DEVELOPMENT OF AN ALGORITHM FOR THE APPLICATION OF GAME THEORY IN SOCIAL NETWORKS

ABSTRACT

Game theory allows you to create various game scenarios and analyze the results. The purpose of this article is to develop an algorithm based on a game-theoretic approach to modeling confrontation in social networks. This article examines the zero-sum game model using the example of the problem of modeling confrontation in a social network, where participants can choose between the strategies of "spreading information" and "blocking information", taking into account the dynamics of relations between participants, changes in strategies and their impact on the dissemination of information. An algorithm for the implementation of this model is proposed.

АННОТАЦИЯ

Теория игр позволяет создавать различные игровые сценарии и анализировать результаты. Целью данной статьи является разработка алгоритма на основе теоретико-игрового подхода при моделировании противоборства в социальных сетях. В данной статье рассматривается модель игры с нулевой суммой на примере задачи моделирования противоборства в социальной сети, где участники могут выбирать между стратегиями «распространение информации» и «блокировки информации» с учетом динамики связей между участниками, изменения в стратегиях и их влияние на распространение информации. Предложен алгоритм реализации данной модели.

Keywords: social networks, zero-sum game model, confrontation, strategy, information dissemination, information blocking.

Ключевые слова: социальные сети, модель игры с нулевой суммой, противоборство, стратегия, распространение информации, блокировка информации.

Introduction. The current stage of human development is characterized by a high level of introduction of information and communication technologies in the vast majority of areas of public life, as well as an unprecedented level of accessibility of these technologies. Information technologies and systems increasingly make it possible to meet various human social needs, and first of all, the need to communicate with other people. The process of exchanging opinions and impressions is significantly accelerated today, since a significant part of it takes place not in the real world, but in a virtual social space implemented in the form of specialized Internet services. In Kazakhstan, such services are popular, for example, Facebook^*, Instagram^*, Twitter *, video hosting YouTube, as well as Odnoklassniki ^*and VKontakte, created in Russia by analogy with foreign Facebook *. The ubiquitous availability of the Internet, together with the increasing ease of connection to these services and the level of convenience of their use, make the audience of participants in the virtual social space practically unlimited by neither social, nor economic, nor age, nor any other framework [4].

Thus, today there is an ever-increasing influence of virtual social space on people's public opinion. On the one hand, the involvement of social network participants in discussions on socio-political and social topics indirectly leads to an increase in civic consciousness and awareness of society, but on the other hand, it opens up wide opportunities for manipulation of public opinion by various actors, including those pursuing destructive goals towards the state and society. Social networks are also used by criminal elements to expand electronic markets for illegal goods and services, as well as to involve community users in fraudulent schemes [2].

In the mid-2000s, in the theory of management of organizational systems, the results of studying the mechanisms of information management (impact on the awareness of system participants) were obtained. These results do not fully take into account the structure of social networks and a number of its other properties, which led to the beginning of the development and application of information management and confrontation mechanisms in social networks by the end of the 2000s [3].

The purpose of the study: To develop and implement an algorithm based on game theory for analyzing and managing the confrontation between users in social networks, in order to minimize negative impacts and optimize the interaction strategy.

To achieve this goal, the following tasks have been set:

- To study existing research on the application of game theory in the context of confrontation and conflict;

- Identify game theory models that can be adapted to analyze conflict interactions in social networks;

- Development of an algorithm of confrontation.

Materials and methods. Let the two centers intend to achieve the opposite opinion of the participants of the social network regarding a new idea (new product). In order to achieve their goals, they develop and simultaneously implement managerial influences, which consist in selecting subsets of social network participant and applying private motivating controls to them. To motivate each selected participant, the center allocates a finite amount of resource, the total supply of which is limited for each of the centers. Further, each participant of the network evaluates the received motivating management and accepts or rejects it.

In this presentation, this type of strategic interaction of the centers is a variant of the well- known zero‒sum model game, an important characteristic of which is the lack of equilibrium in pure strategies in any situation where neither side has enough resources to ensure a priori victory on all available battlefields.

Let's consider the formal representation of this model.

Let's say we have two members on a social network who can choose between two strategies: "dissemination of information" and "blocking of information".

Participant 1 chooses a strategy  from the set  of

Participant 2 chooses a strategy from the same set of

The payment matrix determines the gains and losses of participants depending on the strategies they choose [5].

For a zero-sum game, the payment matrix has the form (see Table 1).

Table 1.

The payment matrix.

where:

 is the gain of participant 1 when choosing the "dissemination of information" strategy, and participant 2 - when choosing the "dissemination of information" strategy.

is the gain of participant 1 when choosing the "information dissemination" strategy, and participant 2 - when choosing the "information blocking" strategy.

 is  the gain of participant 1 when choosing the "blocking information" strategy, and participant 2- when choosing the "dissemination of information" strategy

 is the gain of participant 1 when choosing the "blocking information" strategy, and participant 2 - when choosing the "blocking information" strategy.

Positive numbers , ,,  indicate the gain of the participants, and negative numbers indicate losses. For example, if two participants choose the "dissemination of information" strategy, their gains and losses will be .

The analysis of the Nash equilibrium will allow us to determine which strategies will be most beneficial for network participants, provided that other participants remain with their strategies [1].

Suppose there is a graph of a social network where each node represents a participant, and the connections between the nodes indicate the interaction between the participants. Each participant can choose between two strategies: "dissemination of information" and "blocking of information", while taking into account the payment matrix for the winnings of participants.

Let's describe a mathematical model of confrontation using game theory and dynamic modeling.

There is a social network represented by graph  where  a set of nodes (users), a set of connections (friendship/ subscription) between users.

Each link  has a weight  that reflects the strength or probability of transmitting information over this link.

Each user  has his own information  that he can distribute through connections.

 Each user  chooses his strategy from the set  where  is the set of possible strategies for the user.

Strategy  defines how user  chooses where to get information from and how to distribute his information.

Each user has their own winning function , where  -are the strategies of the other users who are not .

The winning function may depend on many factors, such as the amount of information received, the success of information dissemination, etc.

Changes in the weights on the links can change over time according to the weight change function  where  and  are the information of users  and.

For example, successful dissemination of information can increase the weight of communication, while unsuccessful dissemination can decrease it.

The winning function for user  can be defined as the sum of the winnings from receiving information and the winnings from distributing information:

where  is the gain from receiving information for user  ;  is the gain from distributing information for user  ;  -is a coefficient reflecting the importance of each of these aspects for user .

The weight change function on the link  is defined as:

For example, you can use the following function:

where  is the coefficient of weight change,  -user information  and , -is the current weight of the link.

The win function  combines two aspects: the gain from receiving information   and the gain from spreading information.

The coefficient  allows the user to set the importance of each of its aspects. If  then the user's usefulness depends only on the gain from receiving information. If  then only from the gain from the dissemination of information.

The link weight change function     determines the link weight   over time.

The higher the coefficient of weight change , the faster the weight of the link changes with the successful dissemination of information.

- is the product of user information  and . If both users have a lot of information, then the weight of the link increases.

If the current weight of the connection  is small, then the weight change will be less, and vice versa, if  is large, then the weight change will be greater.

Results and discussion. The following algorithm is proposed for the implementation of a zero-sum game model for confrontation in social networks:

1. Creating a graph of a social network with participants and their connections.

2. Definition of the payment matrix for the game.

3. Choosing a strategy: each participant chooses an initial strategy: "spreading information" or "blocking information", taking into account the weights.

4. To implement the game, for each round of the game, participants in the social network simultaneously choose their strategies. For each pair of related participants, their winnings and losses are determined according to the payment matrix. Winnings and losses are recorded for each participant.

5. To update strategies, after each round of the game, participants can review their strategies according to the results. For example, a participant can choose a strategy that brings the greatest gain or minimizes losses.

6. The gameplay is repeated for several rounds or until a certain stop condition is reached, for example, determining the number of iterations or stabilizing strategies.

7. The analysis of the results is carried out to determine the most successful strategy in this network, to find the balance of the Nash strategy, where no participant has the motivation to change his strategy, knowing the choice of other participants.

As a result of modeling a zero-sum game on a social network, it was revealed that Nash equilibrium is achieved with the strategy of "spreading information" for the majority of participants. This indicates that in this network, such a strategy is the most profitable and sustainable for both participants. It was also revealed that the central nodes of the network have a great advantage in choosing the strategy of "information dissemination", which emphasizes their important role in the dissemination of information on the network.

Conclusion. In the process of doing this work:

- Game theory models have been identified that can be adapted to analyze conflict interactions in social networks. The paper considers a zero-sum game model, which is a decision-making model in which there are two players, each of whom has several strategies for their actions. Each player tries to maximize his game result.

- An algorithm of confrontation based on a zero-sum game has been developed using the example of the problem of modeling confrontation in a social network, where participants can choose between the strategies of "spreading information" and "blocking information", taking into account the dynamics of relations between participants, changes in strategies and their impact on the dissemination of information.

Thus, the application of the zero-sum game model allows you to analyze the strategies of participants in a social network, identify the optimal strategies of participants in a social network, identify optimal strategies and balances, as well as study the influence of the social structure on the results of the game. This helps to understand the dynamics of interaction in the network and make informed decisions to improve processes in it.

The simulation results can help social network developers optimize their functioning, improve user experience and combat negative phenomena such as fake news, cyber attacks and manipulation.

References:

1. Dubina I.N. Mathematical methods: fundamentals of game theory:  textbook for secondary vocational education. - Saratov: Vocational education, 2019.- 196 p.
2. Novikov D.A. Models of information warfare in crowd management // Problems of management. - 2015. -№3. P.29-39.
3. Suprunenko A.V. Models and algorithms for classifying web content based on a game-theoretic approach: abstract of the thesis of the Candidate of Technical Sciences.- Nizhny Novgorod. 2017.-24 p.
4. Toropov B. A., Filimonov O. V. On one approach to modeling the situation of information confrontation in a social network // Artificial societies. – 2020. – Vol. 15. – №3. URL: https://artsoc.jes.su/s207751800010821-2-1 /. DOI: 10.18254/S207751800010821-2
5. Zhuravlev V.A. Mathematical methods and models for making marketing decisions: textbook.-Minsk: BSUIR, 2019.-91p.

* (социальная сеть, запрещенная на территории РФ, как продукт организации Meta, признанной экстремистской – прим.ред.)