral payoff functions for ordinary infected users regarding their decisions to "forward rumors" and "forward debunking information," respectively.

[0014] If the user is spreading rumors, then according to the ratio x P 1-x P and driving gain factor ε P ω P Calculate the behavioral payoff functions for the decisions to "forward rumors" and "forward debunking information";

[0015] If the user is a debunking user, then according to the ratio x O 1-x O and driving gain factor ε O ω O Calculate the behavioral payoff functions for the decisions to "forward rumors" and "forward debunking information".

[0016] The calculation of the coexistence and antagonism coefficient between rumors and debunking includes:

[0017]

[0018] Where Coexistence(t) and Contrast(t) represent the coexistence coefficient and the confrontation coefficient of the rumor and the debunking message at time t, respectively; α1 represents the growth rate of the rumor at time t; α2 represents the growth rate of the debunking message at time t; and k R υ represents the average maximum driving force of the rumor, and υ is the interaction coefficient between the rumor and the debunking message.

[0019] Based on users' willingness to forward rumors and debunking information, the SIPOR model is constructed to predict the spread of rumors, including:

[0020] S31. Based on the user's forwarding status of messages on social networks, users are divided into susceptible state S, ordinary infected state I, rumor state P, rumor debunking state O, and immune state R.

[0021] S32. Construct a multi-user type rumor propagation mechanism, and construct a rumor propagation dynamics model SIPOR based on the mean field theory according to the multi-user type rumor propagation mechanism.

[0022] S33. Based on users' willingness to forward rumors and debunking information, use the SIPOR rumor propagation dynamics model to predict the spread of rumors.

[0023] The mechanisms for spreading rumors across multiple user types include:

[0024] Users in susceptible state S transition to ordinary infected state I with probability α; users in ordinary infected state I transition to rumor state P with probability β and to debunking state O with probability γ; users in rumor state P and debunking state O transition to... η transitions to ordinary infection state I;

[0025] When a user forwards a rumor message more than k times consecutively, their state changes from ordinary infected state I to rumor state P; when a user forwards a debunking message more than q times consecutively, their state changes from ordinary infected state I to debunking state O; when a user in rumor state P forwards a debunking message, their state changes back to ordinary infected user I; when a user in debunking state O forwards a rumor message, their state changes back to ordinary infected user I; users in ordinary infected state I, rumor state P, and debunking state O eventually transition to immune state R with probabilities ε, μ, and ω, respectively.

[0026] Among them, α, β, γ∈[0,1], α+β+γ<1, k, q, ε, μ, and ω are adjustable parameters.

[0027] The SIPOR model for the dynamics of rumor propagation is as follows:

[0028]

[0029] in, This represents the dynamic changes in the susceptible state S; This represents the dynamic changes in the common infection state I. This represents the dynamic changes in the rumor state P. This represents the dynamic change of the rumor-refuting state O. The dynamic changes in immune status R are represented by S(t), I(t), P(t), O(t), and R(t), which respectively represent the user's susceptible state S, normal infection state I, rumor state P, rumor debunking state O, and immune status R at time t.

[0030]

[0031]

[0032] Where, ξ R (t) represents the probability that a user forwards a rumor message at time t, ξ Anti-R(t) represents the probability that a user forwards the debunking message at time t.

[0033] Calculating the probability of a user forwarding a rumor and the probability of a debunking message at time t includes: calculating the probability θ of an ordinary infected user forwarding a rumor at time t based on their motivational drive. R (t) and the probability θ of the debunking message Anti-R (t), calculate the probability ρ of a rumor user forwarding a rumor message at time t based on the user's willingness to do so. R (t) and the probability ρ of the debunking message Anti-R (t), calculate the probability ψ of a debunking user forwarding a rumor message at time t based on the user's willingness to do so. R (t) and the probability ψ of the debunking message Anti-R (t), according to probability θ R (t), ρ R (t), ψ R (t) Calculate the probability that a user forwards a rumor message at time t, based on the probability θ. Anti-R (t), ρ Anti-R (t), ψ Anti-R (t) Calculate the probability that a user forwards the debunking message at time t.

[0034] Beneficial effects:

[0035] 1. This invention introduces the Rosenzweig-MacArthur equation to construct the game-theoretic trend between the rumor group and the debunking group, thereby obtaining the coexistence and confrontation between rumor messages and debunking messages throughout the entire rumor propagation lifecycle. Based on the coexistence and confrontation between rumor messages and debunking messages, the development direction of rumor propagation can be analyzed more accurately. 2. In the rumor propagation process, this invention divides the user's state into ordinary infection state I, rumor state P, and debunking state O. Considering the interaction between users in different states, it uses evolutionary game theory to construct a propagation dynamics model, SIPOR, that better reflects the facts of rumor propagation. This model can more accurately analyze and predict the behavior of users in each state during the rumor propagation process, thereby accurately obtaining the development direction of rumor propagation and improving the accuracy of rumor propagation prediction. Attached Figure Description

[0036] Figure 1 A flowchart illustrating a rumor propagation prediction method based on adversarial behavior and evolutionary game theory, provided for an embodiment of the present invention;

[0037] Figure 2 A schematic diagram illustrating a rumor propagation prediction method based on adversarial behavior and evolutionary game theory provided in an embodiment of the present invention;

[0038] Figure 3This is a schematic diagram illustrating the measurement of real-time user message preferences provided in an embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram illustrating the analysis of user adversarial behavior and the rumor-debunking game situation provided in an embodiment of the present invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] like Figure 1 , Figure 2 As shown, this invention proposes a rumor propagation prediction method based on adversarial behavior and evolutionary game theory. The input of this invention is user basic information, user historical behavior information, user relationship network, and rumor topic information in social networks. The output is the important factors affecting rumor propagation, user state set at any time, user state transition set, and the coexistence and adversarial evolution relationship between rumor messages and debunking messages.

[0042] The specific steps include:

[0043] S1. Obtain user and message data from social networks, including rumor messages and debunking messages; calculate users' real-time preference for rumor messages and debunking messages using a multiple linear regression model based on the user and message data.

[0044] Measuring real-time user message preferences requires considering both user factors and topic-related factors. User factors include user activity, information accessibility, and topic relevance. For topic-related factors, the real-time popularity of the topic message needs to be considered. A multiple linear regression model is used to fit regression coefficients to historical data, and then the user's real-time message preference is calculated based on both user and topic factors.

[0045] like Figure 3 As shown, specifically, calculating a user's real-time preference for a message includes:

[0046] S11: Calculate user factors Var based on user data in (u i ), calculate topic factors Var based on message data. msg (u i );

[0047] Real-time user preferences describe how users, influenced by rumors, decide whether to participate in the rumors or which type of message to forward based on their own factors.

[0048] Var user (u i ) = Act(u i )×Obt(u i )×Pair(u i (1)

[0049]

[0050] Among them, Act(u i ) represents user activity, Obt(u i Pair(u) is the ability to acquire user information. i ) represents the user's interest-topic matching degree, Hot(t) represents the real-time popularity of the message, and w(u) represents the user's interest-topic matching degree. i ,u j ) represents user u i The weight of the received message source, w(u) i ,u j ) > 0 indicates a rumor, w(u) i ,u j ) < 0 indicates a debunking message, u j Let n represent the number of users who are the source of the message.

[0051] S12: Regression coefficients of the fitted multiple linear regression model

[0052] Considering the significant advantages of multiple linear regression models in handling multivariate models, this invention utilizes multiple linear regression models to analyze how user factors and topic factors influence users' real-time preferences for two types of messages:

[0053]

[0054]

[0055] in, Indicates user u i The preference for rumors at time t Indicates user u i At time t, the preference for debunking messages is expressed, where β1, β2, and β3 are regression coefficients obtained by fitting historical real data, and Var msg (u i ) R This indicates the topic factor of rumors and misinformation. msg (u i ) Anti-R This refers to the topic factors in debunking rumors.

[0056] S2. Calculate the driving force of users' willingness to forward rumors and debunking messages based on users' real-time preference for rumors and debunking messages using an evolutionary game model; calculate the coexistence and antagonism coefficients of rumors and debunking messages based on users' willingness to forward rumors and debunking messages using the Rosenzweig-MacArthur model.

[0057] like Figure 4 As shown, users are categorized based on their message forwarding behavior on social networks into three groups: ordinary infected users, rumor users, and debunking users. Ordinary users are topic participants without obvious bias or purpose, rumor users are rumor-mongering users with obvious bias, and debunking users are debunking users with obvious bias.

[0058] This invention defines two game strategies for users: "forwarding rumor messages" and "forwarding debunking messages".

[0059] For ordinary infected users, when exposed to various types of rumors, they engage in a psychological game based on their own understanding and the interplay between different messages, ultimately making a choice. (The text then abruptly shifts to a seemingly unrelated topic: using x...) I 1-x I This represents the proportion of users' neighboring nodes that "forward rumors" and "forward debunking messages." Where 0 ≤ x I ≤1.

[0060] For users spreading rumors, use x respectively P 1-x P This represents the proportion of users' neighboring nodes that "forward rumors" and "forward debunking messages." Where 0 ≤ x P ≤1.

[0061] For users who debunked the rumors, use x respectively. O 1-x O This represents the proportion of users' neighboring nodes that "forward rumors" and "forward debunking messages." Where 0 ≤ x O ≤1.

[0062] The payoff functions for the three parties involved in the game—ordinary users, rumor-mongering users, and debunking users—are shown in Table 1.

[0063] Table 1 Profit Function

[0064]

[0065] Among them, pay R(I) ,pay Anti-R(I) These represent the revenue functions for ordinary infected users forwarding rumors and forwarding debunking claims, respectively. R(P) ,pay Anti-R(P)Represent the revenue functions for users forwarding rumors and forwarding debunking claims, respectively, and pay. R(H) ,pay Anti-R(H) Let ε represent the revenue functions for users who forward rumors and those who forward debunking rumors, respectively. P ε O ε represents the purpose-driven gain factor when rumor-mongers and debunkers forward rumor messages, respectively. P >1, 0<ε O <1. ω P ω O These represent the purpose-driven gain factors when rumor-mongers and debunkers forward debunking messages, respectively, where 0 < ω. P <1, ω O >1.

[0066] Preferably, ε P The value is 1.6, ε O The value is 0.3, and can be adjusted accordingly based on actual circumstances; ω P The value is 0.6, ω O The value is 2.1, and can be adjusted accordingly based on the actual situation.

[0067] These three types of users unconsciously engaged in a three-way game when participating in discussions about rumors. Considering the advantages of evolutionary game theory in studying multi-party game behavior and its ability to maximize the interests of all players, this invention quantifies the forwarding behavior of each type of user by using the maximum payoff obtained through the game. Generally, the sigmoid function is used to map user forwarding behavior to (0,1). The closer the mapping result is to 1, the stronger the user's motivation to forward the topic. Specifically:

[0068] For ordinary infected users, the driving force behind the willingness to forward rumors and debunk rumors is... R(I) Tend Anti-R(I) for:

[0069]

[0070]

[0071] For users who spread rumors, the driving force behind their willingness to forward rumors and debunk them is... R(P) Tend Anti-R(P) for:

[0072]

[0073]

[0074] For users debunking rumors, the driving force behind their willingness to forward rumors and debunk debunking rumors is Tend R(H) TendAnti-R(H) for:

[0075]

[0076]

[0077] Because the spread of rumors involves an adversarial relationship between rumor-mongering and debunking information, some ordinary users may become rumor-mongering or debunking users. This situation is similar to the predator-prey relationship in biology. Specifically, rumor-mongering users are likened to predators, and debunking users to prey; an adversarial relationship naturally exists between them. Therefore, this invention uses the Rosenzweig-MacArthur equation to calculate the coexistence and adversarial coefficients Coexistence(t) and Contrast(t) between rumor-mongering and debunking information:

[0078]

[0079]

[0080] Where α1 represents the growth rate of the rumor at time t, α2 represents the growth rate of the debunking message at time t, and k R υ represents the maximum value of the average willingness to forward rumor messages among ordinary infected users, rumor users, and debunking users (saturated average driving force), and υ is the interaction coefficient between rumor messages and debunking messages.

[0081] The growth rates of rumor messages and debunking messages are defined as follows:

[0082]

[0083]

[0084] Here, RumorCount represents the number of rumor messages in a certain time slice, AntiRumorCount represents the number of debunking messages in a certain time slice, and t1 and t2 represent different time slices (t2>t1).

[0085] The coefficient of influence between rumors and debunking information:

[0086]

[0087] Among them, Hot R (t), Hot Anti-R (t) represents the popularity of the rumor and the debunking message at time t.

[0088] S3. Based on users' willingness to forward rumors and debunking information, construct the rumor propagation dynamics model SIPOR to predict the spread of rumors;

[0089] In order to make the spread of rumors more specific and to take into account the different intentions of different user groups or the different states of rumor and debunking caused by cognitive differences, this invention constructs a rumor propagation dynamics model SIPOR based on user adversarial behavior and evolutionary game theory on the basis of the classic SIR model, so as to analyze the rumor propagation situation more accurately.

[0090] Specifically, the steps for predicting the spread of rumors include:

[0091] S31. Divide users in the model into 5 states: susceptible state S, ordinary infection state I, rumor state P, rumor debunking state O, and immune state R.

[0092] S32. Construct a multi-user type rumor propagation mechanism, and construct a rumor propagation dynamics model SIPOR based on the mean field theory according to the multi-user type rumor propagation mechanism.

[0093] To make the model analysis more accurate and reliable, some factors that have a minor impact on the model results and may unnecessarily complicate the analysis process were excluded when the model was built, resulting in the following assumptions:

[0094] Assuming the total number of users participating in the spread of rumors remains constant, then S(t)+I(t)+P(t)+O(t)+R(t)=1.

[0095] Because the spread of rumors takes time and is affected by the network environment and debunking messages, the number of user nodes in the rumor state will stop increasing after reaching a certain number, meaning that the number of rumor state nodes is saturated.

[0096] When a user node continuously forwards rumor messages or debunking messages to a certain threshold, its status changes from ordinary infection status to rumor status or debunking status, and at the same time, a purpose-driven gain factor is added to the benefits of forwarding the corresponding messages.

[0097] As the popularity of rumors changes, users on the internet will eventually transition from various states to a state of immunity.

[0098] Based on the above assumptions, the guidelines for formulating the multi-user type rumor propagation mechanism of this invention are as follows:

[0099] The susceptible state S transitions to the ordinary infection state I with probability α. The ordinary infection state I transitions to the rumor state P with probability β and to the debunking state O with probability γ. The rumor state P and the debunking state O transition to the rumor state P with probability α. The probability of η shifts to the normal infection state I; where α,β,γ∈[0,1]; since some nodes do not participate in the topic propagation throughout the entire topic propagation process, α+β+γ<1.

[0100] When a user forwards a rumor message more than k times consecutively, their state changes from a normal infected node to a rumor node; when a user forwards a debunking message more than q times consecutively, their state changes from a normal infected node to a debunking node. When the rumor user forwards the debunking message again, their state changes back to a normal infected user; the same applies to debunking users; where k and q are adjustable parameters.

[0101] As the popularity of various messages changes, ordinary infection nodes, rumor nodes, and debunking nodes eventually transform into immune nodes with probabilities of ε, μ, and ω, respectively.

[0102] Based on the multi-user type rumor propagation mechanism principle, the following set of dynamic equations can be constructed:

[0103]

[0104] Since the probability of a user transitioning from a rumor-mongering or debunking state to a normal infected state and then back to a rumor-mongering or debunking state is extremely low, all users will eventually transition to an immune state. User u i There are n neighboring users, and the probability that m of them will undergo a state transition follows a binomial distribution:

[0105]

[0106] As can be seen from formula (23), for ordinary infected users, the probability θ of forwarding rumor messages and debunking messages at time t is... R (t), θ Anti-R (t) are respectively:

[0107]

[0108]

[0109] For users who spread rumors, the probability ρ of forwarding both the rumor and the debunking message at time t is... R (t), ρ Anti-R (t) are respectively:

[0110]

[0111]

[0112] For users debunking rumors, the probability ψ of forwarding both the rumor and the debunking message at time t is... R (t), ψ Anti-R (t) are respectively:

[0113]

[0114]

[0115] In summary, the probability ξ of any user forwarding both the rumor and the debunking message at time t is... R (t), ξ Anti-R (t) are respectively:

[0116] ξ R (t)=I(t)×θ R (t)+P(t)×ρ R (t)+O(t)×ψ R (t) (30)

[0117] ξ Anti-R (t)=I(t)×θ Anti-R (t)+P(t)×ρ Anti-R (t)+O(t)×ψ Anti-R (t) (31)

[0118] During the analysis, the interactions between users and all other users are quite complex. However, if we consider the interactions between all other users as an average force, the analysis for each user becomes relatively simple and clear. Therefore, this invention uses mean-field theory to simplify the interactions between users, resulting in the following set of dynamic equations:

[0119]

[0120] S33. Based on users' willingness to forward rumors and debunking information, use the SIPOR rumor propagation dynamics model to predict the spread of rumors.

[0121] The output of the rumor propagation dynamics model SIPOR is a set of user state states at different times and a set of user state transitions. Relevant departments can understand the spread trend of rumor topics based on the set of user state states at different times, the set of user state transitions, and the coexistence and confrontation coefficients between rumor messages and debunking, and select appropriate times to release debunking information by using the user state sets at different times.

[0122] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rumor propagation prediction method based on adversarial behavior and evolutionary game theory, characterized in that, include: S1. Obtain user and message data from social networks, including rumor messages and debunking messages; calculate users' real-time preference for rumor messages and debunking messages using a multiple linear regression model based on the user and message data. S2. Calculate the driving force of users' willingness to forward rumors and debunking messages based on users' real-time preference for rumors and debunking messages using an evolutionary game model; calculate the coexistence and antagonism coefficients of rumors and debunking messages based on users' willingness to forward rumors and debunking messages using the Rosenzweig-MacArthur model. S3. Based on users' willingness to forward rumors and debunking information, construct the rumor propagation dynamics model SIPOR to predict the spread of rumors; The evolutionary game model includes two types of game decisions: forwarding rumors and forwarding debunking messages. Calculating the driving force behind a user's willingness to forward rumors and debunking messages involves: calculating the user's behavioral payoff function for the two game decisions based on the user's real-time preference for rumors and debunking messages; and calculating the user's willingness to forward the two game decisions based on the behavioral payoff function. Users include: ordinary infected users, rumor-mongering users, and rumor-debunking users; the payoff function for each user's behavioral decision in the game includes: calculating the proportion of users among the user's neighbors who "forwarded rumor messages" x i The ratio of "forwarding debunking messages" to "1-x" i Let i∈{I,P,O}, and obtain the purpose-driven gain factor ε when rumor users and debunking users forward rumor messages. i The purpose-driven gain factor ω when forwarding debunking messages i Among them, I, P, and O represent ordinary infected users, rumor-mongering users, and debunking users, respectively. If the user is a regular infected user, then according to the ratio x I 1-x I Calculate the behavioral payoff functions for ordinary infected users regarding their decisions to "forward rumors" and "forward debunking information," respectively. If the user is spreading rumors, then according to the ratio x P 1-x P and driving gain factor ε P ω P Calculate the behavioral reward functions for the decisions to "forward rumors" and "forward debunking information"; If the user is a debunking user, then according to the ratio x O 1-x O and driving gain factor ε O ω O Calculate the behavioral reward functions for the decisions to "forward rumors" and "forward debunking information"; The calculation of the coexistence and antagonism coefficient between rumors and debunking includes: Where Coexistence(t) and Contrast(t) represent the coexistence coefficient and the confrontation coefficient of the rumor and the debunking message at time t, respectively; α1 represents the growth rate of the rumor at time t; α2 represents the growth rate of the debunking message at time t; and k R The average driving force of the rumor is the maximum value, and υ is the interaction coefficient between the rumor and the debunking message; The mechanisms for spreading rumors across multiple user types include: Users in susceptible state S transition to ordinary infected state I with probability α; users in ordinary infected state I transition to rumor state P with probability β and to debunking state O with probability γ; users in rumor state P and debunking state O transition to... η transitions to ordinary infection state I; When a user forwards a rumor message more than k times consecutively, their state changes from ordinary infected state I to rumor state P; when a user forwards a debunking message more than q times consecutively, their state changes from ordinary infected state I to debunking state O; when a user in rumor state P forwards a debunking message, their state changes back to ordinary infected user I; when a user in debunking state O forwards a rumor message, their state changes back to ordinary infected user I; users in ordinary infected state I, rumor state P, and debunking state O eventually transition to immune state R with probabilities ε, μ, and ω, respectively. Among them, α, β, γ∈[0,1], α+β+γ<1, k, q, ε, μ, and ω are adjustable parameters; The SIPOR model for the dynamics of rumor propagation is as follows: in, This represents the dynamic changes in the susceptible state S; This represents the dynamic changes in the common infection state I. This represents the dynamic changes in the rumor state P. This represents the dynamic change of the rumor-refuting state O. The dynamic changes in immune status R are represented by S(t), I(t), P(t), O(t), and R(t), which respectively represent the user's susceptible state S, normal infection state I, rumor state P, rumor debunking state O, and immune status R at time t.

2. The rumor propagation prediction method based on adversarial behavior and evolutionary game theory according to claim 1, characterized in that, Calculating users' real-time preference for messages includes: calculating user factors based on user data, and calculating topic factors based on data from rumor messages and debunking messages; analyzing the weights of user factors and topic factors using a multiple linear regression model; and weighting and combining user factors and topic factors according to their weights to obtain users' real-time preference for rumor messages and debunking messages.

3. The rumor propagation prediction method based on adversarial behavior and evolutionary game theory according to claim 1, characterized in that, Based on users' willingness to forward rumors and debunking information, the SIPOR model is constructed to predict the spread of rumors, including: S31. Based on the user's forwarding status of messages on social networks, users are divided into susceptible state S, ordinary infected state I, rumor state P, rumor debunking state O, and immune state R. S32. Construct a multi-user type rumor propagation mechanism, and construct a rumor propagation dynamics model SIPOR based on the mean field theory according to the multi-user type rumor propagation mechanism. S33. Based on users' willingness to forward rumors and debunking information, use the SIPOR rumor propagation dynamics model to predict the spread of rumors.

4. The rumor propagation prediction method based on adversarial behavior and evolutionary game theory according to claim 1, characterized in that, Where, ξ R (t) represents the probability that a user forwards a rumor message at time t, ξ Anti-R (t) represents the probability that a user forwards the debunking message at time t.

5. The rumor propagation prediction method based on adversarial behavior and evolutionary game theory according to claim 4, characterized in that, Calculating the probability of a user forwarding a rumor and the probability of a debunking message at time t includes: calculating the probability θ of an ordinary infected user forwarding a rumor at time t based on their motivational drive. R (t) and the probability θ of the debunking message Anti-R (t), calculate the probability ρ of a rumor user forwarding a rumor message at time t based on the user's willingness to do so. R (t) and the probability ρ of the debunking message Anti-R (t), calculate the probability ψ of a debunking user forwarding a rumor message at time t based on the user's willingness to do so. R (t) and the probability ψ of the debunking message Anti-R (t), according to probability θ R (t), ρ R (t), ψ R (t) Calculate the probability that a user forwards a rumor message at time t, based on the probability θ. Anti-R (t), ρ Anti-R (t), χ Anti-R (t) Calculate the probability that a user forwards the debunking message at time t.

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