Bayesian Game Research Articles

Optimization of a Bayesian Game for Peer-to-Peer Trading among Prosumers under Incomplete Information via a CNN-LSTM-ATT

In modern low-carbon industrial parks, various distributed renewable energy resources are employed to fulfill production needs. Despite the growing capacity of renewable energy generation, a significant portion of the power produced by these renewable resources remains unconsumed, resulting in a waste of resources. Within an industrial park, microgrids that both generate and consume energy resources act as energy prosumers. Peer-to-peer (P2P) trading provides an efficient means of utilizing renewable energy among these energy prosumers, who possess both power generation and consumption capabilities. However, within the current market mechanism, each prosumer retains private information that is not disclosed on the network. To address the issue of incomplete information among multiple prosumers during the decision-making process, we develop a Bayesian game model based on the CNN-LSTM-ATT prediction method for P2P electricity transactions among multiple prosumers. The energy prosumers in each industrial park aim to minimize their energy consumption costs by adjusting strategies that include P2P energy trading and managing thermal loads. Prosumers make decisions on the basis of their own characteristics and estimates of other prosumer characteristics, which are obtained from the joint probability distribution predicted by the CNN-LSTM-ATT method. These decisions are aimed at minimizing each prosumer's electricity costs. The simulation results demonstrate the effectiveness of the Bayesian game model proposed in this study.

Linking quantum discord with Bayesian game theory

Linking quantum discord with Bayesian game theory

BUGTGNN: Bayesian Uncertainty and Game Theory for Enhancing Graph Neural Networks through Mathematical Analysis

The ongoing COVID-19 pandemic has emphasized the critical need for rapid and accurate diagnostic methods. Precise classification of chest X-ray images into COVID-19 and non-COVID-19 cases serves as a pivotal tool in effective disease management and control. Existing methods often suffer from trade-offs between accuracy, precision, and computational efficiency, hindering their practical utility. Current approaches mainly rely on traditional machine learning algorithms or Convolutional Neural Networks (CNNs), which while effective, still present limitations in terms of sensitivity, specificity, and computational speed. These constraints necessitate the exploration of innovative techniques for improving classification metrics across multiple dimensions. In this work, we introduce a novel framework for optimizing Graph Neural Networks (GNNs) through mathematical analysis, specifically incorporating spectral methods, dynamic graph sparsification, game-theoretic attention mechanisms, Bayesian uncertainty models, and advanced graph partitioning techniques. When applied to the classification of COVID-19 chest X-rays, our model demonstrated significant improvements—increasing precision by 8.3%, accuracy by 8.5%, recall by 4.9%, specificity by 4.5%, and the Area Under the Curve (AUC) by 5.9%, while simultaneously reducing computational delay by 10.5% across multiple datasets. The proposed optimization strategies showcase the power of interdisciplinary approaches in advancing machine learning techniques for medical applications. The demonstrated improvements in classification metrics and computational efficiency highlight the model's potential for broader adoption in healthcare settings, providing a robust, fast, and more accurate tool for COVID-19 diagnosis.

Defending Against SSDF Attacks From Randomly Appearing Intelligent Malicious Vehicle Users in the CIoV Network by Bayesian Stackelberg Game

Defending Against SSDF Attacks From Randomly Appearing Intelligent Malicious Vehicle Users in the CIoV Network by Bayesian Stackelberg Game

Cloud security in the age of adaptive adversaries: A game theoretic approach to hypervisor-based intrusion detection

Recent advancements in cloud computing have underscored the critical need for robust security mechanisms to counter evolving cyber-threats. Traditional security solutions such as Intrusion Detection Systems (IDSs) often fall short due to their inability to anticipate the strategies of adaptive cyber adversaries. Game theory is considered a popular analytical tool for understanding the strategic interactions between defenders and adversaries, providing a more informed decision-making process. However, existing game-theoretic IDSs often employ non-comprehensive utility functions with limited parameters that fail to capture the complexity of real-world dynamics. This paper introduces a novel Game-Theoretic Hypervisor-based IDS (GHyIDS), which employs comprehensive utility functions and an innovative belief update model to enhance detection accuracy and adaptability in dynamic cloud environments. To overcome the limitations of existing models, we design comprehensive utility functions by incorporating a wider range of real-world parameters, such as trust score, risk, vulnerability, damage severity, worth of the VM, means, opportunities, and access available to the attacker, as well as success rates of attack detection and execution. We propose a Resource-Aware Static Intrusion Detection Bayesian Game (S-IDBG) and extend it into a Dynamic Multi-Stage IDBG (D-IDBG), enabling the system to dynamically adapt to changes in attack patterns and system vulnerabilities. The belief update model is pivotal in continuously refining the system’s strategies based on observed behaviors and outcomes, allowing for precise adjustments to the evolving threats. Our experimental results show a significant improvement over existing models, with our approach achieving approximately 10% increase in detection rate, 20% reduction in false positive rate and 10% reduction in false negative rate in comparative analysis against state-of-the-art models namely, the trust-based Maxmin game and the repeated Bayesian Stackelberg game.

Stationary Bayesian–Markov Equilibria in Bayesian Stochastic Games with Periodic Revelation

Stationary Bayesian–Markov Equilibria in Bayesian Stochastic Games with Periodic Revelation

Nash Equilibria and Undecidability in Generic Physical Interactions—A Free Energy Perspective

We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players’ point of view.

Correlated Equilibria in Large Anonymous Bayesian Games

We consider multipopulation Bayesian games with a large number of players. Each player aims at minimizing a cost function that depends on this player’s own action, the distribution of players’ actions in all populations, and an unknown state parameter. We study the nonatomic limit versions of these games and introduce the concept of Bayes correlated Wardrop equilibrium, which extends the concept of Bayes correlated equilibrium to nonatomic games. We prove that Bayes correlated Wardrop equilibria are limits of action flows induced by Bayes correlated equilibria of the game with a large finite set of small players. For nonatomic games with complete information admitting a convex potential, we prove that the set of correlated and of coarse correlated Wardrop equilibria coincide with the set of probability distributions over Wardrop equilibria and that all equilibrium outcomes have the same costs. We get the following consequences. First, all flow distributions of (coarse) correlated equilibria in convex potential games with finitely many players converge to mixtures of Wardrop equilibria when the weight of each player tends to zero. Second, for any sequence of flows satisfying a no-regret property, its empirical distribution converges to the set of distributions over Wardrop equilibria, and the average cost converges to the unique Wardrop cost. Funding: This work was partially supported by European Cooperation in Science and Technology Action 16228 GAMENET. F. Koessler acknowledges the support of the Agence Nationale de la Recherche [Grant StratCom ANR-19-CE26-0010-01]. M. Scarsini acknowledges the support of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni project [Grant CUP_E53C22001930001], the Ministero dell’Università e della Ricerca Progetti di Rilevante Interesse Nazionale [Grant 2022EKNE5K], and the European Union-Next Generation EU, component M4C2, investment 1.1 (Ministero dell’Università e della Ricerca Progetti di Rilevante Interesse Nazionale Piano Nazionale di Ripresa e Resilienza) [Grant P2022XT8C8]. T. Tomala gratefully acknowledges the support of the HEC foundation and Agence Nationale de la Recherche/Investissements d’Avenir [Grant ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047].

Defense strategy selection based on incomplete information game for the false data injection attack

With the rapid development and wide application of sensing devices and communication networks, the traditional power system has transformed into a cyber physical power system (CPPS) gradually. The constant interaction of information flow and power flow exposes the grid to potential cyber-attack risks. In this paper, the defense strategy selection approaches are proposed based on incomplete information game against false data injection attack (FDIA) in different scenarios. Firstly, the attack-defense tree model containing economic indicators and a measure of attack is established, and the expected revenues of both attacker and defender are calculated in detail. Secondly, the static Bayesian attack-defense game model in which the defender grasps incomplete information is constructed, considering two cases of low-tech attacker and high-tech attacker. Then, the zero-sum attack-defense game model in which the attacker masters incomplete information is structured, considering the changing attack space. Finally, the simulations are carried out on the IEEE 30-bus system, and the optimal defense strategies in the case of two incomplete information are obtained by solving the equilibrium point. The simulation results demonstrate that the proposed method is effective in cyber security defense system, and can provide guiding ideology and theoretical basis for operators to deploy defense measures.

PPSO and Bayesian game for intrusion detection in WSN from a macro perspective

The security of wireless sensor networks is a hot topic in current research. Game theory can provide the optimal selection strategy for attackers and defenders in the attack-defense confrontation. Aiming at the problem of poor generality of previous game models, we propose a generalized Bayesian game model to analyze the intrusion detection of nodes in wireless sensor networks. Because it is difficult to solve the Nash equilibrium of the Bayesian game by the traditional method, a parallel particle swarm optimization is proposed to solve the Nash equilibrium of the Bayesian game and analyze the optimal action of the defender. The simulation results show the superiority of the parallel particle swarm optimization compared with other heuristic algorithms. This algorithm is proved to be effective in finding optimal defense strategy. The influence of the detection rate and false alarm rate of nodes on the profit of defender is analyzed by simulation experiments. Simulation experiments show that the profit of defender decreases as false alarm rate increases and decreases as detection rate decreases. Using heuristic algorithm to solve Nash equilibrium of Bayesian game provides a new method for the research of attack-defense confrontation. Predicting the actions of attacker and defender through the game model can provide ideas for the defender to take active defense.

Information Signaling With Concurrent Monetary Incentives in Bayesian Congestion Games

Information Signaling With Concurrent Monetary Incentives in Bayesian Congestion Games

Enhancing cloud security: harnessing bayesian game theory for a dynamic defense mechanism

Enhancing cloud security: harnessing bayesian game theory for a dynamic defense mechanism

Bayesian equilibrium: From local to global

We study Bayesian games with a continuum of states which partition into a continuum of components, each of which is common knowledge, such that equilibria exist on each component. A canonical case is when each agent’s information consists of both public and private information, and conditional on each possible public signal, equilibria exist. We show that under some regularity conditions on the partition, measurable Bayesian equilibria exist for the game in its entirety. The results extend to pure equilibria, as well as to non-compact state-dependent action sets, uncommon priors, and non-bounded payoffs; the results also apply to several notions of approximate equilibria.

Generalized naming game and Bayesian naming game as dynamical systems.

We study the β model (β-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the β model, we demonstrate the existence of a nongeneric bifurcation with a bifurcation point β_{c}=1/3. As β passes through β_{c}, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities p_{A} and p_{B} as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that p_{A}=p_{B}=p, where p is a constant.

An Improved Bayesian Graphical Game Method for the Optimal Consensus Problem in the Presence of False Information

An Improved Bayesian Graphical Game Method for the Optimal Consensus Problem in the Presence of False Information

Enhancing ecological uncertainty predictions in pollution control games through dynamic Bayesian updating

This study presents a dynamic Bayesian game model designed to improve predictions of ecological uncertainties leading to natural disasters. It incorporates historical signal data on ecological indicators. Participants, acting as decision-makers, receive signals about an unknown parameter-observations of a random variable’s realization values before a specific time, offering insights into ecological uncertainties. The essence of the model lies in its dynamic Bayesian updating, where beliefs about unknown parameters are refined with each new signal, enhancing predictive accuracy. The main focus of our paper is to theoretically validate this approach, by presenting a number of theorems that prove its precision and efficiency in improving uncertainty estimations. Simulation results validate the model’s effectiveness in various scenarios, highlighting its role in refining natural disaster forecasts.

Investigation into Forecasting Personal Loan Defaults and Managing Risk Using Bayesian Game Theory

Investigation into Forecasting Personal Loan Defaults and Managing Risk Using Bayesian Game Theory

Invariant Equilibrium in Discontinuous Bayesian Games

We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is better-reply secure. The invariance property then provides an existence result for all Bayesian games in the class. Results are shown for both pure strategy and behavioral strategy equilibrium. We illustrate the application of the results with an example of a class of contests with bid caps.

Dynamic Bayesian game optimization method for multi-energy hub systems with incomplete load information

The interconnection of Energy Hub can enhance the energy efficiency and reliability associated with the independent operation of energy systems. However, the traditional optimal scheduling methods are hard to tackle the situation with the incomplete load information and competitive constraints of a multi-Energy Hub. This paper proposes a dynamic Bayesian game optimization scheduling strategy considering incomplete information on users’ load-side demand. First, a load forecast error coefficient is introduced to handle the conditional probability problem caused by incomplete information through the Bayesian rule. The constraint relationship among multi-Energy Hub under the dynamic price mechanism is analyzed to meet the economic and environmental coordination goals under load uncertainty. Second, extending from Nash equilibrium to Bayes Nash equilibrium proves the existence and uniqueness of Nash equilibrium solutions in Bayesian game models. The decision game algorithm is used to optimize the scheduling of the multi-Energy Hub and subsequently ensure the autonomous scheduling of the system and solve the information barriers. Finally, an Integrated Energy System composed of three Energy Hubs was used to validate the effectiveness and superiority of the proposed optimization method. Results show that under the Bayesian game decision, the multi-Energy Hub game model has reduced the total cost of the Integrated Energy System by 0.78 %, which can improve the economic benefit and address the environmental pollution problem.

A jamming power control game with unknown user’s communication metric

We consider a jamming problem in which a jammer aims to degrade a user’s communication in which the user might differ in applied applications or communication purposes. Such differences are reflected by different communication metrics used by the user. Specifically, signal-to-interference-plus-noise ratio (SINR) is used as a metric to reflect regular data transmission purposes. Meanwhile, as another metric, latency, modeled by the inverse SINR, is used to reflect emergency communication purposes. We consider the most difficult scenario for the jammer where it does not know which application (metric) the user employs. The problem is formulated as a Bayesian game. Equilibrium is found in closed form, and the dependence of equilibrium on network parameters is illustrated.