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In this article, the zero‐sum game problem of control and disturbance is studied for discrete affine nonlinear switched systems with unknown dynamical models. A two‐level heuristic dynamic programming iterative algorithm for solving the zero‐sum game problem is proposed, which can be used to solve the Hamilton‐Jacobi‐Isaacs equation associated with the optimal regulation control problem. The convergence analysis based on the value function and control strategy is given. For algorithm implementation, neural networks are used to approximate the control strategy, disturbance strategy, and value function of the game dynamic programming, respectively. A model network is used to approximate the system states with an unknown dynamical model. The iterative algorithm steps are given. Finally, the validity of the method is verified by simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new function to trace the trajectory by applying the modified homotopy continuation method for finding the solution of two person zero-sum discounted stochastic ARAT game. For the proposed algorithm, the homotopy path approaching the solution is smooth and bounded. [ABSTRACT FROM AUTHOR]

Is the Constitution big enough to guarantee the rights of small or less popular religions as well as of employees, tenants, and other dependents of religious exemption claimants? This paper will demonstrate how federal First Amendment jurisprudence has created the paradox of a zero-sum game between these two relatively marginalized and powerless groups. First, the history of free exercise cases and related legislation will show how--in this area of law as in many others--the social context of the claimants is critical in understanding the Court's attitudes and reasoning; Supreme Court decisions consistently responded to and shaped public opinion for better or worse. And, throughout the second half of the twentieth century, the Court persistently drew on implicitly Christian concepts to evaluate the religious claims of non-Christian litigants, also evincing a preference for Euro-white ethnocentrism over religionists of other backgrounds. In response to developments in Supreme Court interpretation, Congress enacted the Religious Freedom Restoration Act of 1993 (RFRA) and then the Religious Land Use and Institutionalized Persons Act of 2000 (RLUIPA), which have served as the principal engines for free exercise claims in the intervening decades. The Roberts Court has instituted several profound shifts in free exercise jurisprudence. Perhaps most importantly, it has been sharply circumscribing courts' roles in evaluating religious claims. Beginning with its own cases, the Court has articulated a basic ethos of religious freedom for all who seek it as the default. This all-comers orientation has been a welcome change for members of minority religions. But the consequences of a "no questions asked" religious exceptionalism may well be devastating for the employees and tenants of religious objectors. This paper, therefore, proposes two insights for an alternative framework for assessing freedom of religion claims. First, returning to the concerns animating the watershed mid-twentieth century religious freedom cases, a claimant's religious minority status ought to have some bearing on the handling of their case; a religionist whose faith practices are well represented in and familiar to Congress, courts, and society at large is in a constitutionallycognizably different posture than, for instance, members of a small religious community that consists largely of racial minority non-citizens. Second, the right of free exercise stemming from the First Amendment must be interpreted in congruence with the entirety of the rights of conscience and expression guaranteed therein. Incorporating these insights could serve as a corrective for the accustomed privileging of religious claimants to the detriment of impacted third parties, such as employees. [ABSTRACT FROM AUTHOR]

In this paper, we present two-timescale neurodynamic optimization approaches to distributed minimax optimization. We propose four multilayer recurrent neural networks for solving four different types of generally nonlinear convex–concave minimax problems subject to linear equality and nonlinear inequality constraints. We derive sufficient conditions to guarantee the stability and optimality of the neural networks. We demonstrate the viability and efficiency of the proposed neural networks in two specific paradigms for Nash-equilibrium seeking in a zero-sum game and distributed constrained nonlinear optimization. [ABSTRACT FROM AUTHOR]

Accurate porous media reconstruction has always been one of the significant research hotspots in the numerical simulation of reservoirs. The traditional methods such as multi-point statistics perform porous media reconstruction based on the statistical features of training images, but the process is possibly cumbersome and the result is less effective. Porous media reconstruction has been greatly developed and benefited by applying current flourishing deep learning to its simulation process thanks to the strong capability of extracting features by deep learning. As a typical branch of deep learning methods, generative adversarial network (GAN) can simulate a two-person zero-sum game through confrontation between a generator and a discriminator. However, in real experiments, constrained by the resolution of physical equipment and the size of samples, it is difficult to physically obtain a large-scale image of porous media with high-resolution (HR) since HR and large field of view are usually contradictory for physical equipment. In this paper, a method is proposed based on multistage concurrent GAN to learn the structural features of porous media from one low-resolution 3D image and then stochastically reconstruct larger-sized porous media images. Experimental comparison with some typical methods proves that this method can reconstruct HR images with favorable quality. Article Highlights: Our method is quite fast in multiple reconstructions by reusing model parameters. Our method realizes the super-resolution reconstruction of porous media from one low-resolution image. Our method outperforms SNESIM and some GAN's variants in the accuracy of reconstruction. [ABSTRACT FROM AUTHOR]

This article provides sufficient conditions for the existence of solutions for two‐person zero‐sum games with inf/sup‐compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and we do not assume any convexity/concavity‐type conditions. For such games expected payoff may not exist for some pairs of strategies. The results of this article imply several classic facts. The article also provides sufficient conditions for the existence of a value and solutions for each player. The results of this article are illustrated with the number guessing game. [ABSTRACT FROM AUTHOR]

When the equipment is working, it is very important to avoid the occurrence of malignant accidents by providing a highly reliable safety protection means. In this paper, for multiplayer mixed zero-sum games, an optimal safety tracking control scheme based on adaptive dynamic programming (ADP) is proposed, and a control barrier function (CBF) is introduced into the value function of the system to ensure that the system operates within its safe region. Firstly, through system transformation, the original tracking problem is transformed into a state tracking error problem. Secondly, an augmented Hamilton-Jacobi-Bellman (HJB) equation is derived from the improved augmented error system and the value function. Different from traditional methods, this paper uses a single critic neural network (NN) instead of the actor-critic NN to approximate the Nash equilibrium solution of the system, and introduces a concurrent learning technique that can relax the traditional continuous excitation condition into a simplified condition of recording data. Then, according to the Lyapunov theory, the stability of the system is analyzed in detail. Finally, two simulation examples are used to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

With the development of power technology and communication technology, the power grid and power communication network have become interdependent and closely coupled. The load shedding operation of the power grid is an important means to reduce the occurrence of chain faults and ensure the safe and stable operation of the power grid. Based on the transmission of load control services in the communication network, this paper establishes a model for a dual-network coupled cyber physical power system (CPPS). Considering communication edge faults, the associated load capacity of the communication edge and the expected load loss of the power grid are defined. On this basis, the paper proposes a complete information zero-sum game mechanism called "defense attack defense" for communication edge failures, which takes the expected loss of load from the power grid as the benefit. The paper studies the optimal attack and defense game strategies and provides the algorithm implementation process for the three stages of the game. Considering the bandwidth capacity of the communication edge, this paper uses the Dijkstra algorithm or k shortest paths (KSP) algorithm with the cost factor of the communication edge as the weight to plan the main and backup communication channels for multiple load control services. The simulation results show that the game mechanism proposed in this paper can effectively reduce the expected load loss from the power grid and improve the stability of the CPPS. [ABSTRACT FROM AUTHOR]

This paper deals with a robust H∞$$ {H}_{\infty } $$ tracking problem with a discounted factor. A new auxiliary system is established in terms of norm‐bounded time‐varying uncertainties. It is shown that the robust discounted H∞$$ {H}_{\infty } $$ tracking problem for the auxiliary system solves the original problem. Then, the new robust discounted H∞$$ {H}_{\infty } $$ tracking problem is represented as a well‐known zero‐sum game problem. Moreover, the robust tracking Bellman equation and the robust tracking Algebraic Riccati equation (RTARE) are inferred. A lower bound of a discounted factor for stability is obtained to assure the stability of the closed‐loop system. Based on the auxiliary system, the system is reshaped in a new structure that is applicable to Reinforcement Learning methods. Finally, an online Q‐learning algorithm without the knowledge of system matrices is proposed to solve the algebraic Riccati equation associated with the robust discounted H∞$$ {H}_{\infty } $$ tracking problem for the auxiliary system. Simulation results are given to verify the effectiveness and merits of the proposed method. [ABSTRACT FROM AUTHOR]

This paper takes issue with the widespread claim that positional competitions are zero-sum games. It shows how the notions of ‘positional good’ and ‘positional competition’ have changed in meaning and how this has resulted in conceptual confusion in discussions amongst economists and philosophers. I argue that the Zero-Sum Claim is hardly ever true when it comes to the novel understanding of positionality that currently dominates the philosophical literature. I propose dropping the Zero-Sum Claim and construing positional competitions as win-lose. This is conceptually clearer and deepens our understanding and ethical evaluation of these important competitions in contemporary societies. [ABSTRACT FROM AUTHOR]

This research aims to study the applicability of game theory to system safety and reliability decision‐making problems and corresponding objective conflicts using non‐cooperative games. The non‐cooperative games would solve the games considering non‐cooperative cognitive decision‐makers behaviors, which are commonly ignored by other system safety and reliability analysis (SSRA) techniques, assuming that there would be perfect cooperation between the players (decision‐makers). Game theory can also recognize and understand the decision‐makers' behaviors and provide a "win‐win" situation for all players and the best broader system outcomes. The paper also shows the use of dynamic game theory in system safety and reliability decision‐making problems over time. The results indicate the effectiveness and efficiency of game theory and show how this can better reflect decision‐makers' opinions in system safety and reliability decision‐making problems. [ABSTRACT FROM AUTHOR]

We consider two-player zero-sum differential games of fixed duration, where the running payoff and the dynamics are both linear in the controls of the players. Such games have a value, which is determined by the unique viscosity solution of a Hamilton–Jacobi-type partial differential equation. Approximation schemes for computing the viscosity solution of Hamilton–Jacobi-type partial differential equations have been proposed that are valid in a more general setting, and such schemes can of course be applied to the problem at hand. However, such approximation schemes have a heavy computational burden. We introduce a discretized and probabilistic version of the differential game, which is straightforward to solve by backward induction, and prove that the solution of the discrete game converges to the viscosity solution of the partial differential equation, as the discretization becomes finer. The method removes part of the computational burden of existing approximation schemes. [ABSTRACT FROM AUTHOR]

In a two-player noncooperative game framework, we deal with the affine relaxations of the best response algorithm (where a player's strategy is a best response to the strategy of the other player that comes from the previous step), motivated by the first results obtained for convex relaxations in zero-sum games (J. Morgan, Int. J. Comput. Math., 4 (1974), pp. 143-175) and for nonconvex affine relaxations in non-zero-sum games (F. Caruso, M. C. Ceparano, and J. Morgan, SIAM J. Optim., 30 (2020), pp. 1638-1663). In order to be able to specify the convergence of any type of affine relaxation of the best response algorithm, we define a new class of games, called ratiobounded games. This class contains games broadly used in literature (such as weighted potential and zero-sum games), both in finite and infinite dimensional settings. Its definition relies on a unifying property and on three associate key parameters explicitly related to the data. Depending on how the parameters are ordered, we provide a classification of the ratio-bounded games in four subclasses such that, for each of them, the following issues are answered when the strategy sets are real Hilbert spaces: existence and uniqueness of the Nash equilibria, global convergence of the affine relaxations of the best response algorithm, estimation of the related errors, determination of the algorithm with the highest speed of convergence, and comparison with the known results. Moreover, the investigation is supplemented by illustrating numerical examples and by describing a black-box model with a first-order oracle for an implementation of the algorithm. [ABSTRACT FROM AUTHOR]

Witnessing the pro-Western shifts in the post-Soviet countries, Russia has failed to develop policies that would attract the former Soviet satellites without keeping them in its sphere of influence via hard-power. On the other hand, Western values, political influence and institutions have penetrated Eurasian countries causing Russia's relative decline. This structural dynamic not only entraps Russia in a zero-sum game with the West but also triggers Russian threat perceptions on the unit level. Russian strategic culture emphasizes anxieties about loss of sovereignty or power shifts in the Russian regime that could mean the end of the current establishment, border security, and great power status resurrection. A combination of these threat perceptions and structural shifts manifests in the Thucydides Trap, an ancient dilemma behind the preventive war, in the post-Soviet space. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive critic control method is designed to solve an optimal H ∞ tracking control problem for continuous nonlinear systems with nonzero equilibrium based on adaptive dynamic programming (ADP). To guarantee the finiteness of a cost function, traditional methods generally assume that the controlled system has a zero equilibrium point, which is not true in practical systems. In order to overcome such obstacle and realize H ∞ optimal tracking control, this paper proposes a novel cost function design with respect to disturbance, tracking error and the derivative of tracking error. Based on the designed cost function, the H ∞ control problem is formulated as two-player zero-sum differential games, and then a policy iteration (PI) algorithm is proposed to solve the corresponding Hamilton–Jacobi–Isaacs (HJI) equation. In order to obtain the online solution to the HJI equation, a single-critic neural network structure based on PI algorithm is established to learn the optimal control policy and the worst-case disturbance law. It is worth mentioning that the proposed adaptive critic control method can simplify the controller design process when the equilibrium of the systems is not zero. Finally, simulations are conducted to evaluate the tracking performance of the proposed control methods. [ABSTRACT FROM AUTHOR]

10.3390/math10081212 8 Ibragimov G., Kuchkarova S., Hasim R.M., Pansera B.A. Differential Game for an Infinite System of Two-Block Differential Equations. References 1 Ibragimov G., Kazimirova R., Pansera B.A. Evasion Differential Game of Multiple Pursuers and One Evader for an Infinite System of Binary Differential Equations. The study of differential games has practical applications in the analysis and resolution of conflict issues by the use of differential equations. [Extracted from the article]

In this paper, the safe optimal control method for continuous-time (CT) nonlinear safety-critical systems with asymmetric input constraints and unmatched disturbances based on the adaptive dynamic programming (ADP) is investigated. Initially, a new non-quadratic form function is implemented to effectively handle the asymmetric input constraints. Subsequently, the safe optimal control problem is transformed into a two-player zero-sum game (ZSG) problem to suppress the influence of unmatched disturbances, and a new Hamilton–Jacobi–Isaacs (HJI) equation is introduced by integrating the control barrier function (CBF) with the cost function to penalize unsafe behavior. Moreover, a damping factor is embedded in the CBF to balance safety and optimality. To obtain a safe optimal controller, only one critic neural network (CNN) is utilized to tackle the complex HJI equation, leading to a decreased computational load in contrast to the utilization of the conventional actor–critic network. Then, the system state and the parameters of the CNN are uniformly ultimately bounded (UUB) through the application of the Lyapunov stability method. Lastly, two examples are presented to confirm the efficacy of the presented approach. [ABSTRACT FROM AUTHOR]

The Chinese expansion in Sub-Saharan Africa that is causing concern in Western capitals was done against the background of the abandonment or the "triage" operated by the former colonial powers on this continent after 1990. Press articles (more or less academic) in search of spectacular, prefers the "zero sum game" perspective instead of the "win-win" one. A political strategy of China in the African area would involve a sacrifice of "economic logic" in favour of "political logic", or investments made under any conditions at prices higher than market conditions would dictate at a particular moment. The analysis of China's political behaviour must avoid the spectacular and be based on facts, figures (as far as they are available and credible) and analogies (cautious) with the evolution of other emerging economies throughout contemporary history. China, which stays and invests where Western companies leave, could not have a bad image in Sub-Saharan Africa. Africa appears as part of a new Geo-strategic rivalry between the West and RP China. This rivalry is desirable to be constructive, to respect the rules of the game and above all to bring about structural transformations for the benefit of ordinary African citizens. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the optimal control strategies for model‐free zero‐sum games involving the H∞$$ {H}_{\infty } $$ control. The key contribution is the development of a Q‐learning algorithm for linear quadratic games without knowing the system dynamics. The finite‐horizon setting is more practical than the infinite‐horizon setting, but it is difficult to solve the time‐varying Riccati equation associated with the finite‐horizon setting directly. The proposed algorithm is shown to solve the time‐varying Riccati equation iteratively without the use of models, and numerical experiments on aircraft dynamics demonstrate the algorithm's efficiency. [ABSTRACT FROM AUTHOR]

Non-orthogonal multiple access technology (NOMA), as a potentially promising technology in the 5G/B5G era, suffers fromubiquitous security threats due to the broadcast nature of the wirelessmedium. In this paper, we focus on artificial-signal-assisted and relay-assisted secure downlink transmission schemes against external eavesdropping in the context of physical layer security, respectively. To characterize the non-cooperative confrontation around the secrecy rate between the legitimate communication party and the eavesdropper, their interactions are modeled as a two-person zero-sum game. The existence of the Nash equilibrium of the proposed game models is proved, and the pure strategyNash equilibriumand mixed-strategyNash equilibriumprofiles in the two schemes are solved and analyzed, respectively. The numerical simulations are conducted to validate the analytical results, and showthat the two schemes improve the secrecy rate and further enhance the physical layer security performance of NOMA systems. [ABSTRACT FROM AUTHOR]

This paper investigates the main features of the Genoese insurance market between 1564 and 1572, thanks to the analysis of an unpublished tax register that preserves all insurance policies drafted in Genoa in that period. Marine insurance, intended as an archetypical risk-shifting technique, is probably the oldest financial instrument intended solely to protect against the economic consequences of commercial losses. Conventional premium insurance was developed as a tool to transfer risk during the commercial revolution of the late middle ages. This development was first led by Italian cities, among whom Genoa played a key role. However, Genoese operators involved in the insurance sectors, which belonged almost exclusively to the patrician families ruling the republic, acted as a mutual "risk-community" in a semi-closed market: a sort of "syndicate". They shared among them the risks of maritime routes calling at the port of Genoa. Insurance was a zero-sum game, with low losses and gains that did not allow a true single-sector specialisation. [ABSTRACT FROM AUTHOR]

The article discusses the challenges and frustrations faced by researchers in the publishing process. The author reflects on the increasing difficulty of finding reviewers and the harshness of their feedback. They propose that papers have become a form of currency, with researchers exchanging publications for career advancement and recognition. The author suggests that the current system may not be sustainable and explores potential solutions. [Extracted from the article]

En antologi om natursyn og natur i Danmark: edited by Anne Katrine Gjerløff and Karsten Elmose Vad, Odense, Biologiforbundet, 2021, 200 pp., DKK 250 (pbk), ISBN: 87-91659-04-3 To counter biodiversity loss, it seems more realistic that an appeal to a more abstract feeling of the value of species that one will never encounter and to a sadness at the thought of their disappearance will gather support for more wild nature also in Denmark. In this Danish anthology on nature and views on nature, "Which Nature?". [Extracted from the article]

Attacking a naval vessel with multiple missiles is an important way to improve the hit rate of missiles. Missile-borne radars need to complete detection and antijamming tasks to guide missiles, but communication between these radars is often difficult. In this paper, an optimization method based on multi-agent reinforcement learning is proposed for the collaborative detection and antijamming tasks of multiple radars against one naval vessel. We consider the collaborative radars as one player to make their confrontation with the naval vessel a two-person zero-sum game. With temporal constraints of the radar's and jammer's recognition and preparation interval, the game focuses on taking a favorable position at the end of the confrontation. It is assumed the total jamming capability of a shipborne jammer is constant and limited, and the shipborne jammer allocates the jamming capability in the radar's direction according to the radar threat assessment result and its probability of successful detection. The radars work collaboratively through prior centralized training and obtain a good performance by decentralized execution. The proposed method can make radars collaborate to detect the naval vessel, rather than only considering the detection result of each radar itself. Experimental results show that the proposed method in this paper is effective, improving the winning probability to 10% and 25% in the two-radar and four-radar scenarios, respectively. [ABSTRACT FROM AUTHOR]

An active suspension system ensures the controllability of a vehicle in the vertical direction, which greatly enhances the control redundancy and safety of an intelligent driven vehicle. However, many calibrated model parameters are not conducive to the application of optimal control. To reduce the control cost of active suspension, a model-free H8 output feedback control method is studied in this research. First, the optimal governing equation of the active suspension is transformed into a zero-sum game problem of two players, and an off-policy reinforcement learning algorithm is established to solve the game algebraic Riccati equation. This method could overcome the disadvantage of constant interactions between Q-learning and the environment. Secondly, with the consideration that some state variables are difficult to measure, a data-driven H8 output feedback controller is designed using road sensing information and historical measurement data, and the Bellman equation of the system is solved using the least squares method to obtain the optimal control solution of the active suspension. The simulation and rapid prototype experimental results show that the proposed method could produce the optimal control strategy of the system without model parameters, overcome the strong dependence and sensitivity of traditional design methods to model parameters and improve the robust control effect of the active suspension. [ABSTRACT FROM AUTHOR]

We examined whether there is evidence for racial and gender bias in the voting patterns of contestants on Survivor, a reality-television zero-sum game in which contestants compete for up to 39 days to win $1 million. Among 731 contestants across 40 seasons, we found evidence of racial and gender bias at multiple stages of Survivor. Compared with men, women were more likely to be voted out of their tribe first and were less likely to make it to the individual-competition stage of the game (i.e., the "merge"). They were also less likely to win Survivor. Black, Indigenous, and people of color (BIPOC) contestants, compared with White contestants, were more likely to be voted out of their tribe first and were less likely to make it to the individual-competition stage of the game. These findings suggest a systemic bias in favor of White men and against women of color. [ABSTRACT FROM AUTHOR]

Gods of Mount Tai: Familiarity and the Material Culture of North China, 1000-2000 by Susan Naquin (review) God cults are not zero-sum games, and gods having strong connections and bonds with other gods have more opportunities to develop and gain new shrines and worshippers. Naquin has a short but tantalizing passage (pp. 404-408) on local painted pantheons or assemblages, and this is the kind of material that could be fruitfully focused on to understand the dynamics that make a god popular and successful. [Extracted from the article]

The Scandinavian states' pursuit of status in world politics is well documented. However, little is known about whether these endeavors have resulted in higher status for these states. In this article, we suggest that the Scandinavian countries represent a useful case to explore whether similar foreign policy profiles and common club membership equalizes or exacerbates the unequal distribution of status recognition in world politics. To measure the status recognition of Sweden, Denmark, and Norway, we use a network centrality measure of diplomatic representation and exchange from 1970 to 2010. We also measure how well the states have performed to increase their status recognition given their available status resources (measured by military capabilities and wealth) and their status-seeking effort (measured by relative diplomatic outreach). Our results show that Sweden has received significantly more recognition and performed much better than both Denmark and Norway in the measured period. We offer three explanations for these developments. First, the spoils of seeking status using the Scandinavian brand is akin to a regional zero-sum game in which Sweden, as the most visible state of the three, is the main beneficiary of the status recognition in the direction of the club. Second, status recognition often lags achievements or increases in status resources because the beliefs of foreign policy practitioners are only updated sporadically. This status lag is especially visible when states struggle to convert their resources into status (Norway), or when they succeed in maintaining their status despite experiencing a drop in status resources (Sweden). Third, an increase in status resources will only influence status recognition if it plays into a corresponding narrative. Sweden, in contrast to the nouveau riche Norwegians, has managed to rearticulate its foreign policy in a way that has attracted recognition in world politics. [ABSTRACT FROM AUTHOR]

We study the Hamilton-Jacobi (HJ) approach for a two-person zero-sum differential game with state constraints and where controls of the two players are coupled within the dynamics, the state constraints and the cost functions. It is known for such problems that the value function may be discontinuous and its characterization by means of an HJ equation requires some controllability assumptions involving the dynamics and the set of state constraints. In this work, we characterize this value function through an auxiliary differential game free of state constraints. Furthermore, we establish a link between the optimal strategies of the constrained problem and those of the auxiliary problem and we present a general approach allowing to construct approximated optimal feedbacks to the constrained differential game for both players. Finally, an aircraft landing problem in the presence of wind disturbances is given as an illustrative numerical example. [ABSTRACT FROM AUTHOR]

This work proposes a method for the intelligent deployment of distributed flexible AC transmission system (D-FACTS) devices. In recent years, in the field of moving target defense (MTD) strategies to detect coordinated cyber–physical attacks (CCPAs), establishing how to deploy D-FACTS devices has become an important research point. Although some research results have been proposed, the obtained deployment solutions are unintelligent due to not carefully considering smart attackers' behaviors. A method for achieving the intelligent deployment of D-FACTS devices is proposed in this paper. First, the basic concept of corrupting CCPAs is summarized; second, based on considering practical constraints and the basic concept, a protected transmission line set is confirmed; and third, a zero-sum game model is formulated, and a robust Nash equilibrium solution is computed. Due to the game's characteristics, this solution reflects the smart attackers' sense of action. Relying on the solution, those lines that are most likely to be tripped form a new protected transmission line set. Finally, a comprehensive algorithm using a metric proposed in previous studies is proposed for finding an intelligent solution for the deployment of D-FACTS devices. We validated our results through extensive simulations using IEEE 14-bus, 30-bus, and 118-bus power systems provided by MATPOWER and the real-world load profiles from New York State. Our work, in tracking the targets that attackers are most likely to attack, opens up new ideas for the intelligent deployment of D-FACTS devices. [ABSTRACT FROM AUTHOR]

In the field of computer intelligence, it has always been a challenge to construct an agent model that can be adapted to various complex tasks. In recent years, based on the planning algorithm of Monte Carlo tree search (MCTS), a new idea has been proposed to solve the AI problems of two-player zero-sum games such as chess and Go. However, most of the games in the real environment rely on imperfect information, so it is impossible to directly use the normal tree search planning algorithm to construct a decision-making model. Mahjong, which is a popular multiplayer game with a long history in China, attracts great attention from AI researchers because it contains a large game state space and a lot of hidden information. In this paper, we utilize an agent learning approach that leverages deep learning, reinforcement learning, and dropout learning techniques to implement a Mahjong AI game agent. First, we improve the state transition of the tree search based on the learned MDP model, the player position variable and transition information are introduced into the tree search algorithm to construct a multiplayer search tree. Then, the model training based on a deep reinforcement learning method ensures the stable and sustainable training process of the learned MDP model. Finally, we utilize the strategy data generated by the tree search and use the dropout learning method to train the normal decision-making agent. The experimental results demonstrate the efficiency and stability performance of the agent trained by our proposed method compared with existing agents in terms of test data accuracy, tournament ranking performance, and online match performance. The agent plays against human players and acts like real humans. [ABSTRACT FROM AUTHOR]

A novel policy gradient (PG) adaptive dynamic programming method is developed to deal with nonlinear discrete-time zero-sum games with unknown dynamics. To facilitate the implementation, a policy iteration algorithm is established to approximate the iterative Q-function, as well as the control and disturbance policies via three neural network (NN) approximators, respectively. Then, the iterative Q-function is exploited to update the control and disturbance policies via PG method. To stabilize the training process and improve the data usage efficiency, the experience replay technique is applied to train the weight vectors of the three NNs by using mini-batch empirical data from replay memory. Furthermore, the convergence in terms of the iterative Q-function is proved. Simulation results of two numerical examples are provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-person zero-sum differential game with incomplete information on the initial state, namely, the first player has a private information while the second player knows only a probability distribution on the initial state, and obtain the existence of its value functions. The main novelty lies in the method for which we apply a generalized weak contraction for dynamic systems and terminal cost functions instead of the Lipschitz contractive condition on a partially ordered metric space. [ABSTRACT FROM AUTHOR]

• The study explores changes in charitable giving after a major domestic disaster - Hurricane Sandy. • Total donations increase in the immediate aftermath of Hurricane Sandy. • Donations for Sandy relief are, on average, not substituted with similar projects. • Donations for other disaster recovery projects increase in the immediate aftermath of Hurricane Sandy. • In affected regions, these changes in charitable giving appear to be more pronounced than in regions further away. This paper re-opens the discussion of whether new demand for charitable aid generates additional giving or is ultimately a zero-sum game. I employ the exogenous variation in donations provided by Hurricane Sandy and a unique data set from a large crowdfunding platform to analyze giving patterns around the disaster. The study consists of two parts. The first part examines whether a major disaster like Hurricane Sandy increases the altruism budget and if and how donors substitute their donations to the victims of the disaster. The second part focuses on the disaster experience and whether the altruism budget and substitution differ with the proximity to the disaster and resulting damage. The findings indicate that the altruism budget increases in line with earlier studies and that not only victims of Hurricane Sandy, but also victims of other major disasters benefit from this increase at least in the immediate aftermath. The analyses provide no evidence for substitution with similar projects. Giving for victims of Hurricane Sandy and other disasters seems to be slightly more pronounced in affected regions relative to the control group of regions further away. [ABSTRACT FROM AUTHOR]

Patterns of news consumption are changing drastically. Citizens increasingly rely on social media such as Facebook to read and share political news. With the power of these platforms to expose citizens to political information, the implications for democracy are profound, making understanding what is shared during elections a priority on the research agenda. Nevertheless, to the best of our knowledge, no study has yet explicitly explored how elections transform news sharing behaviour on Facebook. This study begins to remedy this by (a) investigating changes in news coverage and news sharing behaviour on Facebook by comparing election and routine periods, and by (b) addressing the 'news gap' between preferences of journalists and news consumers on social media. Employing a novel data set of news articles (N = 83,054) in Mexico, findings show that during periods of heightened political activity, both the publication and dissemination of political news increases, the gap between the news choices of journalists and consumers narrows, and that news sharing resembles a zero-sum game, with increased political news sharing leading to a decrease in the sharing of other news. [ABSTRACT FROM AUTHOR]

This paper investigates how women leaders in the UK negotiate claims of being competitive by internalizing competition. Competition is a critical component in neoliberal contexts; yet its gendered implications are under research. Through analysis of 18 women leaders' narratives who directly characterize themselves as 'competitive with myself,' we theorize how and why competition is directed at the self. We understand articulations of 'I'm competitive with myself as a discursive strategy, which functions in the narratives in three interconnected ways. 'Competitive with myself' versus 'competitive with others' explains how women leaders internalize competition by rejecting competition with others and distancing from the conventional notion of zero‐sum game competition. 'Competing with myself for perfection' and 'Competitive with myself as a protective shield' explain why women leaders internalize competition—to perfect the self and navigate the double standards of a gendered neoliberal workplace. We argue that 'competitive with myself' as a discursive strategy enables women leaders to openly claim competitiveness, (an undesirable performance for women) and simultaneously distance themselves from it. The study contributes understandings of competition as gendered under neoliberalism and in patriarchal men‐dominated leadership roles and workplaces. Through a nuanced discussion of women leaders' narratives, we identify both an obligation to compete and a possible flexing of gender norms in relation to competition. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed accelerated first-order continuous-time algorithm for O(1=t²) convergence to Nash equilibria in a class of two-subnetwork zero-sum games with bi-linear couplings. First-order methods, which only use subgradients of functions, are frequently used in distributed/parallel algorithms for solving large-scale and big-data problems due to their simple structures. However, in the worst cases, first-order methods for two-subnetwork zero-sum games often have an asymptotic or O(1=t) convergence. In contrast to existing time-invariant first-order methods, this paper designs a distributed accelerated algorithm by combining saddle-point dynamics and time-varying derivative feedback techniques. If the parameters of the proposed algorithm are suitable, the algorithm owns O(1=t²) convergence in terms of the duality gap function without any uniform or strong convexity requirement. Numerical simulations show the efficacy of the algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a zero‐sum dynamic game (ZSDG) design to mitigate frequency deviations in the secondary control layer of islanded AC microgrids. By defining a min‐max optimization problem, where the control input minimizes the frequency deviations while the external disturbances maximizes the cost function, a robust control law is designed. The outcome leads to setting the frequency to its desired value and at the same time effects of disturbances are attenuated by applying the H∞$H_{\infty }$ optimal controller in the secondary control level of AC microgrids. Since the basic ZSDG controller cannot eliminate adverse effects of external disturbances on the system frequency, an extended‐ZSDG (EZSDG) method is introduced to design an effective H∞$H_{\infty }$ controller. Due to the lack of access to the state variables of the microgrids, a full‐order observer is designed to estimate these variables based on the measured output. In simulation results, the validity of the proposed EZSDG is investigated by considering uncertainties in both the communication and physical layers. [ABSTRACT FROM AUTHOR]

The research question in this article concerns how a competitive environment affects the learner's (officer cadet's) personal leadership development and their relationship to their team and with future civilian foundations. More specifically, what are the possible learning effects of the 'hidden' curriculum? This article investigates how more than 250 years of leadership education provides new army officers with new skills and how this environment may affect the cadets' leadership training. The article builds on ethnographic data gathered during the three-year education programme in most of the relevant practical locations and contexts. Data were collected using both interviews and a questionnaire. Regarding trust in their learning environment, cadets reported a mean score of 2.83 on a 1 (low trust) to 5 (high trust) Likert scale, underpinning interview data regarding the lack of trust in the Norwegian Military Academy (NMA) and in their fellow cadets. Cadets also pointed out that competition hindered their learning (mean = 2.50). These findings are interpreted in relation to possible negative effects stemming from internal competition and the evaluation system as a whole. The overall output of this system is a zero-sum game, and thus affects evaluative practices and learning processes. This study is of relevance to higher education officers responsible for designing learning environments. [ABSTRACT FROM AUTHOR]

Consider a stationary process taking values in a finite state space. Each state is associated with a finite one-shot zero-sum game. We investigate the infinitely repeated zero-sum game with incomplete information on one side in which the state of the game evolves according to the stationary process. Two players, named the observer and the adversary, play the following game. At the beginning of any stage, only the observer is informed of the state ξn and is therefore the only one who knows the identity of the forthcoming one-shot game. Then, both players take actions, which become publicly known. The paper shows the existence of a uniform value in a new class of stationary processes: ergodic Kronecker systems. Techniques from ergodic theory, probability theory, and game theory are employed to describe the optimal strategies of the two players. Funding: This work was supported by the Israel Science Foundation [Grant 591/21] and Deutsche Forschungsgemeinschaft [Grant KA 5609/1-1]. [ABSTRACT FROM AUTHOR]

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among n discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at location i takes ti time units and detects the hider—if hidden there—independently with probability α i for i = 1 , ... , n. The hider aims to maximize the expected time until detection, whereas the searcher aims to minimize it. We prove the existence of an optimal strategy for each player. In particular, any optimal mixed hiding strategy hides in each location with a nonzero probability, and there exists an optimal mixed search strategy that can be constructed with up to n simple search sequences. Funding: This work was supported by the Engineering and Physical Sciences Research Council [Grant EP/L015692/1] STOR-i Centre for Doctoral Training. [ABSTRACT FROM AUTHOR]

In this paper, we present a Q-learning framework for solving finite-horizon zero-sum game problems involving the H ∞ control of linear system without knowing the dynamics. Research in the past mainly focused on solving problems in infinite horizon with completely measurable state. However, in the practical engineering, the system state is not always directly accessible, and it is difficult to solve the time-varying Riccati equation associated with the finite-horizon setting directly either. The main contribution of the proposed model-free algorithm is to determine the optimal output feedback policies without measurement state in finite-horizon setting. To achieve this goal, we first describe the Q-function caused by finite-horizon problems in the context of state feedback, then we parameterize the Q-functions as input–output vectors functions. Finally, the numerical examples on aircraft dynamics demonstrate the algorithm's efficiency. [ABSTRACT FROM AUTHOR]

We study zero-sum stochastic games for controlled discrete time Markov chains with risk-sensitive average cost criterion with countable/compact state space and Borel action spaces. The payoff function is nonnegative and possibly unbounded for countable state space case and for compact state space case it is a real-valued and bounded function. For countable state space case, under a certain Lyapunov type stability assumption on the dynamics we establish the existence of the value and a saddle point equilibrium. For compact state space case we establish these results without any Lyapunov type stability assumptions. Using the stochastic representation of the principal eigenfunction of the associated optimality equation, we completely characterize all possible saddle point strategies in the class of stationary Markov strategies. Also, we present and analyze an illustrative example. [ABSTRACT FROM AUTHOR]

Context. The article proposes a method of analyzing the proposals of team members in order to avoid conflict situations at the stage of team formation. Objective. The object of the study is the method of analyzing the proposals of team members while solving project tasks. The purpose of the work is to analyze the developed method of analysis of proposals of team members to avoid or resolve conflict situations at the stage of team activation Method. The developed method is based on the theory of matrix games. Conflicts between individual team members mainly arise at the stage of team formation. For the project manager, it is important to identify the conflict situation in time and find a way out of it to satisfy both team members and without harming the teamwork as a whole. A team created to implement an IT project is often faced with a situation where two of its members have different visions of approaches to creating the final product. At the same time, each of them has experience in the development of similar software products or services by different teams. To effectively solve this situation, we suggest using approaches typical of bimatrix games, when each of these team members is considered as a player. This takes into account the fact that the bimatrix theory of games is based on a conflict between two players whose interests are opposite – an antagonistic zero-sum game is precisely the basis of the developed approach. Results. The proposed method of analysis of proposals of team members contributes to the avoidance or resolution of conflict situations at the stage of their closer interaction. For efficient solution of the said situation, we propose to use approaches being typical for bimatrix games when each of these team members is treated as a player. At the same time, account is taken of the fact that the bimatrix game theory is based on a conflict of two players whose interests are opposite – an antagonistic game with a zero sum being that very element to constitute the basis of the approach developed. Conclusions. The given calculation of the model example shows that the use of the proposed method allows the project manager to give a reasonable preference to another team member, since the expected average profit of this player is greater than that of the first player. In this case, the manager has an opportunity to simulate situations for the players (for the team) and promptly respond to probable deviations of their behavioral strategies from the optimal ones, establish healthy relationships between team members and choose the best proposals for solving project tasks. [ABSTRACT FROM AUTHOR]