Generative AI for Game Theory-based Mobile Networking

Long He, Geng Sun, Dusit Niyato, Hongyang Du, Fang Mei, Jiawen Kang, Mérouane Debbah, Zhu Han

Abstract

With the continuous advancement of network technology, various emerging complex networking optimization problems opened up a wide range of applications utilizating of game theory. However, since game theory is a mathematical framework, game theory-based solutions often require the experience and knowledge of human experts. Recently, the remarkable advantages exhibited by generative artificial intelligence (GAI) have gained widespread attention. In this article, we propose a novel GAI-enabled game theory solution that combines the powerful reasoning and generation capabilities of GAI to the design and optimization of mobile networking. Specifically, we first outline the game theory and key technologies of GAI, and then explore the advantages of combining GAI with game theory. Then, we briefly review the advantages and limitations of existing research and demonstrate the potential application values of GAI applied to game theory in mobile networking. Subsequently, we develop a game theory framework enabled by large language models (LLMs) to realize this combination, and demonstrate the effectiveness of the proposed framework through a case study in secured UAV networks. Finally, we provide several directions for future extensions.

This figure illustrates the interaction between players in a non-cooperative game.

The non-cooperative game framework contains multiple players and an environment in which players interact. Each player has a strategy space that represents the available actions and a utility function that evaluates the player's payoff from taking a certain action. Additionally, the objective of each player is to take actions that maximize their own payoff. The environment represents the medium through which players interact, that matches an action profile to a payoff profile. The flow of player interaction is as follows: in the first interaction (Step 1), each player takes an action from their strategy space and receives the corresponding payoff. In subsequent interactions (Step i), each player updates their action based on the observed strategies of other players to improve their own payoff. When the actions of all players no longer change, a Nash equilibrium is obtained.

This figure showcases the proposed framework.

The LLM-enabled game theory framework. The framework is based on a layered architecture consisting of an input layer, an augmented layer, a decision layer, and an output layer. The input layer captures user input queries. The augmented layer employs RAG technology to enhance user queries. The decision layer utilizes a pluggable LLM to generate responses. The output layer returns the generated results to the user.

This figure demonstrates the operational flow of LLM and RAG components.

In the framework configuration, we call the ChatGPT 4 model through the OpenAI API to implement the pluggable LLM component. Furthermore, the RAG component is built based on the LangChain. In Part A, documents are loaded from the knowledge base, segmented into chunks, encoded into vectors, and stored in the vector database. Then, RAG retrieves the K most relevant chunks to the query of user based on semantic relevance from the vector database. In Part B, the original query and the retrieved chunks are inputted together into LLM to generate the final response.

This figure presents the results of the case study.

The experiment results of the UAV secure communication optimization case. The scenario module presents a system model of the considered scenario. The interaction module showcases the functionality of the proposed framework. The RAG augmentation module emphasizes the operational mechanism of RAG. The evaluation results module demonstrate the effectiveness of the proposed framework.

As shown in the scenario module, consider a UAV communication network consisting of N legitimate UAV users, a destination ground base station, a friendly UAV jammer, and a malicious ground eavesdropper. These legitimate UAV users communicate with the destination base station through $N$ orthogonal channels while facing the risk of eavesdropping by the eavesdropper. The friendly UAV jammer has the capability to transmit cooperative jamming signals simultaneously over these channels to enhance the overall secrecy rate against the eavesdropper. The optimization objective is to maximize the aggregate security rate of all legitimate users through optimal power allocation of the friendly jammer across each channel.

As shown in the interaction module, the UAV secure communication optimization problem is formulated and solved through three rounds of user interaction with the GAI agent. In the first round of interaction, the user describes the optimization problem and asks the GAI agent to give a mathematical formulation of the problem. The GAI agent then retrieves semantically relevant information from the database through RAG technology to generate mathematical optimization problem formulation. This mathematical optimization problem is stated as follows: the optimization objective is to maximize the sum of the security rates of N legitimate user channels, the optimization variable is the power allocation of friendly jammers in each channel and the constraints indicate that the power overhead of friendly jammers does not exceed the total power budget. In the second round of interaction, the GAI agent adopts Stackelberg game to analyze the optimization problem formulated. Specifically, legitimate users are defined as buyers who obtain higher security rates by purchasing jamming service. The friendly jammer is defined as seller who gain profit by selling jamming services. In the third round, the GAI agent generates relevant algorithm code to solve the optimization problem.

The evaluation result module (a) shows the convergence of the algorithm generated by the proposed framework (i.e., GAI algorithm). From this figure, we can see that the GAI algorithm reaches a stable state, i.e., Nash equilibrium, after five iterations. The simulation results illustrate that the proposed framework can obtain a Nash equilibrium solution to the game theory problem. Moreover, the evaluation result module (b) shows the performance of the GAI algorithm with respect to different number of channels, where the expert algorithm indicates that the algorithm designed by network experts can be regarded as the optimal algorithm, and the EPR algorithm indicates that the average power allocation strategy is a benchmark algorithm. Correspondingly, we can observe that the GAI algorithm has the same performance as the expert algorithm. The evaluation results demonstrate the effectiveness of the proposed framework.

Tutorial with an Example

In this part, we show a step-by-step tutorial by using our IAI.

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Run the Program

1) Install the following packets using pip


      pip install langchain
      pip install openai

2) Connect with openAI


      llm = OpenAI(api_key="")
      llm = ChatOpenAI()

3) Format Agent Reply


      from langchain.prompts.chat import ChatPromptTemplate
      prompt = ChatPromptTemplate.from_template()

4) Make A Retriever


      retriever = db.as_retriever()
      retriever.search_kwargs['k'] = 10

5) Make a Chain


      from langchain_core.output_parsers import StrOutputParser
      from langchain_core.runnables import RunnablePassthrough
      retriever_chain = (
        {"context": retriever, "question": RunnablePassthrough()}
        | prompt
        | llm
        | StrOutputParser())

BibTeX

@article{zhang2024interactive,
  title={Generative AI for Game Theory-based Mobile Networking},
  author={He, Long and Sun, Geng and Niyato, Dusit and Du, Hongyang and Mei, Fang and Kang, Jiawen and Debbah, M{\'e}rouane and others},
  journal={arXiv preprint arXiv:2404.09699},
  year={2024}}