Explore the vast range of titles available.

To tackle the challenges presented by the two‐player zero sum game (TZSG) in three‐dimensional space, this study introduces an enhanced deep Q‐learning (DQN) algorithm that utilizes long short term memory (LSTM) network. The primary objective of this algorithm is to enhance the temporal correlation of the TZSG in three‐dimensional space. Additionally, it incorporates the hindsight experience replay (HER) mechanism to improve the learning efficiency of the network and mitigate the issue of the “sparse reward” that arises from prolonged training of intelligence in solving the TZSG in the three‐dimensional. Furthermore, this method enhances the convergence and stability of the overall solution.An intelligent training environment centred around an airborne agent and its mutual pursuit interaction scenario was designed to proposed approach's effectiveness. The algorithm training and comparison results show that the LSTM‐DQN‐HER algorithm outperforms similar algorithm in solving the TZSG in three‐dimensional space. In conclusion, this paper presents an improved DQN algorithm based on LSTM and incorporates the HER mechanism to address the challenges posed by the TZSG in three‐dimensional space. The proposed algorithm enhances the solution's temporal correlation, learning efficiency, convergence, and stability. The simulation results confirm its superior performance in solving the TZSG in three‐dimensional space. The LSTM‐DQN‐HER algorithm is proposed by modelling the MDP and POMDP of a two‐player zero‐sum game problem in three‐dimensional space, and the effectiveness of the proposed algorithm in solving the three‐dimensional two‐player zero‐sum game problem is verified by training and adversarial simulation of the Agent.

Developing normative foundations for optimal play in two-player zero-sum games has turned out to be surprisingly difficult, despite the powerful strategic implications of the Minimax Theorem. We characterize maximin strategies by postulating coherent behavior in varying games. The first axiom, called consequentialism, states that how probability is distributed among completely indistinguishable actions is irrelevant. The second axiom, consistency, demands that strategies that are optimal in two different games should still be optimal when there is uncertainty which of the two games will actually be played. Finally, we impose a very mild rationality assumption, which merely requires that strictly dominated actions will not be played. Our characterization shows that a rational and consistent consequentialist who ascribes the same properties to his opponent has to play maximin strategies. This result can be extended to characterize Nash equilibrium in bimatrix games whenever the set of equilibria is interchangeable.

Although some have heralded recent political and cultural developments as signaling the arrival of a postracial era in America, several legal and social controversies regarding \"reverse racism\" highlight Whites' increasing concern about anti-White bias. We show that this emerging belief reflects Whites' view of racism as a zero-sum game, such that decreases in perceived bias against Blacks over the past six decades are associated with increases in perceived bias against Whites—a relationship not observed in Blacks' perceptions. Moreover, these changes in Whites' conceptions of racism are extreme enough that Whites have now come to view anti-White bias as a bigger societal problem than anti-Black bias.

In this paper, a novel optimal control scheme is established to solve the multi-player zero-sum game (ZSG) issue of continuous-time nonlinear systems with control constraints and unknown dynamics based on the adaptive critic technology. To relax the requirement of system dynamics, a neural network-based identifier is applied to reconstruct the unknown multi-player ZSG system. Then, by developing a new nonquadratic function, the associated Hamilton-Jacobi-Isaacs (HJI) equation of the constrained ZSG is derived. Moreover, an adaptive critic framework is constructed to approximate the optimal cost function. Meanwhile, the strategy sets of optimal control and the worst disturbance are estimated by utilizing the single-critic network, respectively. After that, a modified critic weight updating mechanism with experience replay technique is introduced to relax the requirement of the persistence of excitation condition. Theoretically, by employing the Lyapunov stability theorem, the uniform ultimate boundedness stability of the ZSG system state and the critic network weight approximation error are proved. Finally, a representative example is simulated to validate the efficacy of the constructed framework.

In many practical applications, such as poker, chess, drug interdiction, cybersecurity, and national defense, players often have adversarial stances, i.e., the selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Therefore, adversarial games are important in real-world applications. However, only special adversarial games, such as Bayesian games, are reviewed in the literature. In this respect, this study aims to provide a systematic survey of three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, and zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy-seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

We relax the Kajii and Morris (Econometrica 65:1283–1309, 1997a ) notion of equilibrium robustness by allowing approximate equilibria in close incomplete information games. The new notion is termed “approximate robustness”. The approximately robust equilibrium correspondence turns out to be upper hemicontinuous, unlike the (exactly) robust equilibrium correspondence. As a corollary of the upper hemicontinuity, it is shown that approximately robust equilibria exist in all two-player zero-sum games and all two-player two-strategy games, whereas (exactly) robust equilibria may fail to exist for some games in these categories.

In the well-studied Colonel Blotto game, players must divide a pool of troops among a set of battlefields with the goal of winning a majority. Despite the importance of this game, only a few solutions for special variants of the problem are known. We provide a general technique for computing equilibria of the Colonel Blotto game. Our approach applies to variations of the Colonel Blotto game as well, including an infinite-strategy variant called the General Lotto game. We also apply our technique beyond Colonel Blotto games to create the first polynomial-time algorithms for computing equilibria for a variety of other zero-sum games. Our approach is to reformulate each zero-sum game into a bilinear form, then reduce equilibrium computation to linear optimization over a game-specific polytope.

Purpose Knowledge transfer is a crucial ingredient of employee innovation, yet affective work events may disrupt knowledge flow among employees. This study aims to investigate a previously overlooked, yet frequently occurring affective work experience, namely, that of being envied, and examine how perceptions of being envied may drive contrastive knowledge behaviors of sharing and hiding, which subsequently impact employee innovation. The study further examines how the zero-sum game beliefs of the envied individual may moderate these mechanisms. Design/methodology/approach This study builds on territorial and belongingness theories to delineate the contrastive motivations for knowledge hiding and knowledge sharing. This study tests a moderated mediation model through a multisource survey design involving 225 employees. Findings The results support the notion that perceptions of being envied are linked to both knowledge hiding and knowledge sharing; however, the indirect effect of being envied on innovation is observed only through knowledge sharing. The indirect positive link between perceptions of being envied and innovation via knowledge sharing is weakened when the envied employee holds high zero-sum game beliefs. Originality/value This study advances knowledge scholarship by identifying and testing the organizationally relevant but largely overlooked antecedent of being envied at work. The results provide useful insights to practitioners on how sharing or hiding knowledge serves as a strategic asset in response to being envied at work and how this may in turn impact employee innovation.

This paper extends Berge’s maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets and unbounded payoffs. For games with perfect information, also known under the name of turn-based games, this paper establishes continuity properties of value functions and solution multifunctions. For games with simultaneous moves, it provides results on the existence of lopsided values (the values in the asymmetric form) and solutions. This paper also establishes continuity properties of the lopsided values and solution multifunctions.

This paper is concerned with the Dynkin game (a zero-sum optimal stopping game). The dynamic of the system is modeled by a regime switching diffusion, in which the regime switching mechanism provides the structural changes of the random environment. The goal is to find a saddle point for the payoff functional up to one of the players exiting the game. Taking advantage of the method of penalization and the dynamic programming principle, the value function of the game problem is shown to be the unique viscosity solution to the associated variational inequalities. We also consider a financial example of pricing game option under a regime switching market. Both optimal stopping rules for the buyer and the seller and fair price of the option are numerically demonstrated in this example. All the results are markedly different from the traditional cases without regime switching.