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ABSTRACT This paper deals with the two‐player zero‐sum game problem, which is a bounded L2$$ {L}_2 $$‐gain robust control problem. Finding an analytical solution to the complex Hamilton‐Jacobi‐Issacs (HJI) equation is a challenging task. Hence, a novel Q‐learning algorithm for unknown continuous‐time (CT) affine‐in‐inputs nonlinear systems is proposed for generating an approximate solution to the HJI equation, which is valid in a local domain due to the use of a local approximator, that is, a Neural Network (NN) structure. The approach is model‐free and does not require the knowledge of system drift dynamics, and input and disturbance gains. The algorithm learns online from measurements of state variables in real time. To generate the local approximate solution of the HJI equation for the two‐player zero‐sum game problem for nonlinear systems, the proposed non‐iterative algorithm requires only a single critic NN instead of the commonly used triple NN approximator structure. A persistence of excitation condition is required to guarantee Uniformly Ultimately Boundedness (UUB) and convergence to the optimal solution. The effectiveness of the proposed Q‐learning approach for the two‐player zero‐sum game problem is demonstrated via simulations of a linear F‐16 aircraft plant and a highly complex nonlinear system. Proof of closed‐loop system stability is provided using Lyapunov Analysis, and convergence of the approximate solution to the true saddle‐point solution is guaranteed in a UUB‐sense. [ABSTRACT FROM AUTHOR]

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The competition among cities to host a sports team or a large-scale international sports event is modeled as a winner-pay contest with an entry fee. In the first stage, each contestant (city) decides whether to pay the entry fee (infrastructure required by the team, for example), which allows it to participate in the second stage, that is, the actual contest. We show that the contest organizer's choice of the optimal entry fee does not depend on the number of contestants. Furthermore, in some cases, the result is a form of zero-sum game, in which the sports team or event organizer is the main beneficiary. The findings shed light on this type of competition and under what conditions on the entry fee a city might benefit from hosting a sports team or large-scale international sports event. [ABSTRACT FROM AUTHOR]

In this article, an H∞$$ {H}_{\infty } $$ optimal preview repetitive control (OPRC) scheme is proposed to deal with the disturbance attenuation problem for continuous‐time linear systems with external unknown disturbance and input delay. A general bounded L2$$ {L}_2 $$ gain is applied to the H∞$$ {H}_{\infty } $$ OPRC tracking control problem by introducing a function with discounted performance. First, an augmented system containing system state equation, tracking error dynamics, and modified repetitive control output equation is constructed, which is then transformed into a non‐delayed one by state transformation. Next, the OPRC controller is given and the game algebraic Riccati equation (GARE) is derived by transforming the H∞$$ {H}_{\infty } $$ tracking problem into a 2‐player zero‐sum game problem to give a Nash equilibrium solution of the associated min–max optimization problem. Besides, a value iteration (VI) algorithm is introduced to optimize the solution of continuous time GARE and ensure its convergence. Furthermore, the bounded‐input bounded‐output stability of the closed‐loop system is obtained by giving an upper bound on the discount factor. Finally, the numerical simulation example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper explores an optimal investment and reinsurance problem involving both ordinary and catastrophe insurance businesses. The catastrophic events are modeled as following a compound Poisson process, impacting the ordinary insurance business. The claim intensity for the ordinary insurance business is described using a Cox process with a shot-noise intensity, the jump of which is proportional to the size of the catastrophe event. This intensity increases when a catastrophe occurs and then decays over time. The insurer’s objective is to maximize their terminal wealth under the Monotone Mean-Variance (MMV) criterion. In contrast to the classical Mean-Variance (MV) criterion, the MMV criterion is monotonic across its entire domain, aligning better with fundamental economic principles. We first formulate the original MMV optimization problem as an auxiliary zero-sum game. Through solving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation, explicit forms of the value function and optimal strategies are obtained. Additionally, we provide the efficient frontier within the MMV criterion. Several numerical examples are presented to demonstrate the practical implications of the results. [ABSTRACT FROM AUTHOR]

Abstract Deep neural networks (DNNs) are fundamental to modern applications like face recognition and autonomous driving. However, their security is a significant concern due to various integrity risks, such as backdoor attacks. In these attacks, compromised training data introduce malicious behaviors into the DNN, which can be exploited during inference or deployment. This paper presents a novel game-theoretic approach to model the interactions between an attacker and a defender in the context of a DNN backdoor attack. The contribution of this approach is multifaceted. First, it models the interaction between the attacker and the defender using a game-theoretic framework. Second, it designs a utility function that captures the objectives of both parties, integrating clean data accuracy and attack success rate. Third, it reduces the game model to a two-player zero-sum game, allowing for the identification of Nash equilibrium points through linear programming and a thorough analysis of equilibrium strategies. Additionally, the framework provides varying levels of flexibility regarding the control afforded to each player, thereby representing a range of real-world scenarios. Through extensive numerical simulations, the paper demonstrates the validity of the proposed framework and identifies insightful equilibrium points that guide both players in following their optimal strategies under different assumptions. The results indicate that fully using attack or defense capabilities is not always the optimal strategy for either party. Instead, attackers must balance inducing errors and minimizing the information conveyed to the defender, while defenders should focus on minimizing attack risks while preserving benign sample performance. These findings underscore the effectiveness and versatility of the proposed approach, showcasing optimal strategies across different game scenarios and highlighting its potential to enhance DNN security against backdoor attacks.

Deep neural networks (DNNs) are fundamental to modern applications like face recognition and autonomous driving. However, their security is a significant concern due to various integrity risks, such as backdoor attacks. In these attacks, compromised training data introduce malicious behaviors into the DNN, which can be exploited during inference or deployment. This paper presents a novel game-theoretic approach to model the interactions between an attacker and a defender in the context of a DNN backdoor attack. The contribution of this approach is multifaceted. First, it models the interaction between the attacker and the defender using a game-theoretic framework. Second, it designs a utility function that captures the objectives of both parties, integrating clean data accuracy and attack success rate. Third, it reduces the game model to a two-player zero-sum game, allowing for the identification of Nash equilibrium points through linear programming and a thorough analysis of equilibrium strategies. Additionally, the framework provides varying levels of flexibility regarding the control afforded to each player, thereby representing a range of real-world scenarios. Through extensive numerical simulations, the paper demonstrates the validity of the proposed framework and identifies insightful equilibrium points that guide both players in following their optimal strategies under different assumptions. The results indicate that fully using attack or defense capabilities is not always the optimal strategy for either party. Instead, attackers must balance inducing errors and minimizing the information conveyed to the defender, while defenders should focus on minimizing attack risks while preserving benign sample performance. These findings underscore the effectiveness and versatility of the proposed approach, showcasing optimal strategies across different game scenarios and highlighting its potential to enhance DNN security against backdoor attacks. [ABSTRACT FROM AUTHOR]

We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents { γ 1 , γ 2 , ... } under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI. [ABSTRACT FROM AUTHOR]

This article proposes an H∞$$ {H}_{\infty } $$ optimal leader‐follower consensus control protocol with finite‐time prescribed performance for nonlinear multiagent systems suffering from the actuator fault based on the zero‐sum game framework. First, to guarantee the specified performance of the system within a finite time frame, a novel error transformation function (ETF) is constructed. The ETF proposed in this paper can adjust the mapping range of error transformation to achieve better error convergence performance, thereby enhancing the flexibility of the controller design. Then, to compensate for the negative impact of actuator fault, an error‐related item is separated from the optimal performance index function to design an online fault estimator, which can obtain a better error estimation accuracy. Furthermore, to lessen the need for difficult‐to‐verify persistent excitation signal in adaptive dynamic programming algorithm, both historical and real‐time data are applied to adjust the updating law of neural network weight. Moreover, it demonstrates that the signals within the closed‐loop system are bounded and the expected finite‐time prescribed performance can be ensured in the presence of faults. Finally, a numerical example of multiple single‐link robots manipulator system is executed to validate the efficacy of the developed scheme. [ABSTRACT FROM AUTHOR]

This article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

The authors of the present article pose and consider in detail the highly relevant issue of whether capitalism has a future or whether it will be replaced by some new system. And if it does have a future, then what future will it be? These questions are nothing new, but in the recent few years, just like a hundred years ago, they have acquired exceptional importance, since not only the Left but also the representatives of the largest financial capital started speaking about the end of capitalism. The present article considers the following aspects: what is capitalism as an economic sector and as an economic system? How did capitalism evolve? What are its potentialities? The authors also make some forecasts for the next 50–100 years. Various scenarios for the future of capitalism are considered: from maintaining its leading role to its reduction to a sector. It is assumed that in the coming decades, the development of capitalism may proceed in different ways in developed and developing countries, which may result in a complex continuum of types, transitions, combinations, and forms of capitalism. In some countries, the development of capitalism has reached a level when it has already exhausted itself and needs transformations; meanwhile, there are countries where full-fledged market relations have not yet emerged. The authors analyze two main types of capitalism. The developed countries are likely to experience a shift toward strengthening of distributive institutions. In their turn, the developing countries that continue the processes of economic and socio-political modernization are likely to proceed toward strengthening of capitalist market institutions, though with some important restrictions preventing exploitation and environmental degradation. The authors believe that capitalism will be inevitably transformed in one way or another, but such transformations can vary greatly. [ABSTRACT FROM AUTHOR]

This paper addresses the zero‐sum game problem for strict‐feedback nonlinear multiagent systems with full‐state constraints. Specifically, this paper focuses on the zero‐sum game scenario, wherein multiple agents aim to optimize the control strategies while considering the conflicting objectives of their opponents. To handle the full‐state constraints, a one‐to‐one nonlinear mapping technique is employed to convert the original strict‐feedback system into a more manageable pure‐feedback system without state constraints. In order to find a Nash equilibrium for virtual control signals and external disturbances, a simplified reinforcement learning algorithm is proposed, which tackles the challenges posed by solving the Hamilton–Jacobi–Isaacs equation. Unlike the existing H∞$$ {H}_{\infty } $$ optimal control strategies that deal with matching conditions, the H∞$$ {H}_{\infty } $$ optimal control strategy for strict‐feedback nonlinear systems needs to address the computational complexity issue arising from the repeated derivation of the virtual controller. To overcome the high‐order virtual controller problem, an approach based on the dynamic surface technique is introduced. By incorporating an approximation term of the high‐order virtual controller into the value function, the computational complexity challenge is effectively resolved. Based on the Lyapunov stability theorem, it is proved that all signals of the closed‐loop systems are semi‐global uniformly ultimately bounded and the tracking control performance can be guaranteed. Finally, simulation results are given to verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: With the advent and popularity of electric vehicles (EVs), the intelligent transportation system has adopted them as an alternative to fossil fuel or gasoline vehicles owing to their benefits of reduced greenhouse gas emissions. However, it becomes critical to schedule the vast EVs at the charging station (CS) efficiently while maintaining security, privacy, and optimality during the energy trading. Therefore, we propose a blockchain and zero‐sum game theory‐based energy trading scheme, that is, DEVS, for optimal and secure EV charging at the CS. We incorporate the Interplanetary File System with the blockchain to ameliorate the cost‐efficiency and reliability of EV energy trading. Furthermore, we implement the zero‐sum game theory between players EV and CS to yield an optimal payoff based on pure and mixed strategies during the energy trading procedure. Moreover, we deploy and execute the smart contract (SC) of the blockchain‐based proposed DEVS scheme in the Remix integrated development environment to secure EV energy trading transactions. Additionally, the security of the proposed DEVS scheme is checked and analyzed using a fuzzing‐based Echidna tool for protected energy trading. Finally, the performance evaluation of the proposed DEVS scheme is analyzed using various standard metrics such as profit comparison based on strategies, energy price comparison, CS profit comparison for pure strategy (based on arrival time), convergence comparison, and profit (EV and CS) at saddle point and mixed strategy to avail preserved and optimal energy trading for EVs. [ABSTRACT FROM AUTHOR]

In this paper, an optimisation problem for the monotone mean-variance (MMV) criterion is considered from the perspective of the insurance company. The MMV criterion is an amended version of the classical mean-variance (MV) criterion which guarantees the monotonicity of the utility function. With this criterion we study the optimal investment and reinsurance problem which is formulated as a zero-sum game between the insurance company and an imaginary player. We apply the dynamic programming principle to obtain the corresponding Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. As the main conclusion of this paper, by solving the HJBI equation explicitly, the closed forms of the optimal strategy and the value function are obtained. Moreover, the MMV efficient frontier is also provided. At the end of the paper, a numerical example is presented. [ABSTRACT FROM AUTHOR]

All the n possible returns on a financial asset are the components of an element of a linear space over R. This paper shows how to transfer all these n possible returns on a one-dimensional straight line. In this research work, two or more than two financial assets are studied. More than two financial assets are always studied in pairs, so they are treated inside the budget set of a given decision-maker. Two univariate financial assets give rise to a bivariate financial asset characterized by a bivariate (two-dimensional) distribution of probability. This research work shows how constrained choices being made by a given decision-maker under conditions of uncertainty and riskiness maximize his utility of an ordinal nature. For this reason, prevision bundles are dealt with. Furthermore, every choice identifies a zero-sum game. Since a specific kind of choice associated with two or more than two objects is investigated, new conceptual and mathematical outcomes related to financial decisions are shown. [ABSTRACT FROM AUTHOR]

In this research, we investigate the horse racing game, a two-player game with six strategies. Our objective is to develop a theoretical framework for the game by employing the process of quantization. The Nash equilibrium (NE) of the quantum horse racing game is analyzed through an examination of the payoff matrix, and the results are compared to those of the classical horse racing game. Our findings demonstrate that the quantum horse racing game features both pure and mixed strategy NE, whereas the classical horse racing game possesses only mixed strategy NE. Additionally, our results indicate that the quantum horse racing game can mitigate the risks associated with the zero-sum game while outperforming the classical game. [ABSTRACT FROM AUTHOR]

In this paper, we give an example of a statement concerning two-player zero-sum games which is undecidable, meaning that it can neither be proven or disproven by the standard axioms of mathematics. Earlier work has shown that there exist "paradoxical" two-player zero-sum games with unbounded payoffs, in which a standard calculation of the two players' expected utilities of a mixed strategy profile yield a positive sum. We show that whether or not a modified version of this paradoxical situation, with bounded payoffs and a weaker measurability requirement, exists is an unanswerable question. Our proof relies on a mixture of techniques from set theory and ergodic theory. [ABSTRACT FROM AUTHOR]

The minimax theorem for zero-sum games is easily proved from the strong duality theorem of linear programming. For the converse direction, the standard proof by Dantzig is known to be incomplete. We explain and combine classical theorems about solving linear equations with nonnegative variables to give a correct alternative proof more directly than Adler. We also extend Dantzig's game so that any max-min strategy gives either an optimal LP solution or shows that none exists. [ABSTRACT FROM AUTHOR]

The deep integration of artificial intelligence (AI) and communication technology is the typical feature of the 6G network.On the one hand, AI injects new vitality into the development of the 6G network, which can effectively use the data generated by the historical operation of the network.It enables the network to be self-maintained and selfoptimized, and accelerates the process of network intelligence.On the other hand, the rich scenarios and IoT devices of the 6G network provide a large number of application fields and massive data for AI.These can enable the better deployment of AI, fully demonstrate the performance advantages of AI, and provide high-quality services for users.However, in practice, it is difficult to give full play to the performance advantages of AI due to the difficulty of sample collection, high cost of the collection, and lack of universality which caused by the complexity of the environment.Therefore, academia and industry introduce generative adversarial network (GAN) into the design of wireless networks.The powerful feature learning and feature expression ability of GAN can generate a large number of generated samples, which realizes the expansion of the wireless database.The introduction of GAN can effectively improve the generalization ability of AI models for wireless networks.Owing to the excellent performance of GAN, the generative model represented by GAN has attracted increased attention in the field of wireless networks, and rapidly became the new research hotspot of 6G networks.Firstly, the principle of GAN and its different versions of improved derived models were summarized.Then, the framework, advantages and disadvantages of each model were analyzed.Secondly, the research and application status of these models in wireless networks were reviewed.Finally, the research trends of GAN were proposed for the 6G network requirements, which provided some valuable exploration for future research.

Fuzzy set plays an important role in handling vagueness for controlling uncertain dynamical systems. However, conventional type-1 fuzzy set (T1FS) requires precisely defined membership function, which is usually unavailable in practical control applications. This study pioneers the use of IT2FS for the control design of uncertain dynamical systems to relax this limitation of conventional T1FS-based control design. Concretely, the considered (possibly fast) time-variant uncertainty is bounded with the bound lying within IT2FS (hence interval type-2 fuzzy dynamical system, IT2FDS). A robust control design approach is proposed without invoking any IF-THEN fuzzy rules, providing a two-layer performance. The lower layer renders uniform boundedness and uniform ultimate boundedness for the system by the Lyapunov analysis, ensuring the bottom line. The upper layer improves the fuzzy-based control performance by optimal gain design oriented by a two-player zero-sum game, taking advantage of the interval description of membership function. It is shown that the equilibrium of the game which contains the optimal gain always exists. A semi-analytical solution strategy for the equilibrium is given. This is the first endeavor in exploring IT2FS-based control design without using any IF-THEN rules. It is shown in the demonstrative examples that the proposed IT2FS-based approach can achieve better control performance than the conventional T1FS-based approach. [ABSTRACT FROM AUTHOR]

In this paper, a zero-sum differential game is formulated and solved in which a mobile Evader seeks to escape from within a circle at whose origin lies a stationary, turn-constrained Turret. The scenario is a variant of the famous Lady in the Lake game in which the shore-constrained Pursuer has been replaced with the Turret. As in the former, it is assumed that the Turret's maximum angular rate is greater than the linear velocity of the Evader. Since two outcomes are possible, a Game of Kind arises - either the Evader wins by reaching the perimeter of the circle, or the Turret wins by aligning with the latter's position. A barrier surface partitions the state space into two regions corresponding to these two outcomes and a Game of Degree is solved within each region. The solutions to the Games of Degree are comprised of the Value functions (i.e., the equilibrium value of the cost/utility as a function of the state) and the saddle-point equilibrium control policies for the two players. Like the Lady in the Lake game, the equilibrium policy of the Evader is not uniquely defined where it has angular rate advantage over the Turret. Unlike the Lady in the Lake game, the losing region for the Evader is present for all speed ratios, and there is an additional semi-permeable surface separating center- and shore-bound Evader trajectories. The solution depends heavily upon the speed ratio of the agents; in particular, there are two speed ratio regimes with distinctive solution structures. [ABSTRACT FROM AUTHOR]

Uncertain noncausal systems (UNCSs) are uncertain singular systems that are supposed to be regular along.This study investigates two-player zero-sum games (TPZSGs) for UNCSs using the optimistic value criterion. The first step is to introduce a method to convert a linear uncertain noncausal system (UNCS) considering linear control terms into subsystems including two kinds of uncertain difference equations. Recurrence equations are derived for tackling a TPZSG subject to linear UNCSs. Using recurrence equations, we give an algorithm for solving the TPZSG subject to linear UNCSs and show how to apply the algorithm to find the saddle-point solution and the equilibrium value of this kind of game by a numerical example. To expand on these results, we provide the corresponding equations for solving TPZSGs subject to nonlinear UNCSs. Moreover, we give the saddle-point solution and equilibrium value of a TPZSG for a nonlinear UNCS considering quadratic control terms by solving the equations. [ABSTRACT FROM AUTHOR]

Summary In this article, a self‐learning disturbance compensation control method is developed, which enables the unknown discrete‐time (DT) systems to achieve performance optimization in the presence of disturbances. Different from traditional model‐based and data‐driven state feedback control methods, the developed off‐policy Q‐learning algorithm updates the state feedback controller parameters and the compensator parameters by actively interacting with the unknown environment, thus the approximately optimal tracking can be realized using only data. First, an optimal tracking problem for a linear DT system with disturbance is formulated. Then, the design for controller is achieved by solving a zero‐sum game problem, leading to an off‐policy disturbance compensation Q‐learning algorithm with only a critic structure, which uses data to update disturbance compensation controller gains, without the knowledge of system dynamics. Finally, the effectiveness of the proposed method is verified by simulations. [ABSTRACT FROM AUTHOR]

We consider zero-sum stochastic games in continuous time with controlled Markov chains and with risk-sensitive average cost criterion. Here the transition and the cost rates may be unbounded. We prove the existence of the value of the game and a saddle-point equilibrium in the class of all stationary strategies under a Lyapunov stability condition. This is accomplished by establishing the existence of a principal eigenpair for the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. This, in turn, is established by using a nonlinear version of Krein-Rutman theorem. We then obtain a characterization of the saddle-point equilibrium in terms of the corresponding HJI equation. Finally, we use a controlled population system to illustrate our results. [ABSTRACT FROM AUTHOR]

An attack–defense model is considered in which the attack can deliver several strikes on defense points to maximize the damage. A way of creating a solution to a zero-sum game in mixed strategies is developed. [ABSTRACT FROM AUTHOR]

This article is based on the premise that the South Caucasus has often been the scene of competition between regional and extra-regional powers. In the distant past, this rivalry was predominantly limited to three major powers: the Ottoman Empire, the Persian Empire and the Russian Empire. After a period of near-total Soviet rule over this region, other contenders (e.g., China, Europe and the United States) were provided with opportunities to get actively involved in the region in the aftermath of the USSR collapse. At the same time, Iran and Turkey also decided to enter the regional competition to benefit from the power void. The military conflicts between Armenia and Azerbaijan which occurred soon after the Soviet government fell, gradually enabled some new rival players (e.g., India and Pakistan) to gain a foothold in the South Caucasus. The main reasons for the involvement of the great powers and the other extra-regional players in the South Caucasus are diverse, ranging from mainly economic ones (as in the case of China) to predominantly political ones (as in the case of Iran, Turkey, the U.S. and Russia). Of course, they are all interested in the economic potential of establishing closer trade and investment ties with the regional states. The primary research question is as follows: Why have India and Pakistan been intervening in the conflict zones in the South Caucasus which is located at a distance from their own territories? In the hypothesis, it is argued that the decisions of Pakistan and India to get involved in the interstate conflicts of the South Caucasus is a reflection of the protracted conflict between these two countries over Kashmir. The two South Asian rivals appeared on the scene after the war broke out between Azerbaijan and Armenia, and resulted in Pakistan's decision to send military forces and weapons to help the war efforts of Azerbaijan. This in turn led to India's deep concerns about Islamabad's adventurous moves to improve its power and influence abroad. The victory of Azerbaijan in the war increased New Delhi's worry because the victory of Azerbaijan meant the victory of foreign policies of Pakistan and Turkey, which had unfavorable relations with India. This matter was important from the point of view that the adventures of Islamabad and Ankara were not limited to the South Caucasus, and might have been extended to Central Asia and from there to South Asia. The main concern of India's foreign policymakers was about the expansion of Pakistan's power and influence among the regional states that might then take side with Pakistan in its Kashmir conflict with New Delhi. Furthermore, the geostrategic location of the South Caucasus has been deemed important as a suitable corridor for creating a north-south transport corridor to connect India to Russia and Europe through Central Asia and Iran. The region has the potential to meet some of India's raw material and energy needs, including oil and gas. Utilizing the method of qualitative thematic analysis for hypothesistesting, the findings revealed that the rules of a zero-sum game overshadow the bilateral relations of the countries that are engaged in a protracted conflict over their vital national interest. Pakistan's support for Azerbaijan in its conflict with Armenia was aimed at expanding its influence in a strategic region in the hope of ultimately strengthening its position vis-à-vis India in the Kashmir conflict situation. Not surprisingly, India has acted in a reactionary manner to neutralize Pakistan's foreign policy initiatives by taking side with Armenia. [ABSTRACT FROM AUTHOR]

This study aims to address the limitations of traditional Failure Mode and Effect Analysis (FMEA) in managing safety and reliability within complex systems characterized by interdependent critical factors. We propose an integrated framework that combines FMEA with the strategic decision-making principles of Game Theory, thereby enhancing the assessment and mitigation of risks in intricate environments. The novel inclusion of the Best Worst Method (BWM) and Pythagorean fuzzy uncertain linguistic variables refines the accuracy of risk evaluation by overcoming the inherent deficiencies of conventional FMEA approaches. Through sensitivity analysis, the framework's efficacy in identifying and prioritizing failure modes is empirically validated, guiding the development of targeted interventions. The practical application of our methodology is demonstrated in a comprehensive healthcare system analysis, showcasing its versatility and significant potential to improve operational safety and reliability across various sectors. This research is particularly beneficial for systems engineers, risk managers, and decision-makers seeking to fortify complex systems against failures and their effects. [ABSTRACT FROM AUTHOR]

Load redistribution attacks (LRAs) are a type of false data injection attack that disrupts the normal operation of the power grid by redistributing load. While most LRAs in the literature are based on the DC model, this paper proposes an LRA in the AC model using incomplete network information. To defend against the proposed LRA, the paper proposes using Moving Target Defense (MTD) to actively invalidate the attackers’ knowledge. A zero-sum defense-attack game is formulated between MTD and LRA to select an MTD operating range optimally, considering the trade-off between attack detection effectiveness and the extra operation cost. The paper defines a new payoff function as an expected incremental operation cost, consisting of the defense cost, attack cost, and attack mitigation capability. A Nash Equilibrium of the game provides optimal strategies for selecting the MTD operating range. Simulation results on the modified IEEE 14-bus system demonstrate the effectiveness of MTD in detecting the proposed LRA. The paper shows that MTD not only detects ongoing LRAs but also prevents the construction of such attacks by using the proposed game theoretical framework. The proposed approach highlights the role of MTD in enhancing the cybersecurity of power grids against LRAs.

A singular system, assumed to possess both regularity and freedom from impulses, is categorized as a causal system. Noncausal systems (NSs) are a class of singular systems anticipated to exhibit regularity. This study focuses on investigating zero-sum games (ZSGs) in the context of NSs. We introduce recurrence equations grounded in Bellman's optimality principle. The saddle-point solution for multistage two-player ZSGs can be obtained by solving these recurrence equations. This methodology has demonstrated its effectiveness in addressing two-player ZSGs involving NSs. Analytical expressions that characterize saddle-point solutions for two types of two-player ZSGs featuring NSs, encompassing both linear and quadratic control scenarios, are derived in this paper. To enhance clarity, we provide an illustrative example that effectively highlights the utility of our results. Finally, we apply our methodology to analyze a ZSG in the realm of environmental management, showcasing the versatility of our findings. [ABSTRACT FROM AUTHOR]

A two-person zero-sum stochastic game with a nonnegative stage reward function is superfair if the value of the one-shot game at each state is at least as large as the reward function at the given state. The payoff in the game is the limit superior of the expected stage rewards taken over the directed set of all finite stop rules. If the game has countable state and action spaces and if at least one of the players has a finite action space at each state, then the game has a value. The value of the stochastic game is obtained by a transfinite algorithm on the countable ordinals. [ABSTRACT FROM AUTHOR]

An attack–defense model is considered in which the defense party at each point of defense has several lines and uses a target allocation of its forces. The average damage caused by attack forces breaking through all defense points is used as a criterion for attack effectiveness. The problem of optimizing the defense force distribution over defense lines is solved, and optimal strategies of the parties in a zero-sum game are found. [ABSTRACT FROM AUTHOR]

In contemporary networked control systems (NCSs), ensuring robust and adaptive security measures against dynamic threats like jamming attacks is crucial. These attacks can disrupt the control signals, leading to degraded performance or even catastrophic failures. This paper introduces a novel approach to enhance NCS security by applying stochastic game theory to model and resolve interactions between a defender and a jammer. We develop a two-player zero-sum game where the defender employs mixed strategies to minimize the expected cost of maintaining system stability and control effectiveness in the face of potential jamming. Our model discretizes the state space and employs backward induction to dynamically update the value functions associated with various system states, reflecting the ongoing adjustment of strategies in response to the adversary’s actions. Utilizing linear programming in MATLAB, we optimize the defender’s mixed strategies to systematically mitigate the impact of jamming. The results from extensive simulations demonstrate the efficacy of our proposed strategies in attack scenarios, indicating a substantial enhancement in the resilience and performance of NCSs against jamming attacks. Specifically, the proposed method improved network state stability by 75%, reducing the fluctuation range by over 50% compared with systems without defense mechanisms. This study not only advances the theoretical framework for security in NCSs but also provides practical insights for the design of resilient control systems under uncertainty.