Zero-sum Game Research Articles

Is the decline of war a delusion? The long peace phenomenon and the modernization peace – the explanation that refutes or subsumes all others

ABSTRACT The wars in Ukraine and the Middle East, and the China challenge, revive the question of whether the world is becoming more peaceful. Realists’ claim that we told you so compares oranges with cabbage. Today’s world is divided into a “zone of peace”, encompassing all the developed countries, and a “zone of war”, comprising less developed countries. Within the former, interstate wars, civil wars, and the “security dilemma” itself have all disappeared. The Long Peace since 1945 is widely attributed to nuclear deterrence. However, the sharp decrease in war had begun during the 19th century. The effect of industrialization is the greatest lacuna in IR theory. The Malthusian Trap that plagued premodern societies has been broken. Wealth is no longer finite and a zero-sum game. This transformation has made democracies as well as nondemocracies fight much less, and has sharply increased international trade. It underlies both the democratic/liberal and capitalist/trade interdependence peace.

Breaking the Metric Voting Distortion Barrier

We consider the following well-studied problem of metric distortion in social choice. Suppose that we have an election with n voters and m candidates located in a shared metric space. We would like to design a voting rule that chooses a candidate whose average distance to the voters is small. However, instead of having direct access to the distances in the metric space, the voting rule obtains, from each voter, a ranked list of the candidates in order of distance. Can we design a rule that, regardless of the election instance and underlying metric space, chooses a candidate whose cost differs from the true optimum by only a small factor (known as the distortion )? A long line of work culminated in finding optimal deterministic voting rules with metric distortion 3. However, for randomized voting rules, there is still a significant gap in our understanding: even though the best lower bound is substantially lower at 2.112, the best upper bound is still 3, which is attained even by simple rules such as Random Dictatorship. Finding a randomized rule that guarantees distortion 3 - ɛ for some constant ɛ has been a major challenge in computational social choice, as prevalent approaches to designing voting rules are known to be insufficient. In particular, such a voting rule must use information beyond aggregate comparisons between pairs of candidates, and cannot only assign positive probability to candidates that are voters’ top choices. In this work, we give a rule that guarantees distortion less than 2.753. To do so, we study a handful of voting rules that are new to the problem. One is Maximal Lotteries , a rule based on the Nash equilibrium of a natural zero-sum game that dates back to the 1960s. The others are novel rules that can be thought of as hybrids of Random Dictatorship and the Copeland rule. None of these rules can beat distortion 3 alone; however, a careful randomization between Maximal Lotteries and any of the novel rules can.

Who will win the competitive game between China and United States?

As the world’s two great powers, China and the United States have developed a relationship that strongly affects the rest of the world. In the present study, we compare the benefits and drawbacks of the relationship between China and the United States with the goal of finding ways to avoid this kind of zero-sum game from four perspectives: political, cultural, economic, and military. The governments of China and the United States should first and foremost work on solving their domestic problems rather than seeking a confrontation. Although competition between individuals, industries, regions, and governments is a major force that drives the development and evolution of human society, competitors must avoid dangerous zero-sum games and instead promote cooperation or coopetition. One approach would be to develop a globalized federation of nations that will work to achieve a “common world of harmony and differences”.

Distributed filtering with time-varying topology: A temporal-difference learning approach in dual games

This study aims to develop a dual games (DGs) mechanism and implement a temporal difference learning (TDL) approach to address distributed filter design while considering network-induced time-varying topology from individual optimality and global equilibrium perspectives. In a detailed analysis, each filtering node (FN) treats its individual filtering action and exogenous disturbance as opposing elements, striving to determine the optimal policy while accounting for the worst-case scenario. This competition between FN and the disturbance culminates in a zero-sum game. Simultaneously, FN collaborates effectively with its neighbors to achieve consensus estimation, giving rise to a non-zero-sum game. Notably, an error-based filtering action is built to solve challenges posed by DGs. Ultimately, each FN attains its estimation at a minimum cost, and the entire distributed filtering network achieves the consensus estimation at a Nash equilibrium. Moreover, the transition probability correlation matrices (TPCMs) of the time-varying topology are obtained through direct observation of multi-episodes of topological transition trajectories. It has been proved that with a sufficiently ample number of episodes, TPCMs converge to their optimal values when TPs are known as apriori. Finally, a numerical example and an aero-engine system are presented to illustrate the effectiveness and practical potential of the proposed method.

Identifying influential nodes in social networks from the perspective of attack-defense game.

Influence spread analysis, a critical component of social network studies, focuses on the patterns and effects of information dissemination among interconnected entities. The core of influence spread analysis is to identify influential nodes that involve two distinct aspects: influence maximization (IM) and influence blocking maximization (IBM). However, when IM and IBM occur simultaneously, identifying influential nodes becomes an intricate decision-making challenge. This study addresses identifying influential nodes in social networks through an attack-defense game perspective, where an attacker maximizes influence and a defender minimizes it. We first develop a two-player static zero-sum game model considering resource constraints. Based on the equilibrium strategy of this game, we redefine the concept of influential nodes from various viewpoints. Extensive experiments on synthetic and real-world networks show that, in most cases, the defender preferentially defends critical nodes, while the attacker adopts the decentralized strategy. Only when resources are unevenly matched do both players tend to adopt centralized strategies. This study expands the connotation of influential nodes and provides a novel paradigm for the social network analysis with significant potential applications.

The Significance of Economic Complexity and Renewable Energy for Decarbonization in Eastern European Countries

Emerging states’ path to enhancing the welfare of their citizens has been strongly accompanied by environmental degradation; climate change effects often abrogate their economic results. This zero-sum game must change, and environmental concerns should be considered when the development of a country is discussed and assessed. In this sense, this study’s objective is to analyze the impact of economic complexity and renewable energy consumption in the presence of economic growth and urbanization in selected emerging European countries from 1995 to 2021. We used a multiple-methodologic approach to highlight the supportive effects of economic complexity and renewable energy consumption in mitigating carbon emissions. Furthermore, the effects of economic growth and urbanization were emphasized by applying the cointegration regression (CCR), fully modified OLS, and dynamic OLS (FMOLS–DOLS) approaches. Additionally, we used Driscoll–Kraay estimation regression to test the robustness of our results. The results reveal the beneficial role of renewable energy consumption and economic complexity in the decarbonization process of selected countries. Furthermore, the study highlighted the detrimental influence of urbanization and economic growth, which were feasible considering the emerging status of the countries included in the panel.

The neuropolitical imaginaries of cognitive warfare

The concept of cognitive warfare is currently gaining ground in the policy discussion and in academic research as a way of conceptualizing the ‘weaponization of the neurosciences’. Introducing the Science and Technology Studies-inspired concept of ‘neuropolitical imaginaries’ and assessing discussions on cognitive warfare launched by the NATO Innovation Hub in 2017, this article explores how the contemporary turn to the brain sciences in defense and security reimagines politics. The article argues that seeing the human mind as increasingly vulnerable to external interference redefines the nature of human agency by giving precedence to the skilful ‘cartographer’ employing neuroscientific techniques and methods for persuasion. This emerging vulnerability of the human mind reshapes security into a zero-sum game for ‘cognitive superiority’, making brain science scholars authorities in security. Finally, speaking to the literature on security expertise and science in security, the article argues that the envisaged arms race for cognitive superiority gives rise to a neurosecurity dilemma: as the neurosciences becomes entangled with security, neuroscientific practices simultaneously arise as a core vulnerability, making their work conditional upon compliance with security practices.

Are pragmatism and ethical protections in clinical trials a zero-sum game?

Randomized controlled trials with pragmatic intent aim to generate evidence that directly informs clinical decisions. Some have argued that the ethical protection of informed consent can be in tension with the goals of pragmatism. But the impact of other ethical protections on trial pragmatism has yet to be explored. In this article, we analyze the relationship between additional ethical protections for vulnerable participants and the degree of pragmatism within the PRagmatic Explanatory Continuum Indicator Summary-2 (PRECIS-2) domains of trial design. We analyze three example trials with pragmatic intent that include vulnerable participants. The relationship between ethical protections and trial pragmatism is complex. In some cases, additional ethical protections for vulnerable participants can promote the pragmatism of some of the PRECIS-2 domains of trial design. When designing trials with pragmatic intent, researchers ought to look for opportunities wherein ethical protections enhance the degree of pragmatism.

Strategic safeguarding: A game theoretic approach for analyzing attacker-defender behavior in DNN backdoors

Deep neural networks (DNNs) are fundamental to modern applications like face recognition and autonomous driving. However, their security is a significant concern due to various integrity risks, such as backdoor attacks. In these attacks, compromised training data introduce malicious behaviors into the DNN, which can be exploited during inference or deployment. This paper presents a novel game-theoretic approach to model the interactions between an attacker and a defender in the context of a DNN backdoor attack. The contribution of this approach is multifaceted. First, it models the interaction between the attacker and the defender using a game-theoretic framework. Second, it designs a utility function that captures the objectives of both parties, integrating clean data accuracy and attack success rate. Third, it reduces the game model to a two-player zero-sum game, allowing for the identification of Nash equilibrium points through linear programming and a thorough analysis of equilibrium strategies. Additionally, the framework provides varying levels of flexibility regarding the control afforded to each player, thereby representing a range of real-world scenarios. Through extensive numerical simulations, the paper demonstrates the validity of the proposed framework and identifies insightful equilibrium points that guide both players in following their optimal strategies under different assumptions. The results indicate that fully using attack or defense capabilities is not always the optimal strategy for either party. Instead, attackers must balance inducing errors and minimizing the information conveyed to the defender, while defenders should focus on minimizing attack risks while preserving benign sample performance. These findings underscore the effectiveness and versatility of the proposed approach, showcasing optimal strategies across different game scenarios and highlighting its potential to enhance DNN security against backdoor attacks.

A win–win strategy for environmental governance – role of exogenous personalised gains

ABSTRACT Cooperation on environmental issues is often perceived as a zero-sum game, where individual gains must be sacrificed for collective benefits. This paper offers a the oretical solution that balances individual and collective benefits to foster joint environmental action. Drawing on game theory and insights from the inter-municipal cooperation (IMC) literature, the paper explores how to solve environmental problems that present a collective action dilemma. It aligns with proponents of gain framing for environmental action and introduces the concept of ‘exogenous personalised gains’ in driving environmental action. It demonstrates that if the right exogenous personalised gains are leveraged, joint environmental actions are more likely.

Approximate solution of a zero-sum linear-quadratic differential game by the auxiliary parameter method: analytical/numerical study

ABSTRACT A zero-sum finite horizon linear-quadratic differential game is considered. First, the terminal-value problem for the game-theoretic Riccati matrix differential equation, associated with the considered game by the solvability conditions, is analysed. This problem may not have the solution in the entire time-interval of the game's duration. Using the method of auxiliary parameter, a sufficient condition (in the terms of the game's data) for the existence of the solution to the aforementioned terminal-value problem in the entire time-interval of the game's duration is derived. An approximate analytical solution to this problem also is obtained as a partial sum of some infinite series of functions arising in the method of auxiliary parameter. Based on this approximate solution, suboptimal state-feedback controls of the players are formally designed and justified. It is shown that the pair of these controls constitutes an approximate-saddle point in the considered game. The theoretical results of the article are illustrated by their application to approximate solution of the problem of pursuit-evasion engagement between two flying vehicles.

Unsupervised Representation Learning using Wasserstein Generative Adversarial Network

In recent years, representational learning has attracted considerable attention. However, unsupervised representation learning has received less attention compared to supervised representation learning. This paper introduces a combination of a deep neural network (DNN) and a generative adversarial network (GAN) that can learn features through unsupervised learning. Essentially, the Generative Adversarial Network (GAN) is a deep learning architecture that engages two neural networks in a framework similar to a zero-sum game. Generating new, synthetic data that resembles a known data distribution is the aim of GANs. In June 2014, Ian Goodfellow and associates first developed the idea of Generative Adversarial Network (GAN). The research used a new type of GAN model which is called Wasserstein GAN. There are some distinct differences between traditional GAN and Wasserstein GAN. This paper highlights the differences and benefits of using Wasserstein GAN, as well as the architecture of Wasserstein GAN. This study trained the model on an image dataset to extract features, and subsequently tested it on another dataset, demonstrating that the GAN model learns a hierarchy of representation from object parts in the discriminator. The purpose of this paper is to use unsupervised learning like Convolutional Neural Network (CNN) and Wasserstein Generative Adversarial Network (WGAN) for feature extraction from unlabeled dataset.

Mixed-Zero-Sum-Game-Based Memory Event-Triggered Cooperative Control of Heterogeneous MASs Against DoS Attacks.

This article studies the problem of memory event-triggered cooperative adaptive control of heterogeneous nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks based on the multiplayer mixed zero-sum (ZS) game strategy. First, a neural-network-based reinforcement learning scheme is structured to obtain the Nash equilibrium solution of the proposed multiplayer mixed ZS game scheme. Then, a memory-based event-triggered mechanism considering the historical data is proposed. This effectively avoids incorrect triggering information caused by unknown external factors. Moreover, thanks to the idea of switching topology, the mixed ZS game problem under the influence of node-based DoS attacks is solved efficiently. In accordance with the Lyapunov stability theory, it is proved that all signals of heterogeneous MASs are bounded, all heterogeneous followers can track the trajectory of the leader during the no-attack period, the attacked follower can achieve stabilization control during the attack period, and the remaining nonattacked followers can achieve cooperative control during the attack period. Finally, the effectiveness of the designed memory-event-triggered-based mixed ZS game cooperative control strategy is tested by the given simulation results.

Addressing barriers to big data implementation in sustainable smart cities: Improved zero-sum grey game and grey best-worst method

The optimization of sustainable smart cities is an essential endeavor in modern urban development, aiming to enhance the quality of life for citizens while minimizing environmental impacts. Big data plays a critical role in achieving these goals by enabling the collection, analysis, and utilization of vast amounts of information to make informed decisions. However, implementing big data in smart cities faces significant barriers, including data-sharing challenges, technical limitations, and organizational non-cooperation. Addressing these barriers is crucial for the successful deployment of smart city initiatives. We propose a novel approach to tackle these challenges using the Improved Zero-Sum Grey Game (IZSGG) theory and the Grey Best-Worst Method (G-BWM). This method comprehensively analyzes the risks and uncertainties associated with big data implementation in smart cities. By modeling the interactions between different stakeholders and their competing interests, IZSGG theory provides a framework to identify optimal strategies for data management. The G-BWM further refines these strategies by evaluating and prioritizing the various factors influencing big data utilization. Our findings reveal that the worst-case scenario for a smart city involves the simultaneous occurrence of several risks, all of which have positive values, indicating their potential to significantly disrupt smart city operations. The specific risks identified include: the sharing of data and information, the collection and recording of data, technical limitations and challenges associated with technology, the non-cooperation of organizations, and issues related to the interpretation of complex information. The technical barrier is the most significant with a weight of w(T)=0.6152, indicating its critical role compared to other barriers. Within this category, the sub-barrier of technical and technological constraints is particularly critical, with a weight of 0.39267375.

Solving MADM Problems based on Matrix Games with a New Defuzzification Method for Triangular Intuitionistic Fuzzy Numbers

Abstract: The paper discusses about a new defuzzification method called the Comprehensive Li-Samuel ranking for Triangular Intuitionistic Fuzzy Numbers (TrIFNs) which is improved from the Li-Samuel ranking method associated with membership function and Li-Samuel ranking method associated with non-membership function. The Comprehensive Li-Samuel ranking for TrIFNs is utilised to derive the weights for the Multiple Attribute Decision Making (MADM) problems under TrIFN. The MADM problem is solved based on two-person zero-sum game which is converted into a pair of LPP by using Comprehensive Li-Samuel ranking. The process of transforming decision matrix into a matrix game and deriving decision maker’s and attribute weights from the matrix game are discussed. Numerical illustration is given to justify the viability and effectiveness of the proposed method and comparisons are made with existing ranking methods. The comparison study reveals that the proposed method provides the best maximum optimal solution for the decision problem than the existing methods

An expert system of recommendations for combating cyber threats using CVSS metrics and game theory

This study is focused on the creation of an expert system for generating recommendations on cyber security. The developed expert system uses a game-theoretic model as a inference engine to transform expert knowledge into recommendations for end-users, who may be chief IT security officers (CISOs), system administrators, or cyber security engineers. Expert knowledge is presented in the form of an estimate of the base group of CVSS metrics - Common Vulnerability Score System, for each type of attack and adjusted values of CVSS in the case that the counterattack strategy is applied. Given a set of attacks and a base of expert attack knowledge, the system generates a game matrix of zero-sum game with a cybercriminal and a cyberdefense expert as players. The inference engine of the expert system is a game-theoretic model responsible for solving the game using the Brown-Robinson iterative method and generating cyber protection recommendations. An experiment was conducted on the convergence of the BrownRobinson algorithm on the 2022 vulnerability dataset from the Cybersecurity and Infrastructure Security Agency database, as a result of which it was determined that the convergence of the algorithm for solving the matrix game is achieved at a number of iterations of 1000. As a result of the work, expert system was designed and implemented along with the Web interface, which provides input by experts of CVSS level assessments of collected threats, threats countermeasures and output of recommendations for combating cyber threats

Zero-sum games subject to uncertain stochastic noncausal systems considering polynomial control functions

An uncertain stochastic noncausal system (USNS) is an uncertain stochastic singular system that is expected to be regular but not impulse-free. This study investigates zero-sum games (ZSGs) under the constraint of nonlinear uncertain stochastic noncausal systems (USNSs) considering polynomial control functions. Firstly, a method is introduced to convert USNSs into subsystems, including forward uncertain stochastic difference equations as well as backward uncertain stochastic difference equations. Equilibrium equations are then derived to determine the saddle-point equilibrium solution of the zero-sum game (ZSG) for USNSs. Subsequently, a unified framework is developed to find the saddle-point equilibrium and equilibrium value of the ZSG. Additionally, a numerical example and an analysis of the treatment of industrial wastewater are provided to demonstrate the effectiveness of the proposed framework.

Towards coordinating self-healing instances: Policy-based and non-cooperative game theory-based approaches with location awareness

Self-healing is an essential functionality in Self-Organizing cellular Network (SON). It aims to ensure service continuity by detecting, diagnosing, and compensating network outage after triggering appropriate Cell Outage Compensation (COC) functions according to the outage case. The role of self-healing is increasingly become indispensable, especially in high density network as in 5 G and beyond, in order to maintain the availability and retainability of mobile service and save revenues. However, the essence of COC entails modifications of different Network Control Parameters (NCP) which are under control of SON Functions (SONF) that are related to other self-x functionalities. In addition, it can request different types of compensation functions according to the outage case. Moreover, it requires to harmonize the objectives of the requested stand-alone SONFs over the involved Candidate Cells (CC) in order to re-build a consistent coverage model. Thus, the need for self-coordination is mandatory to guarantee conflict-free outage compensation procedure. In this paper, we propose a novel integrated coordination scheme in order to coordinate Antenna Tilt (AT)-based and Transmission Power (TXP)-based COC functions. Beside their primary targets of conflict avoidance and resolution, we prove that our location-aware coordination mechanisms, which are based on policies and Non-Cooperative Zero-Sum Game (NCZSG) theory, can collaboratively guide greedy stand-alone single-objective COC functions to reach a stable coverage model. The coordination is done even when there is no prior knowledge of the environment or the compensatory algorithms themselves. The choice of optimal Network Control Parameters Values (NCV) is determined according to the function after the coordinator's verification.

Coopetition strategies in a two-stage, multi-agent supply chain under hybrid carbon trading mechanisms

ABSTRACT Managing a multi-agent supply chain within a hybrid carbon trading framework, which integrates Certified Emission Reductions (CERs) and Carbon Quota Trading (CQT), presents a significant challenge. This complexity is further amplified by the interplay of competition and cooperation among agents. Motivated by this, we develop a biform game-based cooperative mechanism for a two-stage supply chain that includes a high-emission manufacturer, a negative-emission manufacture and a downstream retailer. This mechanism is designed to encapsulate both the non-cooperative and cooperative game elements. The former features a product competition game among the manufacturers and retailer, setting the stage for the cooperative game without directly yielding equilibrium solutions. The latter involves a cost-sharing agreement for the CER project's initial investment, informed by various coalitional zero-sum games. Our analytical findings, corroborated by numerical simulations, reveal that the biform game coordination mechanism significantly enhances the volume of CERs traded and consumer surplus, compared to a non-cooperative scenario. It effectively aligns the collaborative efforts of all agents within the supply chain. This research contributes substantially to the literature on coordinating multi-stage, multi-agent supply chains, and the strategic deployment of emission reduction initiatives in supply chains. It also offers valuable managerial insights for the design of government regulations in carbon markets.

A Two-Person Zero-Sum Game Approach for a Retirement Decision with Borrowing Constraints

A Two-Person Zero-Sum Game Approach for a Retirement Decision with Borrowing Constraints