Search

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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]

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 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]

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, an event-triggered adaptive dynamic programming (ADP) method is proposed to deal with the H ∞ problem with unknown dynamic and constrained input. Firstly, the H ∞ -constrained problem is regarded as the two-player zero-sum game with the nonquadratic value function. Secondly, we develop the event-triggered Hamilton–Jacobi–Isaacs(HJI) equation, and an event-triggered ADP method is proposed to solve the HJI equation, which is equivalent to solving the Nash saddle point of the zero-sum game. An event-based single-critic neural network (NN) is applied to obtain the optimal value function, which reduces the communication resource and computational cost of algorithm implementation. For the event-triggered control, a triggering condition with the level of disturbance attenuation is developed to limit the number of sampling states, and the condition avoids Zeno behavior by proving the existence of events with minimum triggering interval. It is proved theoretically that the closed-loop system is asymptotically stable, and the critic NN weight error is uniformly ultimately boundedness (UUB). The learning performance of the proposed algorithm is verified by two examples. [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]

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]

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]

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]

We investigate the interplay between forward uncertain difference equations and backward stochastic difference equations, which belong to distinct mathematical frameworks: uncertainty theory and probability theory, respectively. By establishing the connections between uncertain expectation, probabilistic expectation, and chance expectation, we develop the chance theory framework for analyzing uncertain stochastic hybrid zero-sum games constrained by both forward uncertain difference equations and backward stochastic difference equations. Through an equivalent transformation, we convert these games into deterministic difference equation solving problems. By backward-solving the difference equations and applying mathematical induction, analytical expressions for the equilibrium solutions of two types of uncertain stochastic hybrid zero-sum games are obtained. Furthermore, we explore solution methods for zero-sum games with different operational orders of uncertain and probabilistic expectations and highlight the fundamental differences through numerical examples. • Present uncertain stochastic hybrid zero-sum games of forward and backward systems. • Chance theory framework aids analysis of uncertain stochastic hybrid zero-sum games. • Transforms these games into deterministic difference equation solving problems. • Explores solution methods for games with different expectation operational orders. • Provides numerical examples to illustrate effectiveness of solution methods. [ABSTRACT FROM AUTHOR]

An event‐triggered‐based approximate optimal control is developed for modular robot manipulators (MRMs) using zero‐sum game strategy. By utilizing the joint torque feedback method, robotic systems' dynamic model is formulated and state space equation is derived. According to event‐triggered mechanism and neural network algorithm, the tracking control issue is converted to a zero‐sum game optimal control issue. The optimal control policy and worst disturbance policy are acquired by Hamilton–Jacobi–Isaacs function respectively. The MRM system's tracking error is ultimately uniformly bounded. Finally, experiments demonstrate advantages of the method. [ABSTRACT FROM AUTHOR]

We provide improved convergence rates for constrained convex-concave min-max problems and monotone variational inequalities with higher-order smoothness. In min-max settings where the pth-order derivatives are Lipschitz continuous, we give an algorithm that achieves an iteration complexity of O(1/T p+2/2) when given access to an oracle for finding a fixed point of a pth-order equation. We give analogous rates for the weak monotone variational inequality problem. For p > 2, our results improve upon the iteration complexity of the first-order Mirror Prox method by Nemirovski [SIAM J. Optim., 15 (2004), pp. 229-251] and the second-order method by Monteiro and Svaiter [SIAM J. Optim., 22 (2012), pp. 914-935]. We further instantiate our entire algorithm in the unconstrained p = 2 case. [ABSTRACT FROM AUTHOR]

In this paper, a zero-sum game Nash equilibrium computation problem with event-triggered communication is investigated under an undirected weight-balanced multi-agent network. A novel distributed event-triggered projection subgradient algorithm is developed to reduce the communication burden within the subnetworks. In the proposed algorithm, when the difference between the current state of the agent and the state of the last trigger time exceeds a given threshold, the agent will be triggered to communicate with its neighbours. Moreover, we prove that all agents converge to Nash equilibrium by the proposed algorithm. Finally, two simulation examples verify that our algorithm not only reduces the communication burden but also ensures that the convergence speed and accuracy are close to that of the time-triggered method under the appropriate threshold. [ABSTRACT FROM AUTHOR]

We study risk-free bidding strategies in combinatorial auctions with incomplete information. Specifically, what is the maximum profit that a complement-free (subadditive) bidder can guarantee in a multi-item combinatorial auction? Suppose there are n bidders and Bi is the value that bidder i has for the entire set of items. We study the above problem from the perspective of the first bidder, Bidder 1. In this setting, the worst case profit guarantees arise in a duopsony, that is when n = 2, so this problem then corresponds to playing an auction against a budgeted adversary with budget B2. We present worst-case guarantees for two simple and widely-studied combinatorial auctions; namely, the sequential and simultaneous auctions, for both the first-price and second-price case. In the general case of distinct items, our main results are for the class of fractionally subadditive (XOS) bidders, where we show that for both first-price and second-price sequential auctions Bidder 1 has a strategy that guarantees a profit of at least ( B 1 − B 2 ) 2 when B2 ≤ B1, and this bound is tight. More profitable guarantees can be obtained for simultaneous auctions, where in the first-price case, Bidder 1 has a strategy that guarantees a profit of at least (B 1 − B 2) 2 2 B 1 , and in the second-price case, a bound of B1 − B2 is achievable. We also consider the special case of sequential auctions with identical items, for which we provide tight guarantees for bidders with subadditive valuations. [ABSTRACT FROM AUTHOR]

This study proposes a novel way to deal with uncertainty in a two-person zero-sum matrix game with payoffs expressed as fuzzy rough numbers. Complete and reasonable solutions to these types of games are obtained. In this research we develop two linear programming models with upper and lower approximation intervals of fuzzy rough numbers and handle multi-objective crisp linear programming models by incorporating trapezoidal fuzzy rough numbers as payoffs. To provide each opponent with the optimal strategy and value of the game, the usual simplex approach is applied. Finally, two numerical examples demonstrate the matrix game outcomes using Wolfram Cloud. [ABSTRACT FROM AUTHOR]

We consider a model of robust learning in an adversarial environment. The learner gets uncorrupted training data with access to possible corruptions that may be affected by the adversary during testing. The learner's goal is to build a robust classifier, which will be tested on future adversarial examples. The adversary is limited to k possible corruptions for each input. We model the learner-adversary interaction as a zero-sum game. This model is closely related to the adversarial examples model of Schmidt et al. (2018); Madry et al. (2017). Our main results consist of generalization bounds for the binary and multiclass classification, as well as the real-valued case (regression). For the binary classification setting, we both tighten the generalization bound of Feige et al. (2015), and are also able to handle infinite hypothesis classes. The sample complexity is improved from ... for any α>0. Additionally, we extend the algorithm and generalization bound from the binary to the multiclass and real-valued cases. Along the way, we obtain results on fat-shattering dimension and Rademacher complexity of k-fold maxima over function classes; these may be of independent interest. For binary classification, the algorithm of Feige et al. (2015) uses a regret minimization algorithm and an ERM oracle as a black box; we adapt it for the multiclass and regression settings. The algorithm provides us with near-optimal policies for the players on a given training sample. [ABSTRACT FROM AUTHOR]

• Investigate a novel TrFBWM to yield the TrF criteria weights. • Develop the TrFZSG to rank the alternatives. • Propose a TrF-BWM-ZSG by fusinging the BWM and ZSG. This paper investigates a hybrid emergency decision-making (EDM) method called TrF-BWM-ZSG by combining the BWM (best-worst method) and ZSG (zero-sum game) in trapezoidal fuzzy (TrF) environment. Firstly, this paper defines the entropy and similarity for trapezoidal fuzzy numbers (TrFNs). Based on the entropy and similarity measures, a bi-objective programming model is constructed to distribute the weights for experts. Then, based on the multiplicative consistent trapezoidal fuzzy reference comparisons (TrFRCs), a novel TrFBWM is investigated to yield the TrF criteria weights. This novel TrFBWM highlights two innovations: (i) A crisp goal programming weight-determining model is constructed by using the multiplicative consistent TrFRCs; (ii) A reasonable consistency ratio is defined, in which the consistency index is determined according to the consistent transitivity of TrFRCs. Afterwards, the TrFZSG is developed to achieve the alternatives' ranking order by extending the classical ZSG into TrF environment. Lastly, the availability of the TrF-BWM-ZSG is corroborated through a real EDM case of Henan rainstorm disaster. The advantages of the TrF-BWM-ZSG are manifested by several valuable comparisons. Some desirable results derived by the TrF-BWM-ZSG are received: (i) The optimal alternative selected by the proposed TrF-BWM-ZSG suits the actual rescue situation; (ii) The proposed TrF-BWM-ZSG owns high generality since TrFN can reduce to crisp number, interval and triangular fuzzy number; (iii) The developed novel TrFBWM is helpful to preserve more inherent information of TrFNs. [ABSTRACT FROM AUTHOR]

This article discusses the author's experience with the peer review process in clinical research and the impact it has on funding for respiratory disease research. The author emphasizes the importance of fair and constructive criticism in the peer review process, as well as the need for funding committees and editors to identify and address unfair reviews. The author suggests seeking feedback from trusted colleagues and utilizing internal peer review processes before submitting work. The article concludes by stating that funding and reporting on respiratory research should not be a zero-sum game. [Extracted from the article]

In this work, a new tracking control scheme is developed for underactuated autonomous underwater vehicle(UAUV) with unknown disturbance. First, an error tracking system is constructed using backstepping method, which transforms the tracking control problem into the two-player zero-sum game problem. One player is the optimal controller which is designed to make the UAUV track the desired trajectory. The other player is the unknown disturbance that represent the overall damping effect of the UAUV. Then, the single critic network based online policy iteration algorithm is designed to get the optimal control law and the worst-case disturbance, which can achieve the near-optimal control performance and relax the requirements for initial admissible control conditions. In order to improve the converge velocity of tracking error, the weight update law are designed. Furthermore, a discount coefficient is introduced into the performance index due to the nonlinearity and the complexity of UAUV. In addition, the stability of the UAUV is analyzed based on the Lyapunov stability theory the system is guaranteed to be uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed method is demonstrated through the real-time simulations on the UAUV model. • The tracking control problem is solved for UAUV with unknown disturbances based on an online zero-sum game theory proposed. • Only one critic network is employed to reduce the computation time and convergence time. • An online policy iteration algorithm and weights update law are designed to solve the online zero-sum game problem. • A discount coefficient is introduced into the performance index due to the nonlinearity and complexity of UAUV. [ABSTRACT FROM AUTHOR]

Since the multi-time scales and strong nonlinearity are objectively existed in the practical industrial processes, it is extremely challenging to design control policy for optimizing the industrial operation. Therefore, this paper focuses on the multi-time scale optimal operational control (OOC) problem with unmodeled dynamics. Under the framework of reinforcement learning (RL) technology, a self-learning model-free method by integrating zero-sum game and singular perturbation (SP) theories is proposed in this paper, such that composite controllers with signal compensation can be found under which the suboptimal operation of the whole process can be achieved using only measured data. The remarkable highlight in this paper is the novel design method of the composite controllers with signal compensations for unknown nonlinear systems with multi-rate operations. Finally, the effectiveness of the proposed method is verified by a practical example and a numerical example. [ABSTRACT FROM AUTHOR]

This work presents an output-feedback policy learning algorithm underlining input–output system data for distributed robust optimal synchronization of heterogeneous multi-agent systems. The output-feedback synchronization problem in the context of this work is formulated via robust output regulation and reinforcement learning modeling the interactions among agents by a zero-sum game. The proposed learning and control structure only requires the local system data for each agent and distributed output data among communicating neighbors. We utilize system-level synchysis for the continuous-time state reconstruction for the distributed learning with convergence and stability proofs under the proposed output-feedback policy for solving the zero-sum game. We further show that policy learning is assured under the proposed data criteria relating to input–output data only rather than any inter-immediate gains from policy iterations. Based on the cooperative robust output regulation, this work gains robustness after the learning is complete and establishes an output data-driven distributed optimal robust synchronization without knowing accurate system dynamics. A numerical example shows the effectiveness of the proposed learning algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the problem of minimizing the damaging effect on the frequency-hopping spread-spectrum satellite is formulated using the two-player asymmetric zero-sum game framework. The payoff is modeled as the channel capacity of the defender under white additive Gaussian noise. The defender and the attacker are capable of spreading their signals over a prespecified frequency band. Two scenarios are considered: 1) both the attacker and defender know each other's strategies; and 2) the defender knows the attacker's strategy, but not vice versa. In each of these scenarios, we further consider whether the players have knowledge about the environments. We show how to analytically determine optimal strategies for the players in each scenario and provide simulation results to verify our approach. [ABSTRACT FROM AUTHOR]

Rougher flotation, composed of unit processes operating at a fast time scale and economic performance measurements known as operational indices measured at a slower time scale, is very basic and the first concentration stage for flotation plants. Optimizing operational process for rougher flotation circuits is extremely important due to high economic profit arising from the optimality of operational indices. This paper presents a novel off-policy Q-learning method to learn the optimal solution to rougher flotation operational processes without the knowledge of dynamics of unit processes and operational indices. To this end, first, the optimal operational control for dual-rate rougher flotation processes is formulated. Second, H∞ tracking control problem is developed to optimally prescribe the set-points for the rougher flotation processes. Then, a zero-sum game off-policy Q-learning algorithm is proposed to find the optimal set-points by using measured data. Finally, simulation experiments are employed to show the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

We study search games in which the hider may hide in a finite number of locations. We assume that the cost of searching these locations does not depend on the order in which the locations are searched. From these assumptions we derive that the cost function is submodular, thus placing search games with an immobile hider in the context of coalitional games. [ABSTRACT FROM AUTHOR]

Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear systems and adopt a Wasserstein penalty to address the distribution uncertainty of additive stochastic disturbances. By constructing an equivalent deterministic game of the penalized LQR problem, we propose a Q-learning method with convergence guarantees to learn an optimal minimax controller. [ABSTRACT FROM AUTHOR]

Afghanistan has always drawn the attention of the world due to its geo-strategic location. Its proximity with the Central Asian States makes it more important for the world. The 9/11 episode, US intervention in Afghanistan and now the drawdown of ISAF from Afghanistan have further compelled both Pakistan and India to play a zero-sum game there. This has given great momentum to the Indo- Pak rivalry each with its own set of stated objectives and strategies. This paper analyzes the Indo-Pak rivalry in the post 9/11 scenario. This will also analyze the different objectives and strategies adopted by both the archrivals to increase their rivalry against each other. For Pakistan, Afghanistan is more important for its strategic significance and easy access to the CARs. India, on the other hand, seeks all the objectives that are hostile to Pakistan in order to deprive Pakistan of her strategic depth in Afghanistan. [ABSTRACT FROM AUTHOR]

The game of baccarat has evolved from a parlor game played by French aristocrats in the first half of the 19th century to a casino game that generated over US$41 billion in revenue for the casinos of Macau in 2013. The parlor game was originally a three-person zero-sum game. Later in the 19th century it was simplified to a two-person zero-sum game. Early in the 20th century the parlor game became a casino game, no longer zero-sum. In the mid 20th century, the strategic casino game became a nonstrategic game, with players competing against the house instead of against each other. We argue that this evolution was motivated by both economic and game-theoretic considerations. [ABSTRACT FROM AUTHOR]

We analyze the strategic allocation of resources across two contests as in the canonical Colonel Blotto game. In the games we study, two players simultaneously allocate their forces across two fields of battle. The larger force on each battlefield wins that battle, and the payoff to a player is the sum of the values of battlefields won. We completely characterize the set of Nash equilibria of all two-battlefield Blotto games and provide the unique equilibrium payoffs. We also show how to extend our characterization to cover previously unstudied games with nonlinear resource constraints. [ABSTRACT FROM AUTHOR]

This paper discusses French views of transatlantic and European defence from the late 1940s to France's ‘return’ to the North Atlantic Treaty Organization (NATO) in 2009. It argues that, while until the early 1950s the French Government viewed transatlantic and West European security cooperation as mutually reinforcing enterprises, by the end of that decade French decision-makers had developed conflicting perceptions of transatlantic and European defence. During the 1960s, the dominating political discourse in the Fifth Republic portrayed relations between Atlantic and European solidarity as a ‘zero-sum’ game: What was good for the Alliance was bad for Europe and vice versa. President Charles de Gaulle advocated the creation of a European ‘Third Force’, although links with NATO were never outright severed. During the 1970s and early 1980s, a ‘zero-sum’ attitude to Atlantic and European defence consolidated although as the Cold War came to a close, Mitterrand started a selective but steady re-engagement with the Alliance. By the late 1990s, during the presidency of Jacques Chirac, France was once again ade factofull member of NATO, although full reintegration was completed only in April 2009. This paper suggests that France's return to ‘NATO’ marked no dramatic U-turn in French security policy; rather it was the result of a gradual and steady evolution, which was triggered by the crisis of the East–West structure of international politics during the 1980s. [ABSTRACT FROM PUBLISHER]

In this paper we suggest a new class of search games, namely, screening and hiding versus search games. This new class of search games is motivated by the book Search and Screening by Koopman who is the founder of the modern search theory. In our game a hider is not just trying to find the best places to hide resources from a searcher, but also it applies efforts to screen their allocations making it more difficult for the searcher to find them. This hiding and screening strategy of the hider versus search strategy of the searcher makes the plot more real-world relative comparing to widely investigated in literature just hiding versus search games. For the suggested game we found the equilibrium strategies of both players as well as we proved uniqueness of the equilibrium. [ABSTRACT FROM AUTHOR]

The study deals with the enduring conflict between India and Pakistan over Jammu and Kashmir since 1947. The ongoing conflict is analyzed as an enduring rivalry; characterized by three major wars (1947-48), 1965, 1971, low intensity military conflict (Siachen), mini war at Kargil (1999), internal insurgency, cross border terrorism. We examine the progress and the status of the dispute, as well as the dynamics of the India Pakistan relationship by considering the influence of USA and China in crisis dynamics. We discuss the possible solutions offered by the various study groups and persons. Most of the studies were done in crisp environment. Pramanik and Roy (S. Pramanik and T.K. Roy, Game theoretic model to the Jammu-Kashmir conflict between India and Pakistan. International Journal of Mathematical Archive (IJMA), 4(8) (2013), 162-170.) studied game theoretic model to Jammu and Kashmir conflict in crisp environment. In the present study we have extended the concept of the game theoric model of the Jammu and Kashmir conflict in neutrosophic envirorment. We have explored the possibilities and developed arguments for an application of principle of neutrosophic game theory to understand properly of the Jammu and Kashmir conflict in terms of goals and strategy of either side. Standard 2×2 zero-sum game theoretic model used to identify an optimal solution [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we solve the zero-sum game problems for discrete-time affine nonlinear systems with known dynamics via iterative adaptive dynamic programming algorithm. First, a greedy heuristic dynamic programming iteration algorithm is developed to solve the zero-sum game problems, which can be used to solve the Hamilton–Jacobi–Isaacs equation associated with optimal regulation control problems. The convergence analysis in terms of value function and control policy is provided. To facilitate the implementation of the algorithm, three neural networks are used to approximate the control policy, the disturbance policy, and the value function, respectively. Then, we extend the algorithm to optimal tracking control problems through system transformation. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed scheme. [Copyright &y& Elsevier]