Zero-sum Game Research Articles

Robust neural networks trajectory tracking control with zero-sum game thought for unmanned surface vehicle under marine ranching cruise task

Zero-sum game control of unmanned aerial vehicle confrontation via reinforcement learning

Mather Sets of a Cascade Generated by the FTRL Algorithm of a Two-Agent Zero-Sum Game with Mixed Strategies

ABSTRACT Researching agricultural transitions in India involves reconceptualising agriculture through a range of farming practices and the emerging meanings of sustainability. Most existing studies in India focus on a macro-level analysis of agrarian transition, overlooking the farm-level decision-making processes and practices of change [Bharucha, Z. P., S. B. Mitjans, and J. Pretty. 2020. “Towards Redesign at Scale through Zero Budget Natural Farming in Andhra Pradesh, India.” International Journal of Agricultural Sustainability 18 (1): 1–20]. This paper investigates farmers’ perspectives and experiences of moving towards alternative approaches to agriculture in Haryana villages. During 11 months of fieldwork, I collected data using in-depth interviews and group discussions. By using a multifunctional agriculture framework [Wilson, G. A. 2007. Multifunctional Agriculture: A Transition Theory Perspective. Wallingford: CAB International; Wilson, G. A. 2008. “Global Multifunctional Agriculture: Transitional Convergence between North and South or Zero-sum Game?” International Journal of Agricultural Sustainability 6 (1): 3–21] to formulate the emerging farm typologies in these villages, the paper argues: first, to use farmers’ perspectives to study transition processes in a given socio-economic context; second, to take seriously the diverse visions of sustainability while studying alternative agricultural practices in rural India. Studying farmers’ specific attributes of farms and farming practices is crucial to conceptualising agricultural transitions in diverse socio-cultural contexts in India.

The integration of high-precision vehicle-mounted visual sensors has revolutionized the field of intelligent suspension systems, enabling the implementation of preview control strategies that significantly enhance ride comfort and safety performance in vehicle platoons. Building on this advancement, this study presents a data-driven preview control framework for active suspension systems tailored to heterogeneous vehicle platoons. The proposed framework leverages a vehicle-to-vehicle (V2V) communication topology to incorporate comprehensive road preview information. Initially, a dynamic model of the active suspension system is formulated, encompassing inter-vehicle-distance preview, wheelbase preview, and look-ahead preview mechanisms. Subsequently, the preview H ∞ control problem is recast as a multi-player zero-sum game to address the interactions within the platoon. To reduce the calibration and design costs associated with the control scheme, a model-free Q-learning algorithm is presented. This approach determines the optimal control policy for the system without requiring prior knowledge of the output matrices, while simultaneously ensuring operational safety and ride comfort. Finally, numerical simulations and comparative analyses are conducted to validate the proposed control scheme. The results indicate that, under various road excitation scenarios, the proposed platoon preview control framework consistently outperforms traditional passive suspension systems and non-preview-based independent control schemes. Furthermore, the performance exhibits a strong correlation with the amount of available preview information. Notably, the scheme achieves optimal control performance in constant-speed platooning scenarios.

Abstract This article examines the persistence of common-sense conceptions of race and ethnic identity and the role they play within contemporary politics in the UK. Drawing on the work of Claire Alexander and Rogers Brubaker, the article reflects on why we continue to see ethnic identity as something fixed and static, and why this persists despite theoretical developments which have drawn attention to identity’s fluidity and contingency. Using a conjunctural analysis, the article examines how such conceptions of ethnic identity intersect with two other aspects of the current conjuncture: firstly, neoliberal individualism; and secondly, culture war politics. Consistent with neoliberal individualism, it is assumed that groups compete with each other for recognition and success, mostly within the framework of nation states. Within the divisive politics of culture wars, competition and fixed identities harden into a zero-sum game: greater recognition and rights for one group becomes, by definition, a loss of rights and recognition for another. Solidarity and collectivity become inconceivable, and international politics—particularly international solidarity—becomes unrecognisable within this framework. Ethnic disparity reports are considered, and how these draw attention to how racism is experienced by different groups, but in ways that make it difficult to consider what might be shared. The article then considers two examples from contemporary politics. First of these is a recent controversy surrounding Diane Abbott MP and her claims that racism experienced by those racialised as Black is different from those who can pass for white. Secondly, the article explores reactions to independent candidates in the 2024 election who called for a ceasefire in Gaza. These reactions framed the situation as sectarian politics relating to the ‘Muslim vote’. In both examples, where fixed identities, competitive individualism and zero-sum games are mobilised to narrow the scope of debate, misrepresent people and situations and exclude important political questions from discussion, especially international politics. The article ends by reflecting on the continued appeal of fixed identities, and also what narrow discussions about race can exclude. It calls for a reconsideration of anti-racism to move beyond these impasses and categories.

The Horn of Africa has emerged as one of the world’s most strategically contested regions since 2000, with unprecedented militarisation featuring 15 foreign military bases established by 11 external powers, hosting over 10,500 foreign troops and representing $4.3 billion in military infrastructure investment. This article examines the intensifying competition among the United States, China, Russia, and Middle Eastern powers and analyses its multifaceted impact on Ethiopia's national interests through analysis of spatial distribution patterns, purpose classification networks, and geopolitical alignments. The research reveals that 67% of foreign bases and 86% of foreign forces are positioned within 500 kilometres of Ethiopia's borders, creating concentric rings of military presence around Africa's second-most populous nation that hosts no foreign bases itself. Purpose classification network analysis demonstrates divergent yet overlapping objectives among external powers: counter-terrorism operations (33% of bases), anti-piracy missions (27%), regional conflict interventions (20%), and strategic power projection (13%), each creating distinct implications for Ethiopian security and development efforts. Through systematic examination of military deployments, economic investments, and diplomatic relationships, the study demonstrates that while external power rivalry offers Ethiopia unprecedented opportunities for infrastructure development, economic advancement, and diplomatic leverage, it fundamentally alters the regional security architecture and poses significant challenges to sovereignty, regional stability, and strategic autonomy. Ethiopia faces the complex challenge of navigating between competing external powers while maintaining its traditional non-aligned foreign policy stance, creating sovereignty challenges, intelligence vulnerabilities, and risks of conflict spillover. The analysis identifies four strategic response options-reinforced non-alignment, selective multi-alignment, regional leadership, and issue-based coalition building. Finally, the paper concludes that Ethiopia’s ability to protect and advance its national interests will depend on developing a sophisticated foreign policy framework that transforms regional competition from a zero-sum game into opportunities for multilateral cooperation and development, with broader implications for how developing countries navigate great power competition in an increasingly multipolar world.

Abstract The manipulation of the Impact Factor (IF) through editorial decisions inflating self-citations is a growing concern in academic publishing. This work introduces an agent-based model simulating journals as rational agents competing for IF ranking positions in a zero-sum game, generating synthetic citation networks that reproduce key patterns such as the Matthew Effect and the specialization of manipulation strategies across interconnected disciplines. By comparing IF calculation policies with and without self-citations, statistical analysis of simulation results demonstrates that excluding self-citations significantly reduces incentives for manipulative tactics, offering computational evidence for developing policies that promote scientific integrity within the academic publishing ecosystem.

This article posits that the context of extreme population loss experienced by legacy cities presents an especially fraught challenge to interlocal collaboration and regionalism. The article fuses political science, public administration, and planning perspectives to develop hypotheses around how decline shapes the dynamics of interlocal collaboration for service provision and regional planning. We theorize that sustained decline heightens competition for scarce resources and produces more zero-sum games among local governments. Focusing on one legacy city-region in the United States—Northeast Ohio—we examine several hypotheses with respect to collaborative service provision using quantitative modeling of interlocal financial transfers. We also use an original survey of mayors and managers in one Northeast Ohio county to describe and analyze municipal engagement in collaborative regional planning. We then lay out a research agenda on these topics and a call for further study by scholars of urban politics, public administration, and planning.

Continuous-Time Zero-Sum Games for Markov Decision Processes Under the Risk-Sensitive First Passage Discounted Cost Criterion

We investigate computationally the hyperfine couplings (HFCs) and the consequent paramagnetic nuclear magnetic resonance (pNMR) chemical shifts of a recently synthesised doublet Fe(V) bis(imido) complex. Using conventional global hybrid density-functional theory (DFT) methods with varying exact-exchange admixture, a significant spin contamination problem is observed, leading to a massive spin-density spill-over to the strongly bound imido ligands and to the BH2 group of the carbene framework. As a result, the computed paramagnetic NMR shifts, which are based on a combination of ab initio calculated g-tensor, DFT-calculated orbital shielding and DFT-based HFCs, disagree strongly with the available experimental 1H NMR chemical shifts and predict unrealistic 13C shifts in the spill-over region. While semi-local functionals like PBE do not suffer from the spin-contamination problem, their inherent delocalisation errors also lead to a too spread-out spin-density distribution. We demonstrate that, by applying novel local hybrid and range-separated local hybrid functionals with correction terms for strong-correlation and/or delocalisation errors to the HFC computations, the spin contamination problem is significantly reduced, while keeping delocalisation errors small. This results in more realistic pNMR shifts obtained for this system, also when compared to data obtained using correlated ab initio HFCs. Problems with the use of a global hybrid functional are already observed at the level of the underlying optimised structure, and employing a semi-local functional in structure optimisation is found to improve the situation. With that, the combined ab initio/DFT method with the latest (range-separated) local hybrid functionals is seen to reasonably reproduce the 1H experiment and enable plausible predictions for the hitherto unreported 13C shifts in this challenging iron complex.

An uncertain stochastic dynamical system is a dynamical system incorporating both uncertain noise and random noise. This paper investigates two-person zero-sum games (TPZSGs) for uncertain stochastic discrete-time as well as continuous-time dynamical systems. The first work is to present recursive formulations for tackling a two-person zero-sum game (TPZSG) subject to uncertain stochastic discrete-time dynamical systems in terms of chance theory with Bellman's optimality principle. Then, the recursive formulations have been successfully implemented to treat the TPZSGs subject to linear, bilinear, and nonlinear uncertain stochastic discrete-time dynamical systems. Subsequently, optimality equations for a TPZSG subject to uncertain stochastic continuous-time dynamical systems are developed. The continuous-time TPZSG may be treated by the acquired optimality equations. For illustration, the optimality equations are utilized to solve a counterterrorism model that covers a government and a terrorist group. The equilibrium controls for the government and terrorist group, as well as their connections with the states of income and resources, are examined. These findings demonstrate that the uncertain stochastic TPZSG is an efficient technology for addressing a dynamic game considering both uncertain noise and random noise.

This article investigates the distributed online optimization problem in a zero-sum game between two distinct time-varying multiagent networks. At each iteration, the agents not only communicate with their neighbors but also gather information about agents in the opposing network through a time-varying network, assigning weights accordingly. Moreover, we consider quantized communication and bandit feedback mechanisms, with agents transmitting quantized information and adopting one-point estimators. At each iteration, agents make and submit decisions and then receive the cost function values near their decision points rather than the full cost function information. To guarantee the payoff of each network, we design an algorithm named quantized distributed online bandit optimization in two-network (QDOBO-TN). We use dynamic Nash equilibrium regret to measure the positive payoff discrepancy between the decision sequence produced by Algorithm QDOBO-TN and the Nash equilibrium sequence. Furthermore, we propose a multiepoch version of Algorithm QDOBO-TN. The regret bounds for both algorithms are sublinear with respect to the iteration count T. Finally, we conduct a series of simulation experiments that further validate the effectiveness of the algorithms.

Online social platform competition and rumor control in disaster scenarios: a zero-sum differential game approach with approximate dynamic programming

This study examines religious polarization in North Maluku, proposing moderated identity politics and a hybrid representation model to explain post-conflict electoral behavior. It highlights local leaders who strategically balance identity appeals with cross-group alliances, integrating structural and agential factors to advance electoral theory and offer a replicable model for mitigating identity-based conflict in plural Indonesian regions. Using a mixed-methods sequential explanatory design, quantitative data were first collected from 100 proportionally sampled respondents. Subsequently, in-depth qualitative interviews were conducted with 17 key informants. Data triangulation, comparing survey results with interview findings, ensured consistency and strengthened the validity of the research conclusions. The study presents four novel contribution findings. First, it challenges conventional religious voting, demonstrating Sherly Tjoanda’s Catholic victory in a Muslim-majority province, attributed to economic pragmatism, political legacy, and networks over religious affiliation. Second, it introduces the Hybrid Representation Model, combining development performance with a moderate religious figure. Third, it refines voter decision-making through Post-Conflict Electoral Rationality and welfare populism, illustrating how trauma fosters pragmatism. Finally, it develops Moderated Identity Politics, integrating local factors like Nahdlatul Ulama’s influence and conflict trauma to reduce polarization and promote electoral pragmatism. The 2024 North Maluku gubernatorial election, with the Sherly-Sarbin ticket’s victory, exemplified pragmatic considerations outweighing religious identity. This model outcome establishes Moderated Identity Politics that can depolarize elections by endorsing competence-based, cross-faith alliances, and prioritizes a competence-plus-credibility approach. In contexts with a dominant, moderate Islamic organization and where economic competition is not a zero-sum game.

The “Double Reduction” policy aims to alleviate the burdens of homework and tutoring and reduce the “zero-sum game” of students investing in study time during their regular schooling. However, during winter and summer vacations and online learning from home during the pandemic, students were removed from their regular school environment. Students who lack academic comparison targets may face the risk of decreased academic competitiveness due to weakened metacognitive monitoring. Whether the “Double Reduction” policy can maintain its effectiveness under home learning conditions remains an unsolved question. By analyzing survey data from six junior high schools in City J, Shandong Province, before and after the implementation of learning from home, this study concluded the following findings: first, extracurricular study time has no significant impact on the academic performance of students in regular schooling; second, both absolute and relative extracurricular study time can significantly improve the academic resilience of students learning from home; third, during home-based learning, students from middle socioeconomic status families benefit the most from extended extracurricular study time. Based on the research findings, the “double reduction” policy may decrease the academic competitiveness of students engaging in home-based learning during extended holidays. However, this effect does not apply under regular learning conditions. During periods of learning from home, students with relatively weaker academic foundations can effectively prevent academic decline by extending their study time, even if parents cannot provide adequate academic support. Conversely, students whose parents are most capable of providing support do not benefit from the extended study time.

In an era of increasing digital interconnectedness, the vulnerability of public spaces—or 'soft targets'—has expanded from the physical to the digital realm, giving rise to the complex phenomenon of the 'e-threat'. Traditional security paradigms are often ill-equipped to address these diffuse, data-driven menaces that exploit the convergence of our online and offline lives. This paper introduces a multi-faceted diagnostic model designed to navigate this evolving landscape. Our framework is built upon the critical triangulation of three interconnected planes: a theoreticalplane that conceptualizes the nature of modern threats; an empirical plane that leverages artificial intelligence and advanced data analytics for proactive detection; and a crucial normative plane that embeds ethical principles, human rights, and legal frameworks at the core of any technological application. By analysing the tension between technological capabilities and societal values — drawing on real-world initiatives like the APPRAISE Project with MARPLE — this work argues that effective security is not a zero-sum game. Ultimately, the model demonstrates that safeguarding soft targets against digital-age menaces requires a holistic synergy between technological innovation and an unwavering commitment to democratic governance and the Sustainable Development Goals, ensuring a future that is both safe and free.

The tethered space net robot offers an effective solution for active space debris removal due to its large capture envelope. However, most existing studies overlook the evasive behavior of non-cooperative targets. To address this, we model an orbital pursuit–evasion game involving a tethered net and propose a game theory-based leader–follower tracking control strategy. In this framework, a virtual leader—defined as the geometric center of four followers—engages in a zero-sum game with the evader. An adaptive dynamic programming method is employed to handle input saturation and compute the Nash Equilibrium strategy. In the follower formation tracking phase, a synchronous distributed model predictive control approach is proposed to update all followers’ control simultaneously, ensuring accurate tracking while meeting safety constraints. The feasibility and stability of the proposed method are theoretically analyzed. Additionally, a body-fixed reference frame is introduced to reduce the capture angle. Simulation results show that the proposed strategy successfully captures the target and outperforms existing methods in both formation keeping and control efficiency.

Abstract In this note we extend the result of von Stengel and Koller (Games Econ Behav 21:309–321, 1997) to infinite games. Specifically, we show that every infinite zero-sum game between a team and an adversary admits a pure-strategy team-maxmin equilibrium when (i) the strategy sets are compact, convex subsets of (possibly infinite-dimensional) topological vector spaces, and (ii) the payoff function is bounded, upper-semicontinuous on the team’s strategy-profile set and concave in each team member’s strategy, while being lower-semicontinuous and convex in the adversary’s strategy. Because the vector spaces may have arbitrary dimension, we obtain the following corollary: a mixed-strategy team-maxmin equilibrium exists whenever (i) the strategy sets are compact subsets of metric spaces, and (ii) the payoff function is bounded, measurable, upper-semicontinuous on the team’s strategy-profile set, and lower-semicontinuous on the adversary’s strategy set. The proof employs Sion’s minimax theorem.

IntroductionThis study investigates the long-standing Research Topic of the development of the space concept in children using a competitive, interactive, online, zero-sum game that required players, taking turns with a computer player, to use monochromatic electronic paint to complete coloring in places until an entire 10 × 10 grid was filled.MethodsChildren were 4- to 5-year-olds (n = 26), 6- to 7-year-olds (n = 32), 8- to 10-year-olds (n = 52), as well as adults (n = 48). The total sample consisted of 79 human and 79 machine players (N = 158). The human players colored in places on the grid in yellow, and the machine player in green. While human players could follow their own spatial heuristics, the machine system player was programmed to randomly color in anywhere in the grid. Neighboring places could visually merge into pathways or areas.ResultsChildren explored the array somewhat less than adults, but both explored it less than the machine, which randomly colored in places across the entire array. Both children and adults as well as the machine players created one large area and many smaller ones. Their one large area left a large swath of the spatial array empty. This space was then filled in by the machine player at random places, which merged into a slightly smaller large area or many larger small areas.DiscussionHence, a similar outcome was achieved regardless of whether spatial concepts or random spatial explorations were devised. The use of spatial heuristics was demonstrated with correlational analyses, where long pathways and short-distance moves were significantly correlated with the largest area, but not in their machine opponents.