Zero-sum Game Research Articles

Dynamic event-driven optimal consensus control for state-constrained multiagent zero-sum differential graphical games

In this paper, a dynamic event-driven optimal control scheme is proposed for the zero-sum differential graphical games in nonlinear multiagent systems with full-state constraints. Initially, to address the dual demands of optimality and state constraints, a set of system transformation functions are introduced to satisfy the state constraints of the agents. Then, by applying the principle of differential game theory, the distributed optimal control problem affected by external disturbances is formulated as a zero-sum differential graphical game, and the performance index function related to neighbor informations and disturbances is designed for each follower. Afterwards, to enhance the utilization of communication resource, a novel dynamic event-triggered mechanism characterized by a dynamic threshold parameter and an auxiliary dynamic variable is developed, which not only exhibits greater flexibility but also diminishes the frequency of triggers. Furthermore, the approximate optimal control strategies are obtained by employing an event-driven adaptive dynamic programming algorithm. Ultimately, a simulation example is presented to verify the applicability of the proposed control approach.

Performance linkage in renewable energy supply chain: A comparative analysis with coal power and the entire industry

Establishing an efficient renewable energy supply chain is crucial for mitigating climate change, contingent upon policy influence and market complementarity. Accordingly, this study 1) Draws on the characteristics of “market mechanism” and “price regulation” within China's renewable energy industry to compare the supply chain with the entire industry and the coal power industry, laying the groundwork for an analytical framework to assess performance linkage. 2) Examines the role of markets and policies in moderating performance linkage within the renewable energy supply chain based on cash flow inflow and final commodity pricing. Empirical findings indicate that: 1) China's renewable energy supply chain exhibits weaker market circulation mechanisms than the overall industry, but it has not yet shown zero-sum game characteristics akin to the coal power supply chain. 2) Cash flow inflow and final commodity pricing are identified as pivotal factors enabling China's renewable energy industry to circumvent zero-sum games while still lacking a robust positive cycle. This research aids policymakers in dynamically assessing market-based circulation levels within the renewable energy supply chain and facilitates quantifying price regulation and market funding roles in updating industrial policies.

Is Job Crafting a Zero-Sum Game? Comparing The Well-Being Outcomes of Leader-Crafters and Followers

Is Job Crafting a Zero-Sum Game? Comparing The Well-Being Outcomes of Leader-Crafters and Followers

Observability inequality of backward stochastic heat equations with Lévy process for measurable sets and its applications

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

Bipartite containment control of multi-agent systems subject to adversarial inputs based on zero-sum game

In this paper, we investigate bipartite containment control problem of multi-agent systems (MASs) with signed directed graph under adversarial inputs. Firstly, we define the bipartite containment error and establish the equivalence between the bipartite containment error converging to zero and the achievement of bipartite containment control. Subsequently, we prove that the bounded L2-gain bipartite containment problem under adversarial inputs can be reformulated as a multi-player zero-sum differential graphical game problem and can be solved via the solution to the coupled Hamilton-Jacobi-Isaacs (HJI) equation. To address this, we propose a policy iteration (PI) algorithm and prove its convergence under different updating cases. The proposed algorithm is implemented by neural networks (NNs) and a numerical simulation example is provided to show its effectiveness.

UAV air combat autonomous trajectory planning method based on robust adversarial reinforcement learning

The poor robustness of the air combat autonomous trajectory planning strategy (ATP) trained through vanilla reinforcement learning (RL) methods is attributed to its dependence on the source environment. When this ATP is transformed from the source to the target environment, it may fail to lead to an effective dogfight victory due to disturbances, which can potentially threaten the flight safety of the unmanned combat aerial vehicle (UCAV). In order to enhance the robustness of ATP, we propose a robust RL-based method for generating an ATP strategy. This method can effectively consider uncertainties in the state and potential model misspecifications. First, a jointly trained adversary is designed to apply disturbances in the environment, forming a two-player zero-sum game with the ATP agent. To solve this game problem and learn a robust ATP, the robust adversarial RL method (RARL) is applied. Additionally, in order to prevent non-convergence of strategies resulting from the introduction of the RARL algorithm, a curriculum learning method is proposed that emulates the way human pilots learn, gradually progressing from simpler to more challenging courses. Finally, a quantitative method for evaluating the robustness of the ATP is proposed, taking into consideration the differences in ATP performance between the source and target combat environments. The results of robustness estimations demonstrate that the RARL algorithm, which is proposed herein, effectively enhances the ATP's robustness.

“Zero-sum game” or “win-win cooperation”: an analysis of the evolution effect of competition neutrality based on the participation of four parties

To effectively grasp the interactive evolution mechanism of relevant entities in the process of competitive neutrality and reveal the impact of the implementation effect of the principle of competitive neutrality on the evolution path of the game system is the key to guiding the development of the government, industry associations and enterprises with reasonable policies. The equilibrium point of the game is analyzed by the four-party evolutionary game model, and the influence of the change of relevant parameters on the evolution result of the game system is further simulated by numerical simulation. The results show that the central government supervision plays an important role in guiding the strategy selection of different game players. By raising the penalty standards for non-neutral competitive behavior of market players and increasing the non-neutral penalty for local governments, the system can evolve faster to the ideal state of “loose supervision by the central government, neutral implementation by local governments, strong supervision by industry associations, and active cooperation by enterprises.” Therefore, to improve the execution effect of competitive neutrality, the central government shall formulate a reasonable regulatory system, and to maximize inspire the enthusiasm of local government, industry associations and enterprises, to promote stability in the sustainable development of the market.

An empirical Bayes approach for estimating skill models for professional darts players

Abstract We perform an exploratory data analysis on a data-set for the top 16 professional darts players from the 2019 season. We use this data-set to fit player skill models which can then be used in dynamic zero-sum games (ZSGs) that model real-world matches between players. We propose an empirical Bayesian approach based on the Dirichlet-Multinomial (DM) model that overcomes limitations in the data. Specifically we introduce two DM-based skill models where the first model borrows strength from other darts players and the second model borrows strength from other regions of the dartboard. We find these DM-based models outperform simpler benchmark models with respect to Brier and Spherical scores, both of which are proper scoring rules. We also show in ZSGs settings that the difference between DM-based skill models and the simpler benchmark models is practically significant. Finally, we use our DM-based model to analyze specific situations that arose in real-world darts matches during the 2019 season.

Геополитика как идеология

The article presents arguments in favor of interpreting geopolitics as one of the widespread types of “false consciousness,” i.e., ideology. The author shows that the revival of the concept of geopolitics, as well as the ideas about the world of politics associated with this concept, was associated with the actualization of the neo-imperial view of the world. The basis of these ideologized ideas about politics as an arena for the implementation of the “intraspecific” struggle of states is a social Darwinist view of the world, according to which all peoples are enemies, conflict between states is the main form of relations between them according to the principle of a “zero-sum game”, and all unions, alliances and blocs are just tactical ploys that do not cancel the immanent common hostile essence. In other words, the ideology of geopolitics is based on the concept of “looking at neighbors through a gun sight.” The article is of a scientific and analytical nature and does not imply a direct connection with current policy issues.

Research on Autonomous Manoeuvre Decision Making in Within-Visual-Range Aerial Two-Player Zero-Sum Games Based on Deep Reinforcement Learning

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

Bangladesh-India Land Boundary Agreements, 1974-2015: Context, Correlations and Territoriality

Bangladesh and India share 4096.7 km. land boundary, which was drawn between India and the eastern part of Pakistan (East Bengal) by the Radcliffe Award during the partition of 1947. This boundary became the Bangladesh-India boundary after the liberation of Bangladesh in 1971. Therefore, the Pakistan-India land boundary disputes over the un-demarcated boundary, adverse possessions and enclaves transformed into Bangladesh-India ones. These land boundary disputes witnessed one summit-level agreement between Pakistan and India and three summit-level agreements between Bangladesh and India. However, the land boundary disputes were eventually resolved under the land swap deal of 2015. This striking background led to the question as to why these issues were hung up for 68 years, what contexts led to several summit-level agreements on the same issues, and what were the correlations among the agreements. Against this background, this article attempts to shed light on how India, being the big neighbour, dominated the entire trajectory of the land boundary disputes and how it changed its agreed positions from one agreement to another. However, the main objective of this article is to see whether India’s territoriality towards its border with Bangladesh was gradually transformed into the pattern of a zero-sum game during the period from 1974 to 2015, and what was the corresponding territoriality of Bangladesh. Journal of the Asiatic Society of Bangladesh (Hum.), Vol. 69(1), 2024, pp. 89-106

Novel Dynamic Defense Strategies in Networked Control Systems under Stochastic Jamming Attacks

In contemporary networked control systems (NCSs), ensuring robust and adaptive security measures against dynamic threats like jamming attacks is crucial. These attacks can disrupt the control signals, leading to degraded performance or even catastrophic failures. This paper introduces a novel approach to enhance NCS security by applying stochastic game theory to model and resolve interactions between a defender and a jammer. We develop a two-player zero-sum game where the defender employs mixed strategies to minimize the expected cost of maintaining system stability and control effectiveness in the face of potential jamming. Our model discretizes the state space and employs backward induction to dynamically update the value functions associated with various system states, reflecting the ongoing adjustment of strategies in response to the adversary’s actions. Utilizing linear programming in MATLAB, we optimize the defender’s mixed strategies to systematically mitigate the impact of jamming. The results from extensive simulations demonstrate the efficacy of our proposed strategies in attack scenarios, indicating a substantial enhancement in the resilience and performance of NCSs against jamming attacks. Specifically, the proposed method improved network state stability by 75%, reducing the fluctuation range by over 50% compared with systems without defense mechanisms. This study not only advances the theoretical framework for security in NCSs but also provides practical insights for the design of resilient control systems under uncertainty.

Two-Person Adversarial Games are Zero-Sum: An elaboration of a folk theorem

The observation that every two-person adversarial game is an affine transformation of a zero-sum game is traceable to Luce and Raiffa (1957) and made explicit in Aumann (1987). Recent work of Adler et al. (2009) and of Raimondo (2023) in increasing generality, proves what has so far remained a conjecture. We present two proofs of an even more general formulation: the first draws on multilinear utility theory developed by Fishburn and Roberts (1978); the second is a consequence of Adler et al.’s 2009 proof itself for a special case of a two-player game in which each player has a set of three actions.

Two-person zero-sum game with terminal state constraints

In this paper, the discrete-time two-person zero-sum game with terminal state constraints is considered. By applying the variational method, the maximum principle for zero-sum game with terminal constraint is derived along with the forward and backward difference equations (FBDEs). The main contributions of this paper are two-fold. On the one hand, by decoupled solving the FBDEs, the analytical solution to the zero-sum game with terminal state constraint is given. On the other hand, the necessary and sufficient conditions for the reachability of the system are obtained. In this way, the solvability of the zero-sum game with terminal state constraint is re-expressed by the reachability of the system.

584 A Systematic Review of Generative Adversarial Networks (GANs) in Plastic Surgery

Abstract Aim Generative Adversarial Networks (GANs), based on zero-sum game theory, involve two neural networks—the generator and discriminator—to create realistic synthetic data. They're becoming increasingly significant in medicine and plastic surgery. This review assesses GANs' impact in Plastic Surgery, offering a framework for their application and evaluation in various subspecialties, highlighting their potential in research and patient care advancements. Method Following PRISMA guidelines, a systematic review was performed of all applications of GANs within Plastic Surgery and its subspecialties published from 2014 to 2022. Three independent reviewers screened studies using COVIDENCE review management software, from databases including PubMed, Embase, PsychInfo, Scopus and Google Scholar. Results A total of 70 studies were captured by the search, of which seven studies were included in the final analysis. The Kappa score for interrater reliability was 0.97. The most common subspecialty represented was craniofacial (n=4). Proposed uses of GANs ranged from facial recognition, burn estimation, scar prediction and post-breast cancer reconstruction anomaly scoring. All proposed GANs were conditional, with four of the studies using primarily collected training datasets, and the remainder using public datasets. Average dataset training size was 54,593 (range: 300,575-6). All of the studies had different reporting structures, and only four studies had a form of cross-evaluation qualitatively (n=1) or quantitatively (n=3) Conclusions GANs can transform research and patient care. Standardised reporting and diverse dataset transparency are essential. Despite their creation needing computational expertise, it's vital for plastic surgeons to understand GAN development to fully leverage their potential in plastic surgery and related fields.

Nash’s Existence Theorem for Non-Compact Strategy Sets

In this paper, we apply the classical FKKM lemma to obtain the Ky Fan minimax inequality defined on nonempty non-compact convex subsets in reflexive Banach spaces, and then we apply it to game theory and obtain Nash’s existence theorem for non-compact strategy sets, which can be regarded as a new, simple but interesting application of the FKKM lemma and the Ky Fan minimax inequality, and we can also present another proof about the famous John von Neumann’s existence theorem in two-player zero-sum games. Due to the results of Li, Shi and Chang, the coerciveness in the conclusion can be replaced with the P.S. or G.P.S. conditions.

Time-optimal surveillance between two differential drive robots with a limited field of view

Keeping an intelligent agent under surveillance with an autonomous robot as it travels in the environment is one of the essential tasks in robotics. This work addresses a pursuit-evasion surveillance problem between two Differential Drive Robots moving on a plane without obstacles. One of them, the pursuer, is equipped with a limited field-of-view sensor and aims to maintain the other robot (evader) inside its detection region for as much time as possible. On the contrary, the evader wants to escape as soon as possible. Unlike prior studies that address the same problem, based on heuristic approaches, we frame it as a zero-sum differential game, and we use differential game theory to find a solution with theoretical guarantees. In particular, we compute the players' time-optimal motion strategies to achieve their goals near the end of the game and provide analytical expressions describing them. These strategies are in Nash equilibrium, meaning that any unilateral deviation by a player from these strategies does not provide such player benefit toward its goal. Our analysis exhibits the existence of a Transition Surface in which the evader switches its controls. We also determine the game's winner based on the players' initial configurations and velocities.

International Counter-Trafficking: A Zero-Sum Game?—Introduction to the Special Issue

“Human trafficking” is widely described as a matter of concern [...]

Strategy investments in zero-sum games

We propose an extension of two-player zero-sum games, where one player may select available actions for themselves and the opponent, subject to a budget constraint. We present a mixed-integer linear programming (MILP) formulation for the problem, provide analytical results regarding its solution, and discuss applications in the security and advertising domains. Our computational experiments demonstrate that heuristic approaches, on average, yield suboptimal solutions with at least a 20% relative gap with those obtained by the MILP formulation.

Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density.

ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.