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In many game theoretic environments, the precise crisp values of payoffs are not always easy to gather as real-life decision-making problems are not inevitably precise and symmetrically distributed in nature. Hence, there is a need to explore matrix games having unbalanced probabilistic linguistic information. To fill this research gap, this study proposes a concept of probabilistic multiplicative unbalanced linguistic (PM-UL) game in which the players express their responses in terms of PM-UL term. This type of PM-UL game is a useful technique for multiple criteria analysis. Further, to thoroughly capture the uncertainty involved in payoffs of such games, they are converted to probabilistic unbalanced linguistic clouds (PULCs) that describe the uncertainties of qualitative payoffs by implementing the uncertain transformation between PM-UL payoffs and quantitative values. The PULCs are represented by three numerical characteristics, i.e. expectation, entropy and hyperentropy. Hence, this model overcomes the inherent limitation of existing linguistic games where only the fuzziness of concepts is evaluated, by providing a PULC strategy and PULC value of the game. This procedure overcomes the loss of information occurring in the process of transformation of payoff values into quantitative ones. The defined methodology is implemented on a real-life working problem to demonstrate the effect and applicability in decision-making circumstances. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid load frequency control (LFC) scheme is proposed for multi-area interconnected power systems to decouple the intricate double control objectives, by dividing all subareas into the responsible areas and the free areas. The LFC in the responsible area has the function of regulating both the local frequency and the tie-line power, while the control objective of the LFC in the free area is thus simplified to regulate the local frequency only. Then, addressing the complex network coupling and uncertain dynamics, an integrated LFC controller is proposed for the free areas, which consists of two parts, namely, the coupling attenuation baseline controller and the disturbance compensation controller. The coupling attenuation baseline controller satisfying the predefined bounded L2-Gain condition is derived based on the solution to a multi-player zero-sum differential game. Additionally, a novel generalized integral observer is designed to estimate the system's integrated disturbance, and the corresponding disturbance compensation controller is derived. After that, the ultimately uniformly bounded (UUB) stability of the integrated LFC controller combining baseline controller and disturbance compensation controller is proven rigorously. Finally, the performance superiority of the proposed hybrid LFC scheme is validated by the simulations in challenging operating modes. [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 investigates a parameter-free H∞ differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H∞ control problem is reformulated as a zero-sum game between two players, leading to the establishment of the Hamilton–Jacobi–Isaacs (HJI) equation with a Nash equilibrium solution. To minimize reliance on model parameters during the solution process, an actor–critic framework employing neural networks is utilized to approximate the control policy and value function. An off-policy reinforcement learning method is implemented to iteratively solve the HJI equation. In this approach, the disturbance policy is derived directly from the value function, requiring only a limited amount of driving data to approximate the HJI equation's solution. The primary innovation of this method lies in its capacity to effectively address system nonlinearities without the need for model parameters, making it particularly advantageous for practical engineering applications. Numerical simulations confirm the method's effectiveness and applicable range. The off-policy reinforcement learning approach ensures the safety of the design process. For low-frequency road disturbances, the designed H∞ control policy enhances both ride comfort and stability. [ABSTRACT FROM AUTHOR]

This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equations. We propose a formulation of the optimization problem that encompasses both the actuator location and its associated minimum norm control. Specifically, we transform the problem into a two-person zero-sum game problem, resulting in the development of four equivalent formulations. Finally, we establish the crucial result that the solution to the relaxed optimization problem serves as an optimal actuator location for the classical problem. [ABSTRACT FROM AUTHOR]

The affine formation maneuver (AFM) control problem using the zero-sum differential game is studied for a second-order multi-agent system (MAS) against cyber-injection attacks on the actuators. First and foremost, the distributed control signals and the cyber-injected attack signals are viewed as two competing teams. Then, the leader-follower tracking error system is established where the followers aim to track the AFMs of the leaders. The leader-follower distributed optimal control policies and the cyber-attack attenuation policies are derived from the Nash equilibrium solution of the Hamilton-Jacobi-Isaac (HJI) equation. The solution of the HJI equation is estimated with the aid of the critic neural network. The weights of the critic system are learned online based on the adaptive dynamic programming (ADP) scheme. The uniformly ultimately bounded stability of the closed-loop system under the formulated zero-sum differential game control strategy has been proven by the Lyapunov stability theorem. A simulation example illustrates that the presented control method can attenuate cyber-injection attacks on the actuators and maintain the AFMs of the agents. [ABSTRACT FROM AUTHOR]

This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order α ∈ (0 , 1) and a Bolza cost functional. The differential game is associated to the Cauchy problem for the path-dependent Hamilton–Jacobi–Bellman–Isaacs equation with so-called fractional coinvariant derivatives of order α and the corresponding right-end boundary condition. A notion of a viscosity solution of the Cauchy problem is introduced, and the value functional of the differential game is characterized as a unique viscosity solution of this problem. [ABSTRACT FROM AUTHOR]

This paper endeavours to directly establish the observability inequality of backward stochastic heat equations involving a Lévy process for measurable sets. As an immediate application, we attain the approximate controllability of forward stochastic heat equations featuring a Lévy process. Subsequently, we embark upon the formulation of a nuanced optimization problem, encompassing both the determination of an optimal actuator location and its associated minimum norm control. This formulation is elegantly cast as a two-person zero-sum game problem. We then proceed to articulate a set of conditions–both sufficient and necessary–required for optimizing the solution through the prism of a Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem. [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]

In recent years, with the accelerated development of technology towards automation and intelligence, autonomous decision-making capabilities in unmanned systems are poised to play a crucial role in contemporary aerial two-player zero-sum games (TZSGs). Deep reinforcement learning (DRL) methods enable agents to make autonomous manoeuvring decisions. This paper focuses on current mainstream DRL algorithms based on fundamental tactical manoeuvres, selecting a typical aerial TZSG scenario—within visual range (WVR) combat. We model the key elements influencing the game using a Markov decision process (MDP) and demonstrate the mathematical foundation for implementing DRL. Leveraging high-fidelity simulation software (Warsim v1.0), we design a prototypical close-range aerial combat scenario. Utilizing this environment, we train mainstream DRL algorithms and analyse the training outcomes. The effectiveness of these algorithms in enabling agents to manoeuvre in aerial TZSG autonomously is summarised, providing a foundational basis for further research. [ABSTRACT FROM AUTHOR]

We consider a class of zero-sum stopper versus singular-controller games in which the controller can only act on a subset d0 < d of the d coordinates of a controlled diffusion. Due to the constraint on the control directions these games fall outside the framework of recently studied variational methods. In this paper we develop an approximation procedure, based on L1-stability estimates for the controlled diffusion process and almost sure convergence of suitable stopping times. That allows us to prove existence of the game's value and to obtain an optimal strategy for the stopper under continuity and growth conditions on the payoff functions. This class of games is a natural extension of (single-agent) singular control problems, studied in the literature, with similar constraints on the admissible controls. [ABSTRACT FROM AUTHOR]

In this paper, we study discounted stochastic games with an additive rewards and transitions (ARAT) structure. We assume that the transition probabilities are dominated by some probability measures on a countably generated measurable state space and are norm continuous in actions of the players. We prove the existence of Markov perfect equilibria in which the players can use randomization on two pure actions in each state. When the state space is countable, then we show that there exists a pure Markov perfect equilibrium. Assuming additionally that the transition probabilities have no conditional atoms, we establish some existence results on pure Markov perfect equilibria for ARAT games with uncountable state space using a version of Lyapunov's theorem for conditional expectation of correspondences due to Dynkin and Evstigneev. We also include a wide-ranging discussion on equilibria for discounted stochastic games with a general state space. [ABSTRACT FROM AUTHOR]

Content moderation is typically viewed as an affront to free expression. When companies remove online abuse, they face accusations of censorship. Lost in the discussion is the fact that victims of intimate privacy violations and cyberstalking typically-and regrettably-withdraw from on- and offline activities. Online assaults chase targeted individuals offline; they silence victims. Content moderation can secure opportunities for people to speak. Legal and corporate prohibitions against intimate privacy violations and cyberstalking can help provide the reassurance that victims need to stay online. They can endow individuals with a sense of trust so they continue to use networked technologies to express themselves. Those prohibitions are consonant with First Amendment doctrine and free speech values. Combating online abuse isn't a zero-sum game with free speech as the loser. Rather, it can free us to speak by changing the culture that rewards abuse and encourages self-censorship. [ABSTRACT FROM AUTHOR]

Recent work on incorporating strong-correlation (sc) corrections into the scLH22t local hybrid functional [A. Wodyński and M. Kaupp, J. Chem. Theory Comput. 18, 6111–6123 (2022)] used a hybrid procedure, applying a strong-correlation factor derived from the reverse Becke–Roussel machinery of the KP16/B13 and B13 functionals to the nonlocal correlation term of a local hybrid functional. Here, we show that adiabatic-connection factors for strong-correlation-corrected local hybrids (scLHs) can be constructed in a simplified way based on a comparison of semi-local and exact exchange-energy densities only, without recourse to exchange-hole normalization. The simplified procedure is based on a comparative analysis of Becke's B05 real-space treatment of nondynamical correlation and that in LHs, and it allows us to use, in principle, any semi-local exchange-energy density in the variable used to construct local adiabatic connections. The derivation of competitive scLHs is demonstrated based on either a modified Becke–Roussel or a simpler Perdew–Burke–Ernzerhof (PBE) energy density, leading to the scLH23t-mBR and scLH23t-tPBE functionals, which both exhibit low fractional spin errors while retaining good performance for weakly correlated situations. We also report preliminary attempts toward more detailed modeling of the local adiabatic connection, allowing a reduction of unphysical local maxima in spin-restricted bond-dissociation energy curves (scLH23t-mBR-P form). The simplified derivations of sc-factors reported here provide a basis for future constructions and straightforward implementation of exchange-correlation functionals that escape the zero-sum game between low self-interaction and static-correlation errors. [ABSTRACT FROM AUTHOR]

A finite zero-sum game defined on a subset of the unit square is considered. The game is a generalized progressive discrete silent duel, in which the kernel is skew-symmetric, and the players, referred to as duelists, have identical linear accuracy functions featured with an accuracy proportionality factor. As the duel starts, time moments of possible shooting become denser by a geometric progression. Apart from the duel beginning and end time moments, every following time moment is the partial sum of the respective geometric series. Due to the skew-symmetry, both the duelists have the same optimal strategies and the game optimal value is 0. If the accuracy factor is not less than 1, the duelist’s optimal strategy is the middle of the duel time span. If the factor is less than 1, the duel solution is not always a pure strategy saddle point. In a boundary case, when the accuracy factor is equal to the inverse numerator of the ratio that is the time moment preceding the duel end moment, the duel has four pure strategy saddle points which are of the mentioned time moments. For a trivial game, where the duelist possesses just one moment of possible shooting between the duel beginning and end moments, and the accuracy factor is 1, any pure strategy situation, not containing the duel beginning moment, is optimal. [ABSTRACT FROM AUTHOR]

The article has its roots in the concept of a community with a shared future for humanity, a Chinese innovation aimed at realizing the development and prosperity of human societies. This concept rests on an exploration, based in Marxism and sinicized Marxism, of how world history has evolved, and embodies six global initiatives as fundamental measures to respond to the real needs of world development at the current stage. Specifically, the Belt and Road Initiative, based on a new pattern of cooperation, strives to build a new model of common prosperity in both economic and cultural terms for countries around the world. The Global Development Initiative aims to upgrade the development agenda and formulate new guidelines for the common socio-economic development of all countries. The Global Security Initiative seeks to eliminate the old-style mentality formed by the zero-sum game thinking of the Cold War epoch, and to formulate a new conception of shared security for the international community. The Global Civilization Initiative sets out to disprove the myths of Western civilization and to develop a new concept of mutual learning between civilizations, while the Global AI Governance Initiative aims to build consensus and on that basis, to shape the common governance of scientific and technological progress. [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]

Professor Peter Sudhölter, a renowned mathematician and economist, passed away on April 2, 2024, after a courageous battle with cancer. Throughout his career, he made significant contributions to the field of cooperative game theory, publishing 61 articles and one book. He obtained his PhD in mathematics from the University of Bielefeld in 1988 and went on to become a full professor at the University of Southern Denmark in 2013. Sudhölter's research focused on various topics, including cooperative games, non-transferable utility games, and the characterization of equilibrium concepts. His work has had a lasting impact on the field and will continue to influence future research. [Extracted from the article]

A generalized class of the discrete game of timing is solved as a finite zero-sum game defined on a symmetric lattice of the unit square. The game is a progressive discrete silent duel whose kernel is skew-symmetric, and the players, referred to as duelists, have identical shooting accuracy functions featured with an accuracy proportionality factor a and a power constant β describing nonlinearity of the shooting accuracy. As the duel starts, time moments of possible shooting become denser by a geometric progression. Apart from the duel beginning and end time moments, every following time moment is the partial sum of the respective geometric series. Due to the skew-symmetry, both the duelists have the same optimal strategies and the game optimal value is 0. As the duelist has a single bullet, there is no reason for considering solutions in mixed strategies, if any, with non-singleton supports. If a ⩾ 2 β − 1 , the duelist's optimal strategy is the middle of the duel time span; otherwise, the duel solution may be not a pure strategy solution. The case of quadratic accuracy for β = 2 is further considered, which is reasoned by that linearly developing real-time processes are quite rare, and the quadratic accuracy is a non-linearity pattern that makes an interaction model more reliable by slightly diminishing the duelist's confidence. Thus, the case of a < 2 β − 1 is thoroughly studied for pure strategy solutions. A boundary case of a is found, by which the duel has four pure strategy solutions which are of the time moment preceding the duel end moment and the duel end moment itself. • Discrete game of timing is solved as a finite zero-sum game on a symmetric lattice. • Duelist is featured with shooting accuracy proportionality and nonlinearity factors. • The breaking point of the accuracy is found above which pure strategy solutions exist. • Pure strategy solutions are found below the breaking point for the quadratic accuracy. [ABSTRACT FROM AUTHOR]

This paper aims to present alternative characterizations for different types of set-valued robustness concepts. Equivalent scalar representations for various set order relations are derived when the sets are the union of sets. Utilizing these findings in conjunction with image space analysis, specific isolated sets are defined for different notions of robust solutions. These isolated sets serve as the basis for deriving both necessary and sufficient robust optimality conditions. The validity of the results is demonstrated through several illustrative examples. Additionally, the paper concludes with an application of our present approach to two-player zero-sum matrix games. [ABSTRACT FROM AUTHOR]

This paper studies two-player stochastic differential games with diffusion control on finite time horizons. The players' state processes are described in terms of controlled martingale problems, and we allow for correlation between the players' states, described by some correlation coefficient. We consider zero-sum ranking games in the sense that the criterion to optimize only depends on the difference of the two players' state processes at the finite time horizon. We explicitly compute saddle points of the game depending on the correlation coefficient. In particular, for correlation coefficients smaller than some explicit threshold, the game has a value and a saddle point (in strict controls). For correlation coefficients exceeding the threshold, we introduce the larger class of relaxed controls that can be interpreted as mixed strategies. We show that the game has a value and a saddle point in relaxed controls for all correlation coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we consider the adaptive stabilization problem for a basic class of linearquadratic noncooperative stochastic differential games when the systems matrices are unknown to the regulator and the players. This is a typical problem of game-based control systems (GBCS) introduced and studied recently, which have a hierarchical decision-making structure: there is a controller at the upper level acting as a global regulator which makes its decision first, and the players at the lower level are assumed to play a typical zero-sum differential games. The main purpose of the paper is to study how the adaptive regulator can be designed to make the GBCS globally stable and at the same time to ensure a Nash equilibrium reached by the players, where the adaptive strategies of the players are assumed to be constructed based on the standard least squares estimators. The design of the global regulator is an integration of the weighted least squares parameter estimator, random regularization and diminishing excitation methods. Under the assumption that the system matrix pair (A, B) is controllable and there exists a stabilizing solution for the corresponding algebraic Riccati equation, it is shown that the closed-loop adaptive GBCS will be globally stable, and at the same time reach a Nash equilibrium by the players. [ABSTRACT FROM AUTHOR]

This study proposes an organizational mechanism that links ideology to the use of terrorism in mass dissident campaigns. Ideology affects the level of competition among factions within mass dissident campaigns by shaping whether actors see their interactions as a positive- or zero-sum game. We identify ideological diversity within a campaign and the degree to which ideologies embrace the principle of pluralism as key factors affecting the intensity of factional competition and, consequently, the occurrence of terrorism. We introduce new data on the ideologies of campaigns from the Nonviolent and Violent Campaigns and Outcomes 2.0 dataset and use causal mediation analysis to test our proposed mechanism. We find that greater ideological diversity within a campaign increases the likelihood of terrorism by increasing factional competition. We also find that the presence of a pluralist ideology is associated with a lower likelihood of terrorism by the lowering of factional competition. By shedding light on the mechanisms that link ideology to terrorism, this study helps advance our understanding of why dissident groups might decide to use terrorism tactics within the context of a campaign of mass resistance. [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]

The potential emergence of artificial general intelligence (AGI) systems has sparked intense debate among researchers, policymakers, and the public due to their potential to surpass human intelligence in all domains. This note argues that for an AI to be considered "general", it should achieve superhuman performance not only in zero-sum games but also in general-sum games, where winning or losing is not clearly defined. In this note, I propose a game-theoretic framework that captures the strategic interactions between a representative human agent and a potential superhuman machine agent. Four assumptions underpin this framework: Superhuman Machine, Machine Strategy, Rationality, and Strategic Unpredictability. The main result is an impossibility theorem, establishing that these assumptions are inconsistent when taken together, but relaxing any one of them results in a consistent set of assumptions. This note contributes to a better understanding of the theoretical context that can shape the development of superhuman AI. • A game between a human vs an Artificial General Intelligence system is introduced. • An AI system is general if it is successful in both zero-sum and general-sum games. • Assumptions are Superhuman AI, Machine Strategy, Rationality, and Unpredictability. • An impossibility theorem shows that these assumptions lead to inconsistency. • The result is tight; relaxing any of the assumptions resolves the inconsistency. [ABSTRACT FROM AUTHOR]

Political polarization is a systemic-level and multifaceted process that severs cross-cutting ties and shifts perceptions of politics to a zero-sum game. When it turns pernicious, political actors and supporters view opponents as an existential threat and the capacity of democratic institutions to process political conflict breaks down. The article identifies four common fault lines of polarization globally – who belongs, democracy, inequality and social contract. It argues that while Latin American countries experience, to varying degrees, all four of the fault lines, it is the deep-seated, persistent social hierarchies oriented around class, race, and place that stand out relative to other countries. Reaching consensus on reforms that may renew or reformulate agreements on the terms of the social contract, boundaries of community membership, and redressing social inequality is a tall task. Yet the region's sustained consensus on the democratic rules of the game can provide the mechanisms for addressing this task if new majority coalitions can be formed. [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]

This article develops distributed optimal control policies via Q‐learning for multi‐agent systems (MASs) by solving dual games. According to game theory, first, the distributed consensus problem is formulated as a multi‐player non‐zero‐sum game, where each agent is viewed as a player focusing only on its local performance and the whole MAS achieves Nash equilibrium. Second, for each agent, the anti‐disturbance problem is formulated as a two‐player zero‐sum game, in which the control input and external disturbance are a pair of opponents. Specifically, (1) an offline data‐driven off‐policy for distributed tracking algorithm based on momentum policy gradient (MPG) is developed, which can effectively achieve consensus of MASs with guaranteed l2$$ {l}_2 $$‐bounded synchronization error. (2) An actor‐critic‐disturbance neural network is employed to implement the MPG algorithm and obtain optimal policies. Finally, numerical and practical simulation results are conducted to verify the effectiveness of the developed tracking policies via MPG algorithm. [ABSTRACT FROM AUTHOR]

Porous media reconstruction is quite significant in the fields of environmental supervision, oil and natural gas engineering, biomedicine and material engineering. The traditional numerical reconstruction methods such as multi-point statistics (MPS) are based on the statistical characteristics of training images (TIs), but the reconstruction quality may be unsatisfactory and the process is time-consuming. Recently, with the rapid development of deep learning, its powerful ability in predicting features has been used to reconstruct porous media. Generative adversarial network (GAN) is one of the generative methods of deep learning, which is derived from the two-person zero-sum game through the confrontation between the generator and discriminator. However, the traditional GAN cannot pay special attention to the effective features in learning, and the degradation problem easily occurs with the increase of layer numbers. Besides, high-resolution (HR) and large FOV (field of view) are usually contradictory for physical imaging equipment. Therefore, in practical experiments, due to the limitations of the resolution of imaging equipment and the sample size, it is difficult to obtain large-scale HR images of porous media physically. At this point, numerical super-resolution (SR) reconstruction seems to be a cost-efficient way. In this paper, residual networks and attention mechanisms are combined with single-image GAN (SinGAN), which can learn the structural characteristics of porous media from a low-resolution (LR) 3D image, and then reconstruct 3D HR or large-scale images of porous media. Comparison to some other numerical methods has proved that our method can reconstruct high-quality HR images with practicability and effectiveness. [ABSTRACT FROM AUTHOR]

The increased use of social media has triggered a visual shift in digital political communication. One central strategy is visual (self-) personalization and many studies have analyzed why and to what extent political communication is focused on individuals. Yet, most research has concentrated on personalization, leaving aside the question of whether it comes at the expense of policy issues or whether people are brought into focus as facilitators of such issues. We fill this research gap by analyzing how visual (self-) personalization on Instagram pages of parties and politicians during election campaigns has changed over time and whether it comes at the cost of addressing policy issues. We use data from three quantitative content analyses of Instagram posts published by parliamentary parties (n = 7) and top candidates (n = 18) in the 'hot phases' before three national German elections (N = 2313), covering all nationwide elections since Instagram has become a common campaign tool. It is shown that personal depictions are very common in Instagram campaigns of parties and candidates while addressing policy issues in posts varies between elections. Using a multilevel binomial regression model, we show that addressing policy issues is negatively related to personalization but further analysis shows that it is not a zero-sum game at the cost of addressing policy issues. Our results provide insights into how the presentation of politics might change when image- and video-based platforms continue to gain importance in political communication. [ABSTRACT FROM AUTHOR]

This document is an introduction to a special issue on international counter-trafficking. It acknowledges that human trafficking is a complex and fluid concept, and that counter-trafficking efforts often prioritize securitarian, moralistic, and neoliberal concerns. The special issue includes articles that provide valuable insights into the experiences of sex workers, Quran teachers, Nigerian migrant women, and women in counter-trafficking programs in Italy and Spain. These articles challenge dominant narratives about trafficking and highlight the need for more critical approaches to counter-trafficking. The author expresses gratitude to the contributors and the journal for their interest in this important topic. [Extracted from the article]

This paper investigates the robust H∞$$ {H}_{\infty } $$ optimal formation control for the position subsystem of quadrotor unmanned aerial vehicles (UAVs) subject to external disturbances and collision constraints. To prevent collision with both members of the formation and external obstacles, a collision avoidance potential function is constructed using relative position and velocity information. The basic bounded control input can ensure the stable flight and collision avoidance of a quadrotor UAV system. Based on the approximate dynamic programming (ADP) framework and two‐player zero‐sum differential game theory, the H∞$$ {H}_{\infty } $$ optimal controller is designed to further enhance the control performance of the system. The optimal value function is approximated by a single layer neural network, which avoids solving complex nonlinear Hamilton‐JacobiIsaac (HJI) equation. The stability of the closed loop system is proved. The effectiveness of the robust H∞$$ {H}_{\infty } $$ optimal formation controller based on learning is validated through MATLAB simulation in two distinct scenarios. [ABSTRACT FROM AUTHOR]

This paper considers an infinitely repeated three-player zero-sum game with two-sided incomplete information, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a generalization of the model in Aumann et al. (Repeated games with incomplete information. MIT Press, New York, 1995) of two-player zero-sum one-sided incomplete information games. Under a correlated prior, the informed player faces the problem of how to optimally disclose information among two uninformed players in order to maximize his long-term average payoffs (i.e., undiscounted payoffs). Our objective is to understand the adverse effects of "information spillover" from one game to the other in the equilibrium payoff set of the informed player. We provide conditions under which the informed player can fully overcome such adverse effects and characterize equilibrium payoffs. In a second result, we show how the effects of information spillover on the equilibrium payoff set of the informed player might be severe. Finally, we compare our findings on the equilibrium-payoff set of the informed player with those of Bayesian Persuasion models with multiple receivers. [ABSTRACT FROM AUTHOR]

This article, titled "Case Material: 'Patricia'", discusses the therapy process with a 38-year-old woman named Patricia who sought help to understand her anger towards others. Patricia had a difficult childhood, feeling unwanted by her mother and experiencing sexual molestation by two teenage boys. Throughout therapy, Patricia exhibited anger, sarcasm, and a tendency to sabotage positive interactions. The therapist reflects on their own experiences and challenges in working with Patricia, including a breast cancer diagnosis. Towards the end of therapy, Patricia began to show progress and acceptance of her traumatic past. The article highlights the complex dynamics and milestones in the therapeutic relationship. [Extracted from the article]

The most difficult decision problems arise when several parties with several criteria must reach a consensus. This problem can be modelled as a game with vector-valued payoffs. If the players are allowed to use mixed strategies, there can be many Nash equilibria, and therefore many outcomes. The role of negotiation is to choose a specific outcome, or to restrict the set of outcomes to a small subset. One promising approach to negotiation support is scalarization of the vector payoff function. Here we apply Germeier scalarizing function, also known as the Rawlsian function, to mixed-strategy multicriteria games. After developing the mathematical background, we extend to these games the principle of Best Guaranteed Value, the value that a player may count on regardless of the other players' actions. We suggest that a good outcome for negotiation in a multicriteria game is a Nash equilibrium outcome that provides each player with the payoffs that are better than its Best Guaranteed Value. We describe all such outcomes, thereby defining a new negotiation support mechanism. [ABSTRACT FROM AUTHOR]

Bilingualism is linked to both enhanced and hampered performance in various cognitive measures, yet the extent to which these bilingual advantages and disadvantages co-occur is unclear. To address this gap, we perform a systematic review and two quantitative analyses. First, we analyze results from 39 studies, obtained through the PRISMA method. Less than 50% of the studies that show up as results for the term "bilingual disadvantage" report exclusively a disadvantage, that shows bilinguals performing worse than monolinguals in a task. A Bayesian analysis reveals robust evidence for bilingual effects, but no evidence for differences in the proportion of advantages and disadvantages, suggesting that when results from different cognitive domains such as executive functions and verbal fluency are analyzed together, bilingual effects amount to a zero-sum game. This finding was replicated by repeating the analysis, using the datasets of two recent meta-analyses. We propose that the equilibrium we observe between positive and negative outcomes may not be accidental. Contrary to widespread belief, advantageous and disadvantageous effects are not stand-alone outcomes in free variation. We reframe them as the connatural components of a dynamic trade-off, whereby enhanced performance in one cognitive measure is offset by an incurred cost in another domain. [ABSTRACT FROM AUTHOR]

To attenuate the effect of disturbances on control performance, a multi‐step adaptive critic control (MsACC) framework is developed to solve zero‐sum games for discrete‐time nonlinear systems. The MsACC algorithm utilizes multi‐step policy evaluation to obtain the solution of the Hamilton–Jacobi–Isaac equation, which is faster than that of the one‐step policy evaluation. The convergence rate of the MsACC algorithm is adjustable by varying the step size of the policy evaluation. In addition, the stability and convergence of the MsACC algorithm are proved under certain conditions. In order to realize the MsACC algorithm, three neural networks are established to approximate the control input, the disturbance input, and the cost function, respectively. Finally, the effectiveness of the MsACC algorithm is verified by two simulation examples, including a linear system and a nonlinear plant. [ABSTRACT FROM AUTHOR]

This paper rescues Deirdre McCloskey's ideas about Rhetoric in Economics and some issues left out in subsequent discussions. There is a parallel between the ideas of McCloskey and Bruno Latour, and the complementarities of their perspectives are very relevant for the development of Economics. Some reflections are here offered to improve the practice of Economics, which are related to the social constructions of facts in the field, to the internalization of political aspects, and to the importance of alternating between fact and fiction in a dynamic that does not result in a zero-sum game, underlining the characteristic of Economics as being inherently rhetorical. [ABSTRACT FROM AUTHOR]

This paper studies zero-sum splitting games with finite sets of states. Players dynamically choose a pair of martingales { p t , q t } t , in order to control a terminal payoff u (p ∞ , q ∞) . A first part introduces the notion of "Mertens–Zamir transform" of a real-valued matrix and use it to approximate the solution of the Mertens–Zamir system for continuous functions on the square [ 0 , 1 ] 2 . A second part considers the general case of finite splitting games with arbitrary correspondences containing the Dirac mass on the current state: building on Laraki and Renault (Math Oper Res 45:1237–1257, 2020), we show that the value exists by constructing non Markovian ε -optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions. [ABSTRACT FROM AUTHOR]

We consider a finite-horizon two-person zero-sum differential game in which the system dynamics is described by a linear differential equation with a Caputo fractional derivative and the goals of the players' control are to minimize and maximize a quadratic terminal-integral cost function, respectively. We present conditions for the existence of a game value and obtain formulas for players' optimal feedback control strategies with memory of motion history. The results are based on the construction of a solution to an appropriate Hamilton–Jacobi equation with fractional coinvariant derivatives under a natural right-end boundary condition. [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]

The paper is a continuation of author's research on the existence of an ε-equilibrium in the sense of piecewise program strategies in two-person zero-sum games associated with a nonlinear nonautonomous controlled differential equation in a Banach space and a general cost functional. As in the preceding paper on this subject, the main result consists in sufficient conditions for an ε-equilibrium. The difference is that this time we investigate a game without discriminating the players or fixing a Volterra chain. The results are illustrated as applied to a game associated with a nonlinear pseudoparabolic partial differential equation governing the evolution of an electric field in a semiconductor. [ABSTRACT FROM AUTHOR]

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]

We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper and lower value functions satisfy a dynamic programming principle (DPP). We first prove the dynamic programming principle (DPP) for a truncated version of the upper value function in a straightforward manner. Relying on a uniform convergence argument then enables us to show the DPP for the general setting. Following this, we use an approximation based on a combination of truncation and discretization to show that the upper and lower value functions coincide, thus establishing that the game has a value and that the DPP holds for the lower value function as well. Finally, we show that the DPP admits a unique solution and give conditions under which a saddle point for the game exists. As an example, we consider a stochastic differential game (SDG) of impulse versus classical control of path-dependent stochastic differential equations (SDEs). [ABSTRACT FROM AUTHOR]

In this article, we present an iterative algorithm based on differential dynamic programming (DDP) for finite‐horizon two‐person zero‐sum differential games. The technique of DDP is used to expand the Hamilton–Jacobi–Isaacs (HJI) partial differential equation into higher‐order differential equations. Using value function and saddle point approximations, the DDP expansion is transformed into algebraic matrix equation in integral form. Based on the algebraic matrix equation, a DDP iterative algorithm is developed to learn the solution to the differential games. Strict proof is proposed to guarantee the iterative convergences of the value function and saddle point. The new algorithm is fundamentally different from existing results, in the sense that it overcome the technical obstacle to address the time‐varying behavior of HJI partial differential equation. Simulation examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The Colonel Blotto game is one of the most classical zero-sum games, with diverse applications in auctions, political elections, etc. We consider the discrete two-battlefield Colonel Blotto Game, a basic case that has not yet been completely characterized. We study three scenarios where at least one player's resources are indivisible (discrete), and compare them with a benchmark scenario where the resources of both players are arbitrarily divisible (continuous). We present the equilibrium values for all three scenarios, and provide a complete equilibrium characterization for the scenario where both players' resources are indivisible. Our main finding is that, somewhat surprisingly, the distinction between continuous and discrete strategy spaces generally has no effect on players' equilibrium values. In some special cases, however, the larger continuous strategy space when resources are divisible does bring the corresponding player a higher equilibrium value than when resources are indivisible, and this effect is more significant for the stronger player who possesses more resources than for the weaker player. [ABSTRACT FROM AUTHOR]

The well-known H ∞ control design gives robustness to a controller by rejecting perturbations from the external environment, which is difficult to do for completely unknown affine nonlinear systems. Accordingly, the immediate objective of this paper is to develop an on-line real-time synergetic learning algorithm, so that a data-driven H ∞ controller can be received. By converting the H ∞ control problem into a two-player zero-sum game, a model-free Hamilton–Jacobi–Isaacs equation (MF-HJIE) is first derived using off-policy reinforcement learning, followed by a proof of equivalence between the MF-HJIE and the conventional HJIE. Next, by applying the temporal difference to the MF-HJIE, a synergetic evolutionary rule with experience replay is designed to learn the optimal value function, the optimal control, and the worst perturbation, that can be performed on-line and in real-time along the system state trajectory. It is proven that the synergistic learning system constructed by the system plant and the evolutionary rule is uniformly ultimately bounded. Finally, simulation results on an F16 aircraft system and a nonlinear system back up the tractability of the proposed method. • A model-free Hamiltonian–Jacobi–Isaacs equation is derived for H ∞ control problems. • A real-time on-line evolutionary rule for tuning neural network weights is developed. • The system and neural network approximation errors achieve synergetic learning. [ABSTRACT FROM AUTHOR]

We examine the Target–Attacker–Defender (TAD) pursuit-evasion game. This is a two team, zero-sum differential game consisting of the aforementioned three agents obeying simple motion. The game terminates at the first time t f when the Attacker achieves point capture of either the Target or Defender. The Attacker chases the Target in such a manner as to minimise the distance between itself and the Target, minus the distance between itself and the Defender at termination time; and the Target and Defender work as a team to achieve the exact opposite goal. This paper introduces and verifies the most elegant characterisation of the state-feedback Nash equilibrium. Whereas previous methods in the literature segregated the state space into at least three separate regions, we introduce a new unifying paradigm given by the Holographic Principle, and conjecture that this principle is more broadly applicable to a large class of simple motion pursuit-evasion games. [ABSTRACT FROM AUTHOR]

Network attack and defence games are gradually becoming a new approach through which to study the protection of infrastructure networks such as power grids and transportation networks. Uncertainty factors, such as the subjective decision preferences of attackers and defenders, are not considered in existing attack and defence game studies for infrastructure networks. In this paper, we introduce, respectively, the attacker's and defender's expectation value, rejection value, and hesitation degree of the target, as well as construct an intuitionistic fuzzy goal-based attack and defence game model for infrastructure networks that are based on the maximum connectivity slice size, which is a network performance index. The intuitionistic fuzzy two-player, zero-sum game model is converted into a linear programming problem for solving, and the results are analysed to verify the applicability and feasibility of the model proposed in this paper. Furthermore, different situations, such as single-round games and multi-round repeated games, are also considered. The experimental results show that, when attacking the network, the attacker rarely attacks the nodes with higher importance in the network, but instead pays more attention to the nodes that are not prominent in the network neutrality and median; meanwhile, the defender is more inclined to protect the more important nodes in the network to ensure the normal performance of the network. [ABSTRACT FROM AUTHOR]

How would human players negotiate a spatial array with a randomly behaving partner? In an interactive, online, zero-sum grid game, we tested whether and how players create areas and place sequences by coloring-in places in a 20 × 20 matrix (261 human adults, 261 machine partners, N = 522). Several indicators showed that human players followed an intentional strategy rather than coloring in places ad libitum. First, human players built a larger largest cluster from places than the machine. Second, they were sensitive to task instructions and could modify their strategy accordingly. When instructed to build an area, they built a bigger one. When set under time pressure, they colored-in faster and only had time to build a smaller cluster from places. Third, the most compelling human strategy to create an area was lining up pathways (place sequencing). Despite these differences, the resulting spatial field structure was similar in human and machine players. [ABSTRACT FROM AUTHOR]