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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

• 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]

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]

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]

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]

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]

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]

A complex system exhibiting uncertainty as well as randomness may be portrayed by an uncertain random singular difference equation. This paper investigates two‐person nonzero‐sum and zero‐sum games based on uncertain random singular difference equations. First, an approach is proposed to translate the two‐person nonzero‐sum game into an equivalent game for a standard uncertain random dynamic system. The relevant recursive equations are developed to search the Nash equilibrium for the converted game. Solving the related recursive equations yields the solution to such a game. Following that, a Max‐Min Theorem is provided for finding the saddle‐point equilibrium of an uncertain random two‐person zero‐sum game. Finally, a numerical example is offered to demonstrate the validity of the findings. [ABSTRACT FROM AUTHOR]

In this paper, we deal with two-person zero-sum games with fuzzy goals. We investigated the cases where the membership functions of the players are nonlinear. We examined how the solutions should be if the membership functions of players were exponential functions. In case players' membership functions are exponential, we developed a new method for the maximin solution according to a degree of attainment of the fuzzy goals. An application was made to show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. We will establish continuity properties of the value function under total variation, setwise, and weak convergence of information structures. Our analysis reveals that the value function for a bounded game is continuous under total variation convergence of information structures in both zero-sum games and team problems. Continuity may fail to hold under setwise or weak convergence of information structures; however, the value function exhibits upper semicontinuity properties under weak and setwise convergence of information structures for team problems, and upper or lower semicontinuity properties hold for zero-sum games when such convergence is through a Blackwell-garbled sequence of information structures. If the individual channels are independent, fixed, and satisfy a total variation continuity condition, then the value functions are continuous under weak convergence of priors. We finally show that value functions for players may not be continuous even under total variation convergence of information structures in general non-zero-sum games. [ABSTRACT FROM AUTHOR]

In this paper, we study the stochastic zero-sum differential game in finite horizon in a general case. We first prove that the BSDE associated with a specific generator (the Hamiltonian function for the game) has a unique solution. Then we characterize the value function as that solution to prove the existence of a saddle point for the game. Finally, in the Markovian framework, we show that the value function is the unique viscosity solution for the related partial differential equation. [ABSTRACT FROM AUTHOR]

We consider zero-sum stochastic games for controlled continuous time Markov processes on a general state space with risk-sensitive discounted cost criteria. The transition and cost rates are possibly unbounded. Under a stability assumption, we prove the existence of a saddle-point equilibrium in the class of Markov strategies and give a characterization in terms of the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. Also, we illustrate our results and assumptions by an example. [ABSTRACT FROM AUTHOR]

Generative Adversarial Networks (GANs) have been used for many applications with overwhelming success. The training process of these models is complex, involving a zero-sum game between two neural networks trained in an adversarial manner. Thus, to use GANs, researchers and developers need to answer the question: "Is the GAN sufficiently trained?". However, understanding when a GAN is well trained for a given problem is a challenging and laborious task that usually requires monitoring the training process and human intervention for assessing the quality of the GAN generated outcomes. Currently, there is no automatic mechanism for determining the required number of epochs that correspond to a well-trained GAN, allowing the training process to be safely stopped. In this paper, we propose AutoGAN, an algorithm that allows one to answer this question in a fully automatic manner with minimal human intervention, being applicable to different data modalities including imagery and tabular data. Through an extensive set of experiments, we show the clear advantage of our solution when compared against alternative methods, for a task where the GAN outputs are used as an oversampling method. Moreover, we show that AutoGAN not only determines a good stopping point for training the GAN, but it also allows one to run fewer training epochs to achieve a similar or better performance with the GAN outputs. [ABSTRACT FROM AUTHOR]

This paper is concerned with the control law synthesis for robot manipulators, which guarantees that the effect of the sensor faults is kept under a permissible level, and ensures the stability of the closed-loop system. Based on Lyapunov's stability analysis, the conditions that enable the application of the simple bisection method in the optimization procedure were derived. The control law, with certain properties that make the construction of the Lyapunov function much easier—and, thus, the determination of stability conditions—was considered. Furthermore, the optimization problem was formulated as a class of problem in which minimization and maximization of the same performance criterion were simultaneously carried out. The algorithm proposed to solve the related zero-sum differential game was based on Newton's method with recursive matrix relations, in which the first- and second-order derivatives of the objective function are calculated using hyper-dual numbers. The results of this paper were evaluated in simulation on a robot manipulator with three degrees of freedom. [ABSTRACT FROM AUTHOR]

In this paper, we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc indicating the preferred option for that player. Response graphs, and particularly their sink strongly connected components, play an important role in modern techniques in evolutionary game theory and multi-agent learning. We show that the response graph is a simple and well-motivated model of strategic interaction which captures many non-trivial properties of a game, despite not depending on cardinal payoffs. We characterise the games which share a response graph with a zero-sum or potential game respectively, and demonstrate a duality between these sets. This allows us to understand the influence of these properties on the response graph. The response graphs of Matching Pennies and Coordination are shown to play a key role in all two-player games: every non-iteratively-dominated strategy takes part in a subgame with these graph structures. As a corollary, any game sharing a response graph with both a zero-sum game and potential game must be dominance-solvable. Finally, we demonstrate our results on some larger games. [ABSTRACT FROM AUTHOR]

Although quests for religious origins have been theoretically deconstructed by scholars, discourse about religion in much of the public sphere remains enamored with originality, especially to bolster claims among groups competing over shared spaces. At the Sri Lankan Sufi shrine of Dafther Jailani in Kuragala, an obsession with origins has dramatically reorganized the space, used to justify the physical deconstruction of Muslim pilgrim buildings by the Sri Lankan military. Dafther Jailani also faces other threats from arbiters of originality, including orthodox Sunni Muslims who claim to be stewards of authentic Islam, alongside the Buddhist nationalists who seek to make Kuragala a protected archeological site synonymous with non-Muslim space. Both Buddhists and Muslims have mixed mythical narratives and empirical evidence to advance their claims, and even artifacts from human prehistory at Kuragala are appropriated to provide a new secular excuse for extremist Buddhists to enact an absence of Muslims. Such debates over origins are shown to be a zero-sum game, as one group must lose for another to gain. Yet these gains are ultimately hollow, as mutually valued spaces are emptied of living history to better resemble an ideal past. To combat such erasures, historians of religion must strike a balance between the empirical and ethical, critiquing not only factual errors in these arguments, but also correct information being used incorrectly, to argue in the normative terms of the religious actors themselves that there is much lost and little gained in primordial preoccupations. [ABSTRACT FROM AUTHOR]

In this paper, the position–force–based approximate optimal control method is developed for reconfigurable robots using zero-sum game strategy. By utilizing the Newton–Euler iteration technique, the robotic system's dynamic model is formulated and the state space equation is derived. According to adaptive dynamic programming (ADP) and neural network algorithm, the trajectory tracking control problem is transformed into a zero-sum game-based optimal control issue. The optimal control policy and worst disturbance policy are obtained by Hamilton–Jacobi–Issacs (HJI) function, respectively. Unlike the conventional learning–based robotic control method, the proposed zero-sum game-based method no need extra sub-controller that can reduce the computational burden. The reconfigurable robot system's tracking error is uniformly ultimately bounded by the Lyapunov theorem. Finally, simulation experiments demonstrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

The zero-sum game between the strength of deep in-situ thermal insulation coring structures and the performance of passive thermal insulation materials seriously restricts the exploration and development of deep resources. In this paper, an innovative thermal insulation coring structure based on passive thermal insulation material is designed, and a strength analysis of thermal insulation material is carried out based on the elastic theory of multilayer cylinders, which reveals the stress distribution and deformation law of thermal insulation material in a deep in-situ environment. The reliability of the results is verified by comparisons between the numerical simulation and theoretical derivation. The results show that for deep coring environments of 150 °C and 140 MPa, the wall thickness and diameter of the corer can be greatly reduced by directly coating the insulation material on the surface of the core barrel. This paper can provide a reference for the design and engineering application of deep rock in situ thermal insulation coring systems. [ABSTRACT FROM AUTHOR]

As an effective vehicle, uncertainty theory is applicable for handling subjective indeterminacy. Based on uncertainty theory, the Hurwicz model of the zero-sum uncertain differential game with jump is formulated, in which the dynamic system is portrayed by an uncertain differential equation satisfying both the canonical Liu process and V-jump uncertain process. An equilibrium equation for solving the saddle-point of the above game is proposed. In addition, the game with a linear dynamic system and the quadratic objective function is further analysed. At last, a resource extraction problem using our theoretical results is described. [ABSTRACT FROM AUTHOR]

In this article, the H∞$$ {H}_{\infty } $$ safe control problem of continuous‐time affine nonlinear safety‐critical systems is studied based on the barrier function (BF) and adaptive dynamic programming (ADP). We show that the safety constraints in this article occur under the condition that the system initial state is unsafe and have not been adequately addressed in the existing work. First, the H∞$$ {H}_{\infty } $$ control problem is transformed into a zero‐sum game problem, and a new safe Hamilton–Jacobi–Isaacs equation is proposed by combining with the BF, which makes the unsafe behavior be punished in the learning process. In addition, a damping coefficient is introduced into the BF to punish the unsafe behavior more flexibly. Aiming at the requirement that the initial system state must be strictly constrained in the safe set, a new weight updating method based on ADP is proposed, which can reasonably avoid the influence of the BF on neural network (NN) parameters when the initial system state is unsafe. Furthermore, based on the Lyapunov stability theory, it is proved that the system states of safety‐critical systems and the NN parameters are uniformly ultimately bounded under the safety constraints and disturbances effect. Finally, the effectiveness of the proposed method is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

We consider an extended version of sabotage games played over Attack Graphs. Such games are two-player zero-sum reachability games between an Attacker and a Defender. This latter player can erase particular subsets of edges of the Attack Graph. To reason about such games we introduce a variant of Sabotage Modal Logic (that we call Subset Sabotage Modal Logic) in which one modality quantifies over non-empty subset of edges. We show that we can characterize the existence of winning Attacker strategies by formulas of Subset Sabotage Modal Logic. [ABSTRACT FROM AUTHOR]

Conventionally, as the system dynamics is known, the finite-horizon optimal control of zero-sum games relies on solving the time-varying Riccati equations. In this paper, with unknown system dynamics being considered, a Q-function-based finite-horizon control method is introduced to approximate the solutions of the time-varying Riccati equations. First, a time-varying Q-function explicitly dependent on the time-varying control and disturbance is defined. Then the defined time-varying Q-function is utilised to represent the time-varying control and disturbance which are equivalent to the solutions of the time-varying Riccati equations by relaxing the system dynamics. Finally, a model-free method is introduced to approximate the defined time-varying Q-function. Simulation studies are conducted to demonstrate the validity of the developed method. [ABSTRACT FROM AUTHOR]

This paper shows that dropout training in generalized linear models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game, nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability δ. This result implies that dropout training indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. The paper makes a concrete recommendation on how to select the tuning parameter δ. The paper also provides a novel, parallelizable, unbiased multi-level Monte Carlo algorithm to speed-up the implementation of dropout training. Our algorithm has a much smaller computational cost compared to the naive implementation of dropout, provided the number of data points is much smaller than the dimension of the covariate vector. [ABSTRACT FROM AUTHOR]

Model-based reinforcement learning (RL), which finds an optimal policy after establishing an empirical model, has long been recognized as one of the cornerstones of RL. It is especially suitable for multi-agent RL (MARL), as it naturally decouples the learning and the planning phases, and avoids the non-stationarity problem when all agents are improving their policies simultaneously. Though intuitive and widely-used, the sample complexity of model-based MARL algorithms has not been fully investigated. In this paper, we aim to address the fundamental question about its sample complexity. We study arguably the most basic MARL setting: two-player discounted zero-sum Markov games, given only access to a generative model. We show that model-based MARL achieves a sample complexity of Õ(|S∥A∥B|(1 - γ)-3ε-2) for finding the Nash equilibrium (NE) value up to some ε error, and the ε-NE policies with a smooth planning oracle, where γ is the discount factor, and S, A, B denote the state space, and the action spaces for the two agents. We further show that such a sample bound is minimax-optimal (up to logarithmic factors) if the algorithm is reward-agnostic, where the algorithm queries state transition samples without reward knowledge, by establishing a matching lower bound. This is in contrast to the usual reward-aware setting, where the sample complexity lower bound is ...(|S|(|A| + |B|)(1 - γ)-3ε-2), and this model-based approach is near-optimal with only a gap on the |A|, |B| dependence. Our results not only illustrate the sample-efficiency of this basic model-based MARL approach, but also elaborate on the fundamental tradeoff between its power (easily handling the reward-agnostic case) and limitation (less adaptive and suboptimal in |A|, |B|), which particularly arises in the multi-agent context. [ABSTRACT FROM AUTHOR]

Even though wide access to any warranted information in the modern age, the problem of unfounded belief is still relevant, since these beliefs often lead to negative consequences (e.g., vaccination refusal, homeopathic treatment, etc.). The aim of this study was testing the relationship of social worldviews with paranormal beliefs and conspiracy beliefs. We assumed dimensionality hypothesis based on functional standpoint that there should be a general factor (underlying all the domains of paranormal beliefs and generic conspiracist beliefs), which has associations with the social worldviews as well. Derived our analysis from the survey of 228 participants (Mage = 30.6, SD = 11.7), we found that (a) the structure of paranormal and generic conspiracist beliefs can be described by a bifactor model; (b) the general factor of paranormal and generic conspiracist beliefs in the bifactor model was positively associated with global belief in just world and dangerous worldview; (c) paranormal beliefs were positively associated with global belief in just world and negatively associated with competitive worldview; (d) generic conspiracist beliefs were positively associated with dangerous worldview, competitive worldview, and zero-sum game belief; (e) contrary to our hypotheses, there was no evidence for any negative association of paranormal beliefs with dangerous worldview or zero-sum game belief and for any negative association of generic conspiracist beliefs with global belief in just world. We claim that the unfounded beliefs can be of some functional nature, demonstrating a connection with social worldviews, which opens up new perspectives for considering this problem within the framework of social psychology. [ABSTRACT FROM AUTHOR]

This paper presents an approach for the solution of a zero-sum differential game associated with a nonlinear state-feedback H ∞ control problem. Instead of using the approximation methods for solving the corresponding Hamilton–Jacobi–Isaacs (HJI) partial differential equation, we propose an algorithm that calculates the explicit inputs to the dynamic system by directly performing minimization with simultaneous maximization of the same objective function. In order to achieve numerical robustness and stability, the proposed algorithm uses: quasi-Newton method, conjugate gradient method, line search method with Wolfe conditions, Adams approximation method for time discretization and complex-step calculation of derivatives. The algorithm is evaluated in computer simulations on examples of first- and second-order nonlinear systems with analytical solutions of H ∞ control problem. [ABSTRACT FROM AUTHOR]

In this article we consider zero and non-zero sum risk-sensitive average criterion games for semi-Markov processes with a finite state space. For the zero-sum case, under suitable assumptions we show that the game has a value. We also establish the existence of a stationary saddle point equilibrium. For the non-zero sum case, under suitable assumptions we establish the existence of a stationary Nash equilibrium. [ABSTRACT FROM AUTHOR]

Summary: This article presents a multiplayer zero‐sum game optimal control for modular robot manipulators (MRMs) via adaptive dynamic programming (ADP). The dynamic model of MRMs with interconnected dynamic couplings (IDCs) is formulated. The control law and IDC effect are regarded as players in each module. The optimal tracking control problem of the MRM system can be transformed into a multiplayer zero‐sum game. Base on ADP algorithm, the Hamilton–Jacobi–Issacs (HJI) equation is solved via critic neural network. Then, the optimal control law can be derivated. The closed‐loop robotic system is proved to be asymptotic stable and experiments are conducted to verify the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

This paper presents a novel prespecified finite-time and overshoot-restrained fault-tolerant tracking control scheme to compensate the intermittent faults in linear uncertain systems. Starting from the system tracking error dynamics model, we design a speed excitation function to improve the response speed of the control. A finite-time performance index function is established in the zero-sum game framework for the fault-free H ∞ optimal control policy. Based on Lyapunov stability theory, a fault compensation oriented fault estimation and diagnosis method is proposed to ensure the uniformly ultimately bounded stability of tracking errors. It is noteworthy that the proposed speeding fault-tolerant control can accelerate the trajectory tracking, narrow the upper bound of tracking errors and restrain the overshoot. Numerical and practical experiments fully illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

Game Theory (GT) is the study of strategic decision making. By virtue of its importance, several GT based methodologies for Feature Selection (FS) are proposed in recent times. FS problem can be abstracted as a game by considering each feature as a player and their values as their strategies. Additionally, overall goal of the game is set to classify a data instance appropriately. Most of the existing GT based FS techniques are restricted to Zero Sum Games, Non-Zero Sum Games and Cooperative Games. The classical setting of assuming that all the details of players are known to all players cannot hold in many real-world problems. When the given features are independent, they cannot be treated alike and a characteristics based uncertainty persists among the features. This uncertainty is handled by none of the game forms used in the existing methods. Unlike the mentioned game techniques, Bayesian Games (BG) address the games with imperfect information. This paper investigate the FS problem in terms of BG and proposes a novel method to select the best features. The proposed BG based FS method is a filter type FS method and it starts with identifying Principle Features (PF) and proceeds to play global pairwise Bayesian games between those PF to obtain feature scores. Later, the features are ranked using these scores. In the final stage, a forward selection method with Support Vector Machine (SVM) is used to evaluate the classification performance of the ranked features and helps in the selection of the optimal set of features. Besides these, to improve the scalability of the proposed method MapReduce paradigm is exploited. In order to show the efficacy of the proposed method, experiments are carried out with seven real-world datasets from UCI and Statlog repositories. The promising results showed a significant improvement in the classification performance with fewer selected features than which is achieved using the existing methods. [ABSTRACT FROM AUTHOR]

Generalized grey target decision method (GGTDM) for mixed attributes has different decision-making bases (DMBs) owing to different mechanisms. A combination GGTDM based on zero-sum game theory is proposed to obtain the desirable decision-making effect by fully using the characteristics and information of different DMB based GGTDMs. First, two players are set to compete in the zero-sum game. One player takes different DMB based GGTDMs as the set of his strategies, while the other player adopts the alternatives as the other player's set of strategies. Then, the ranking values of all alternatives decided by different GGTDMs are converted into scores by equivalent way, and the scores are regarded as the payoffs of the two players. Next, the zero-sum game based linear programming model is built to obtain the solutions when reaching the Nash equilibrium. Finally, the combination decision-making values of all alternatives can be calculated based on the strategy solutions for all GGTDMs. And the decision making is based on the value with which the smaller the better. The application analysis verifies that the proposed method has its feasible and can make full use of the advantages of different DMB based GGTDMs and avoid their shortcomings. [ABSTRACT FROM AUTHOR]

This study presents a hybrid algorithm consisting of game theory and the first order Taylor series approach to find compromise solutions to multi-objective linear fractional programming (MOLFP) problems. The proposed algorithm consists of three phases including different techniques: in the first phase, the optimal solution to each LFP problem is found using the simplex method; in the second phase, a zero-sum game is solved to determine the weights of the objective functions via the ratio matrix obtained from a payoff matrix; in the last phase, fractional objective functions of the MOLFP problem are linearized using the 1st order Taylor series. A compromise solution is found by solving the single-objective LP problem constructed in the third phase by using the weights. This algorithm can provide compromise solutions to the problem by constructing different ratio matrices in the second phase. The novelty of this study is that the decision-makers can choose the most suitable solution for their strategy among the compromise solutions. Numerical examples are provided to illustrate the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

The article analyzes historical monuments as instruments of Russia's attempts to impose its aesthetic hegemony in the post-Communist world. Drawing on case studies from the Czech Republic and Estonia, it argues that this hegemony is precarious and vulnerable due to inability to deal with the inherent ambiguity and complexity of historical events and figures. The Russian approach regards historical truth in absolute terms and is underpinned by a zero-sum game understanding of historical narratives. It does not tolerate a multiplicity of perspectives on history and has no appreciation for postmodernist deconstruction of historical symbols. This conflicts with a more diverse, reflexive and inclusive politics of memory as an intrinsic element of cityscapes of Prague and Tallinn where some of the controversial monuments connected with the Soviet occupation have been removed. Russia's reaction to these changes reveals an inherently vulnerable nature of its aesthetic hegemony which is deeply dependent on recognition of the absolute nature of its historical truth that the monuments are supposed to embody. [ABSTRACT FROM AUTHOR]

In this paper, a synergetic learning structure-based neuro-optimal fault tolerant control (SLSNOFTC) method is proposed for unknown nonlinear continuous-time systems with actuator failures. Under the framework of the synergetic learning structure (SLS), the optimal control input and the actuator failure are viewed as two subsystems. Then, the fault tolerant control (FTC) problem can be regarded as a two-player zero-sum differential game according to the game theory. A radial basis function neural network-based identifier, which uses the measured input/output data, is constructed to identify the completely unknown system dynamics. To develop the SLSNOFTC method, the Hamilton–Jacobi–Isaacs equation is solved by an asymptotically stable critic neural network (ASCNN) which is composed of cooperative adaptive tuning laws. Besides, with the help of the Lyapunov stability analysis, the identification error, the weight error of ASCNN, and all signals of closed-loop system are guaranteed to be converged to zero asymptotically, rather than uniformly ultimately bounded. Numerical simulation examples further verify the effectiveness and reliability of the proposed method. [ABSTRACT FROM AUTHOR]

We study a robust monopoly pricing problem with a minimax regret objective, where a seller endeavors to sell multiple goods to a single buyer, only knowing that the buyer's values for the goods range over a rectangular uncertainty set. We interpret this pricing problem as a zero-sum game between the seller, who chooses a selling mechanism, and a fictitious adversary or 'nature', who chooses the buyer's values from within the uncertainty set. Using duality techniques rooted in robust optimization, we prove that this game admits a Nash equilibrium in mixed strategies that can be computed in closed form. The Nash strategy of the seller is a randomized posted price mechanism under which the goods are sold separately, while the Nash strategy of nature is a distribution on the uncertainty set under which the buyer's values are comonotonic. We further show that the restriction of the pricing problem to deterministic mechanisms is solved by a deteministic posted price mechanism under which the goods are sold separately. [ABSTRACT FROM AUTHOR]

This essay argues that within competitive sport zero-sum logic and the theory of mutualism are compatible and complementary. Drawing on Robert Simon’s theory of mutualism and Scott Kretchmar’s argument for zero-sum logic, this article shows how athletes can strive for a clear-cut victory and shared benefits such as athletic excellence fully and wholeheartedly at the same time. This paper will also consider how acknowledgment of this dynamic could advance understandings for ethical theories for sport. It will then conclude by describing a subjective approach that will make the affinity of zero-sum logic and mutualism more accessible for sports people. [ABSTRACT FROM AUTHOR]