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Keywords = empirical game theory

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32 pages, 1540 KB  
Article
Multi-Agent Interaction and Stability Conditions of Disruptive Innovation by AI Firms in Innovation Ecosystems
by Han Zhang, Hua Zou and Xin Wen
Systems 2026, 14(5), 568; https://doi.org/10.3390/systems14050568 - 16 May 2026
Viewed by 113
Abstract
Technology enterprises are leveraging artificial intelligence (AI) to foster disruptive innovation, aiming to seize first-mover advantages in technological catch-up and strategic transformation. Most existing studies adopt static research methods such as empirical analysis to explore corporate disruptive innovation from the dimensions of technology, [...] Read more.
Technology enterprises are leveraging artificial intelligence (AI) to foster disruptive innovation, aiming to seize first-mover advantages in technological catch-up and strategic transformation. Most existing studies adopt static research methods such as empirical analysis to explore corporate disruptive innovation from the dimensions of technology, market, organization and value creation. However, few scholars dynamically investigate the impacts of multi-stakeholder interactions on the disruptive innovation of AI enterprises from the perspective of innovation ecosystem by employing evolutionary game theory. Against this backdrop, this paper adopts the evolutionary game approach to explore how the bounded rational strategic interactions among AI enterprises, incumbent enterprises and governments in the innovation ecosystem affect the evolutionary dynamics of AI enterprises’ disruptive innovation behaviors. It also examines under what conditions of benefits, costs, risks and policies the system can evolve toward a stable strategic equilibrium. The findings reveal that the sustainable advancement of disruptive innovation by AI enterprises is not merely driven by the unilateral willingness of individual firms. Instead, it is jointly shaped by the innovation investment of AI enterprises, cooperative responses of incumbent enterprises, and regulatory and supportive policies of governments, as well as comprehensively influenced by base benefits, R&D investment pressure, technology spillover effects and niche competition risks. This research provides theoretical references for improving the innovation governance and policy support system of the AI industry. Future research can further analyze the influence of strategic interactions among more heterogeneous stakeholders on the evolutionary process of disruptive innovation of AI enterprises. Full article
(This article belongs to the Section Artificial Intelligence and Digital Systems Engineering)
55 pages, 2971 KB  
Article
On Least Squares Approximations of Shapley Values and Applications to Interpretable Machine Learning
by Tim Pollmann and Jochen Staudacher
Foundations 2026, 6(2), 18; https://doi.org/10.3390/foundations6020018 - 11 May 2026
Viewed by 172
Abstract
The Shapley value is the predominant point-valued solution concept in cooperative game theory and has recently become a foundational method in interpretable machine learning. In this domain, a prevailing strategy for circumventing the computational intractability of exact Shapley values is to approximate them [...] Read more.
The Shapley value is the predominant point-valued solution concept in cooperative game theory and has recently become a foundational method in interpretable machine learning. In this domain, a prevailing strategy for circumventing the computational intractability of exact Shapley values is to approximate them via a weighted least squares optimization framework. In this paper, we investigate an existing algorithmic framework for weighted least squares Shapley approximation, assessing its feasibility for feature attribution. Methodologically, we conduct a theoretical variance analysis within a Monte Carlo sampling framework, investigate an approach for sample reuse across strata, and establish a relation to Unbiased KernelSHAP. Our analysis reveals three main findings: (i) a structural equivalence between least squares sampling and Unbiased KernelSHAP; (ii) the non-zero covariance between sampled coalitions introduced by reusing samples across strata in one of the existing least squares-based approaches; and (iii) the absence of a universally optimal sampling strategy across tasks. We validate these results empirically on several cooperative games and practical machine learning problems. Full article
(This article belongs to the Section Mathematical Sciences)
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19 pages, 1710 KB  
Article
Research on Comprehensive Evaluation Model of Virtual Power Plant Operational Benefits Based on DEMATEL-CRITIC-EDAS
by Ranran Li, Hecheng Yuan, Jianing Zhang, Qiushuang Li, Jiarui Li, Wanying Li and Zhengsen Ji
Processes 2026, 14(10), 1545; https://doi.org/10.3390/pr14101545 - 11 May 2026
Viewed by 195
Abstract
Different types of Virtual Power Plants (VPPs) play distinct roles within power systems. To scientifically evaluate the operational benefits of VPPs, this paper constructs a comprehensive evaluation framework based on combined weighting and the Evaluation based on Distance from Average Solution (EDAS) method. [...] Read more.
Different types of Virtual Power Plants (VPPs) play distinct roles within power systems. To scientifically evaluate the operational benefits of VPPs, this paper constructs a comprehensive evaluation framework based on combined weighting and the Evaluation based on Distance from Average Solution (EDAS) method. First, an evaluation index system is established encompassing four dimensions: economic, environmental, social, and technical. Subsequently, a hybrid model integrating DEMATEL, CRITIC, Game Theory, and EDAS is proposed. Specifically, the DEMATEL method is employed to analyze the causal relationships among indicators and determine subjective weights, while the CRITIC method is used to calculate objective weights. Game Theory is then applied to optimize the combination of weights, and the EDAS method is utilized to rank the alternatives. Empirical analysis of five VPP scenarios indicates that the renewable energy accommodation rate and hardware investment costs are the core driving factors affecting operational benefits. Specifically, the renewable-energy accommodation rate exhibits the highest combined weight of 0.08, and the hardware investment cost reaches 0.07. Among the scenarios, a wind-solar-storage hybrid VPP demonstrates the optimal comprehensive performance. The results are consistent with comparative methods such as TOPSIS, verifying the reliability of the proposed framework and providing a scientific reference for VPP investment decision-making. Full article
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47 pages, 518 KB  
Article
Deterministic Q-Learning with Relational Game Theory: Polynomial-Time Convergence to Minimal Winning Coalitions in Symmetric Influence Networks and Extension
by Duc Nghia Vu and Janos Demetrovics
Mathematics 2026, 14(9), 1526; https://doi.org/10.3390/math14091526 - 30 Apr 2026
Viewed by 286
Abstract
This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties [...] Read more.
This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties of relational dependencies and Armstrong’s axioms to transform the problem into one solvable in polynomial time. Our framework reduces the state space from exponential O(2n) to O(n2) through a sufficient statistic representation based on coalition size, follower reach, and terminal status, while achieving O(n4) time complexity under deterministic, static, and sufficiently symmetric influence structures. The QLRG framework introduces three critical innovations: (1) a principled agent selection mechanism derived directly from the Q-function that eliminates heuristic weight tuning; (2) a formal Boost action defined through temporal closure operators that captures influence spread dynamics; and (3) a constrained MDP formulation that enforces relational consistency through action elimination rather than penalty terms. We prove that the Bellman optimality operator forms a contraction mapping, guaranteeing deterministic convergence to optimal policies with established rates of O(1/√k) for decreasing learning rates or linear convergence up to bias for constant rates. To bridge the gap between this idealized model and the asymmetry inherent in real OSNs, we further develop a cluster-based sufficient statistics approach. By partitioning the network into communities with bounded internal variation, we relax the global symmetry requirement while preserving polynomial state space complexity, and obtaining a single within-community swap changes the optimal Q-value by at most εi1γ, which is a local Lipschitz continuity result. The implications of this are both theoretical and practical, and they form the bedrock for relaxing the global symmetry assumption in the QLRG framework. Empirical validation on synthetic networks satisfying the symmetry assumption demonstrates that QLRG consistently identifies minimal winning coalitions matching the optimal solutions found by exhaustive search, while operating with polynomial-time complexity. Unlike conventional approaches, our framework simultaneously satisfies four critical properties: deterministic convergence, policy optimality, minimal coalition identification, and computational tractability. The work bridges computational social science and operations research, providing a mathematically rigorous foundation for strategic decision-making in influencer marketing and coalition formation. While the framework requires symmetry assumptions that may only hold approximately in real-world OSNs, it establishes an idealized baseline for future extensions addressing stochasticity, dynamics, and partial observability. This research represents a paradigm shift from empirical improvements to theoretically grounded convergence guarantees for coalition formation problems, demonstrating how structural mathematical insights can transform intractable problems into efficiently solvable ones without sacrificing solution quality. Full article
23 pages, 1354 KB  
Article
Human Risk Assessment of Falling from Height in Building Construction Based on Game Theory Combination Weighting and Matter–Element Extension Model
by Chaofan Liu, Mantang Wei, Ran He, Yingchen Wang, Lili Xu and Xiaoxiao Geng
Buildings 2026, 16(9), 1676; https://doi.org/10.3390/buildings16091676 - 24 Apr 2026
Viewed by 275
Abstract
Compared with other construction operations, high-altitude operations are more dangerous. Falling from a height is the main type of accident in construction. It is important to study the human risk of falling from height to reduce falling accidents. Based on the Human Factors [...] Read more.
Compared with other construction operations, high-altitude operations are more dangerous. Falling from a height is the main type of accident in construction. It is important to study the human risk of falling from height to reduce falling accidents. Based on the Human Factors Analysis and Classification System (HFACS) model, a preliminary evaluation index system for fall risk in building construction was established. Through the Delphi method and sensitivity analysis, the initial indicators were screened, the index factors that did not meet the requirements were removed, and the final human risk index evaluation system was determined. The system includes five first-level indicators and 17 s-level indicators of organizational influence, unsafe supervision, preconditions for unsafe behavior, and unsafe behavior. Subsequently, the analytic network process–entropy weight method (ANP-EWM) is used to subjectively and objectively weight the evaluation indicators, and the combined weight is obtained through game theory. The matter–element extension model is constructed to evaluate the human risk of falling from height in construction. Finally, an empirical analysis is carried out with the Y project as a case study. The novelty of this study lies in integrating human-factor analysis with the matter–element extension model for fall risk assessment in construction, while combining ANP, the entropy weight method, and game theory to balance subjective and objective weighting. The proposed model provides a practical tool for evaluating and controlling human risk in high-altitude construction operations. The results show that the correlation degree calculated according to the matter–element extension model is K4 = 3.5, and the human risk of falling from height in the construction of Y project has generally reached an excellent level. However, the evaluation level of some evaluation indexes is still low, which is consistent with the actual situation of construction enterprises in Y project. This model provides a direction for the study of human risk assessment of falling from different construction heights. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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19 pages, 313 KB  
Review
Cognitive Diagnosis Computerized Adaptive Testing (CD-CAT) for Adolescent Internet Gaming Disorder: A Conceptual Assessment Framework
by Min Jia and Jing Liu
Behav. Sci. 2026, 16(4), 558; https://doi.org/10.3390/bs16040558 - 8 Apr 2026
Viewed by 462
Abstract
Internet Gaming Disorder (IGD) has become a major behavioral health concern among adolescents, yet current assessment tools remain limited. These tools often fail to capture the disorder’s complex symptom variations and lack clinical interpretability. This study, taking an interdisciplinary approach that combines clinical [...] Read more.
Internet Gaming Disorder (IGD) has become a major behavioral health concern among adolescents, yet current assessment tools remain limited. These tools often fail to capture the disorder’s complex symptom variations and lack clinical interpretability. This study, taking an interdisciplinary approach that combines clinical psychology and psychometrics, summarizes recent progress in understanding adolescent IGD and the development of its assessment methods. We compare the diagnostic criteria of the DSM-5 TR and ICD-11 and argue that the nine DSM-5 TR criteria are particularly suited for transformation into distinct diagnostic attributes due to their detailed and actionable nature. We then review the strengths and weaknesses of Classical Test Theory (CTT), Item Response Theory (IRT), and Cognitive Diagnostic Models (CDMs) in assessing IGD. The review emphasizes the limitations of total-score and single latent-trait approaches in capturing the disorder’s multidimensional symptoms. Based on these insights, we propose a conceptual assessment framework, Cognitive Diagnosis Computerized Adaptive Testing (CD-CAT), that integrates CDMs with computerized adaptive testing. Rather than presenting an empirically validated system, this framework offers a theoretically grounded proposal that specifies the key components, logical relationships, and methodological pathways necessary for advancing precision assessment of adolescent IGD. CD-CAT uses a system of attributes and a Q-matrix based on the DSM-5 TR criteria to efficiently classify IGD symptoms in adolescents, reducing the number of items required while enhancing clinical relevance. Lastly, we discuss the theoretical contributions of the proposed framework, acknowledge its limitations as a conceptual proposal, and outline directions for future empirical research. Full article
18 pages, 792 KB  
Article
From Virtual Worlds to Real Places: A Journey Through Video Game Play, Flow, and Place Attachment
by Ismail Shaheer
Tour. Hosp. 2026, 7(4), 99; https://doi.org/10.3390/tourhosp7040099 - 3 Apr 2026
Viewed by 1059
Abstract
This study employs a reflexive autoethnography, guided by flow and place attachment theory, to examine how gaming experiences influence attachments to virtual environments and inspire real-world travel intentions. Data comprise reflexive journal notes written over a 10-month period after playing multiple video games [...] Read more.
This study employs a reflexive autoethnography, guided by flow and place attachment theory, to examine how gaming experiences influence attachments to virtual environments and inspire real-world travel intentions. Data comprise reflexive journal notes written over a 10-month period after playing multiple video games and analysed using reflexive thematic analysis following a hybrid deductive–inductive approach. The analysis identified eight themes across three dimensions: temporal immersion, escapism, narrative immersion, and self-expression under flow; emotional, cognitive, and behavioural attachment under place attachment; and place-induced travel intention as the behavioural outcome. The findings establish flow as a critical antecedent to the development of place attachment within virtual environments. Consistent with emerging scholarship, the study confirms that attachment formation does not require physically tangible places; rather, it can emerge through digitally mediated presence and interaction, indicating that virtual environments are capable of eliciting place attachment. More significantly, it demonstrates that these virtual attachments can fluidly extend toward real places depicted in games, revealing a cross-environmental continuity in attachment processes. The integrated framework thus contributes a novel theoretical proposal linking flow, virtual and real place attachment, and tourism behaviour, an area that remains conceptually fragmented and empirically underdeveloped. Full article
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34 pages, 4634 KB  
Article
Research on Collaborative Emission Reduction Between Ports and Shipping Companies in the Context of New Energy
by Lixin Shen, Xingliang Peng, Xinyu Liu, Tomaž Kramberger and Yuhong Wang
Sustainability 2026, 18(7), 3345; https://doi.org/10.3390/su18073345 - 30 Mar 2026
Viewed by 516
Abstract
Collaborative decarbonization between ports and shipping companies is critical to the low-carbon transition of maritime supply chains. Driven by the new energy transition, vertical technology spillovers have become a key force shaping vertical collaborative emission reduction. However, the mechanisms through which spillovers affect [...] Read more.
Collaborative decarbonization between ports and shipping companies is critical to the low-carbon transition of maritime supply chains. Driven by the new energy transition, vertical technology spillovers have become a key force shaping vertical collaborative emission reduction. However, the mechanisms through which spillovers affect strategic interactions remain unclear, the theoretical basis for emission reduction strategies is insufficient, and practical issues such as benefit sharing and coordination mechanisms are underexplored. To fill these gaps, this study makes three contributions. Theoretically, we incorporate vertical technology spillovers and joint benefit–cost sharing into the port–shipping collaborative emission reduction framework, enriching supply-chain-level spillover theory. Methodologically, we combine an evolutionary game model with a scale-free network to simulate strategy diffusion and conduct scenario comparisons, linking theoretical modeling with industrial practice. Empirically, we confirm that ports act as leaders in collaborative decarbonization, and port-centered resource allocation drives the systemic low-carbon transition of the maritime sector. The findings show that the share of agents adopting active emission reduction strategies first rises and then falls with vertical technology spillover intensity, peaking at a moderate level. The impacts of core factors vary significantly across spillover scenarios. Port-centered resource allocation and benefit distribution are crucial to improving overall participation willingness. Ports are not merely participants but irreplaceable coordinators in the maritime supply chain. These results provide targeted policy and practical guidance for ports and shipping companies to promote global green and low-carbon maritime development. Full article
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28 pages, 1825 KB  
Article
Combinatorial Game Theory and Reinforcement Learning in Cumulative Tic-Tac-Toe via Evaluation Functions
by Kai Li and Wei Zhu
Stats 2026, 9(2), 28; https://doi.org/10.3390/stats9020028 - 10 Mar 2026
Viewed by 1013
Abstract
We introduce cumulative tic-tac-toe, a novel variant of the classic 3×3 tic-tac-toe game in which play continues until the board is completely filled. Each player’s final score is determined by the total number of three-in-a-row sequences they form. Using combinatorial game [...] Read more.
We introduce cumulative tic-tac-toe, a novel variant of the classic 3×3 tic-tac-toe game in which play continues until the board is completely filled. Each player’s final score is determined by the total number of three-in-a-row sequences they form. Using combinatorial game theory (CGT), we establish that under optimal play, the game is a draw, and we characterize its theoretical properties. To empirically validate and optimize practical play, we develop a reinforcement learning (RL) framework based on temporal-difference (TD) learning, which is enhanced with a domain-informed evaluation function to accelerate convergence. The experimental results show that our triplet-coverage difference (TCD) evaluation function reduces the average number of training episodes by approximately 23.1% compared with a random-initialization baseline, a statistically significant improvement at the 5% significance level. These results demonstrate the efficiency of our CGT–RL approach for cumulative tic-tac-toe and suggest that similar methods may be useful for analyzing related combinatorial games. We also discuss potential analogies in domains such as competitive resource allocation and coalition formation, illustrating how cumulative-scoring games connect abstract game-theoretic ideas to practical sequential decision problems. Full article
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23 pages, 414 KB  
Article
Measuring Pitcher Production Fairly in Baseball Using the Shapley Value
by Michael McBride
Games 2026, 17(2), 15; https://doi.org/10.3390/g17020015 - 10 Mar 2026
Viewed by 642
Abstract
This paper introduces fairer measures of individual pitcher performance in baseball using the Shapley Value from coalitional game theory. The paper’s key conceptual innovation is a novel two-stage procedure for constructing the coalitionary game value functions for runs allowed and outs recorded by [...] Read more.
This paper introduces fairer measures of individual pitcher performance in baseball using the Shapley Value from coalitional game theory. The paper’s key conceptual innovation is a novel two-stage procedure for constructing the coalitionary game value functions for runs allowed and outs recorded by a baseball team’s defense. This procedure enables the Shapley Value calculation to fairly divide credit for runs and out between different pitchers and between pitchers and fielders. It also results in two new statistics—Shapley Pitcher Runs (SPR) and Shapley Pitcher Outs (SPO)—that, unlike traditional pitching statistics, consistently satisfy several mathematical fairness axioms. A third statistic, called Shapley Run Average, provides a fairer measure of pitcher efficiency. I calculate these statistics for the 2022 Major League Baseball regular season and the 1955–2022 World Series championships. Using SPR and SPO as the standard for fairness, empirical analysis reveals that the traditional pitching statistics systematically and unfairly overcredit pitchers by 40–50%, with starting pitchers miscredited more severely than relievers. Analysis of SRA identifies efficient pitchers whose performance is obscured by conventional statistics and enables a reassessment of historic World Series performances. Overall, this work demonstrates another application of the Shapley Value to creating new performance measures in team sports. Full article
(This article belongs to the Section Applied Game Theory)
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12 pages, 270 KB  
Essay
Cooperation Collapse in the Harmony Game: Revisiting Scodel and Minas Through Evolutionary Game Theory
by Shade T. Shutters
Games 2026, 17(2), 14; https://doi.org/10.3390/g17020014 - 9 Mar 2026
Viewed by 941
Abstract
Between 1959 and 1962, Alvin Scodel, J. Sayer Minas, and colleagues conducted some of the earliest laboratory studies of strategic interaction using non-zero-sum games. Working at the margins of economics in the Journal of Conflict Resolution, they documented a striking pattern: subjects [...] Read more.
Between 1959 and 1962, Alvin Scodel, J. Sayer Minas, and colleagues conducted some of the earliest laboratory studies of strategic interaction using non-zero-sum games. Working at the margins of economics in the Journal of Conflict Resolution, they documented a striking pattern: subjects frequently chose options that reduced an opponent’s payoff by more than their own, even when mutual cooperation was both individually and collectively optimal. These results—especially the behavior observed in their so-called Game H4, a Harmony Game in which cooperation strictly dominated defection—anticipate a central insight of evolutionary game theory: what matters for adaptation is relative payoff, not absolute gain. This essay reinterprets the Scodel–Minas experiments through a Darwinian lens, arguing that they provide an early empirical challenge to Nash-equilibrium reasoning and to models that evaluate strategies solely in terms of absolute utility. By reconstructing the H4 payoff structure and embedding it within a simple evolutionary framework, I show how small levels of “competitive” behavior can destabilize cooperative equilibria that appear self-evident under standard assumptions. I then revisit three later “puzzles” in the evolution of cooperation—altruistic punishment, the fragility of “win–win” treaties, and rejections in ultimatum bargaining—to ask how differently they might have been framed had the Scodel–Minas findings been part of the canonical experimental literature. Rather than treating these phenomena as surprising anomalies, a historically informed, relative-payoff perspective suggests that they could have been recognized much earlier as natural expressions of an already documented pattern. Full article
(This article belongs to the Special Issue Evolution of Cooperation and Evolutionary Game Theory)
19 pages, 4253 KB  
Article
Towards a Conceptual Participatory Framework to Promote Health Literacy in Adolescents by Integrating Self-Determination Theory and Game Design
by Michela Franchini, Giada Anastasi, Stefania Pieroni, Francesca Denoth, Benedetta Ferrante, Alessia Formica and Sabrina Molinaro
Int. J. Environ. Res. Public Health 2026, 23(3), 328; https://doi.org/10.3390/ijerph23030328 - 6 Mar 2026
Viewed by 1016
Abstract
Adolescents are heavy users of digital media but often lack critical skills, increasing their vulnerability to harmful online content. The integration of game elements into learning and training offers a promising strategy to support positive behavioural change and strengthen adolescents’ skills. This paper [...] Read more.
Adolescents are heavy users of digital media but often lack critical skills, increasing their vulnerability to harmful online content. The integration of game elements into learning and training offers a promising strategy to support positive behavioural change and strengthen adolescents’ skills. This paper describes the development of a conceptual framework for Dress-DIGITARIAN, a serious game aimed at improving health literacy, coping skills, and self-esteem, grounded in Self-Determination Theory (SDT). The framework was constructed to generate higher-order understanding through a multi-level process: analyzing general theory (SDT), integrating mid-range models (the Octalysis framework), and incorporating empirical insights derived from two data collection phases with the target population. This integrative approach informed and guided the game’s design through participatory methods. Developed through collaboration between schools and research institutions, this approach bridges theory and practice by aligning game mechanics with adolescents’ psychological needs. It also underscores the value of involving adolescents in research, not only to enhance scientific rigour but also to empower them as agents of change capable of contributing to health promotion policies and educational innovation. This study does not report the results of a completed intervention or outcome evaluation, which will be conducted in the sixth phase at the end of the current school year. Future research is needed to assess the model’s effectiveness and scalability and to identify areas for further refinement. Full article
(This article belongs to the Special Issue Health Promotion in Childhood and Adolescence)
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25 pages, 4484 KB  
Article
Innovative Teaching for Enhancing Pro-Environmental Behavior Among First-Year University Students: Evidence from a Solomon Four-Group Experimental Design
by Surasak Jotaworn, Wanjai Lamprom and Issara Siramaneerat
Soc. Sci. 2026, 15(3), 162; https://doi.org/10.3390/socsci15030162 - 3 Mar 2026
Viewed by 557
Abstract
Given the persistent challenges in promoting pro-environmental behavior and student engagement in higher education, particularly in environmental courses, this study examines the effects of creative teaching strategies—specifically icebreaker games and activities—on cognitive understanding, attitudes, and pro-environmental behaviors among first-year university students in environmental [...] Read more.
Given the persistent challenges in promoting pro-environmental behavior and student engagement in higher education, particularly in environmental courses, this study examines the effects of creative teaching strategies—specifically icebreaker games and activities—on cognitive understanding, attitudes, and pro-environmental behaviors among first-year university students in environmental education. Grounded in the Green Competency framework and game-based learning theory, the study addresses an empirical gap concerning the sustained impacts of active learning approaches. A Solomon four-group experimental design was employed with 200 students enrolled in the Environmental Society course at Rajamangala University of Technology Thanyaburi (RMUTT). Pre- and post-tests assessed changes across the three learning domains. ANOVA and Scheffé post hoc analyses revealed statistically significant improvements in cognition, attitudes, and behaviors among students exposed to the intervention, particularly those receiving both pre-testing and innovative instruction. Regression analysis indicated that cognitive understanding was the strongest predictor of pro-environmental behavior (β = 0.531, p < 0.001), while demographic variables showed no significant influence. The findings demonstrate that well-designed icebreaker activities can enhance student engagement and foster lasting behavioral change when aligned with course objectives. This study contributes to the sustainability education literature by linking active pedagogy, emotional engagement, and behavioral outcomes and offers practical implications for student-centered curriculum design in higher education. Full article
26 pages, 446 KB  
Article
A Mathematical Framework for Modeling Global Value Chain Networks
by Georgios Angelidis
Foundations 2026, 6(1), 8; https://doi.org/10.3390/foundations6010008 - 3 Mar 2026
Viewed by 677
Abstract
Global value chains (GVCs) have evolved into highly interconnected and geographically fragmented production networks, increasing exposure to systemic disruptions and revealing the limitations of static input–output and conventional network approaches. This study develops a unified analytical framework for modeling the structure, dynamics, and [...] Read more.
Global value chains (GVCs) have evolved into highly interconnected and geographically fragmented production networks, increasing exposure to systemic disruptions and revealing the limitations of static input–output and conventional network approaches. This study develops a unified analytical framework for modeling the structure, dynamics, and resilience of GVCs by integrating input–output economics with network theory, control theory, optimal transport, information theory, and cooperative game theory. The framework represents GVCs as time-varying, multi-level networks and formalizes shock propagation through stochastic normalization and state-space dynamics. Entropy-regularized optimal transport is employed to model friction-dependent substitution and supply chain reconfiguration, while Koopman operator methods approximate nonlinear adjustment dynamics. Cooperative flow-based indices are introduced to assess systemic importance and bargaining power. The analysis produces a coherent set of structural and dynamic indicators capturing vulnerability, adaptability, and controllability across country–sector nodes. Overall, the framework provides an empirically applicable toolkit for diagnosing structural fragilities, comparing resilience across economies, and supporting scenario-based evaluation of industrial and trade policies in complex global production networks. Full article
(This article belongs to the Section Mathematical Sciences)
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22 pages, 2511 KB  
Article
A Socio-Constructivist Conceptual and Design Framework for Educational Escape Room Games
by Amanda Glavaš
Educ. Sci. 2026, 16(3), 375; https://doi.org/10.3390/educsci16030375 - 1 Mar 2026
Viewed by 837
Abstract
Game-based learning approaches, particularly escape room games (ERGs), have gained increasing attention in mathematics and STEM education due to their theoretical potential to foster engagement, interest, positive attitudes, communication, teamwork, and problem-solving skills. This paper presents a theoretical and design-based conceptual analysis of [...] Read more.
Game-based learning approaches, particularly escape room games (ERGs), have gained increasing attention in mathematics and STEM education due to their theoretical potential to foster engagement, interest, positive attitudes, communication, teamwork, and problem-solving skills. This paper presents a theoretical and design-based conceptual analysis of educational ERGs (EERGs) within mathematics education, where issues of interest, engagement, negative attitudes and limited real-world relevance remain persistent challenges. This paper aims to develop a socio-constructivist conceptual and design framework for EERGs by synthesizing relevant educational theory, research literature and professional game design practice. Based on literature and design-informed analysis, the paper proposes a classification of puzzle types and structural configurations, analyzing the epistemic mechanisms through which these elements are theoretically expected to foster student competencies and dispositions such as positive attitudes towards learning, collaboration, communication, problem-solving and engagement. The paper also presents an author-developed game prototype as an illustrative design heuristic derived from the conceptual framework and professional practice. Finally, the paper discusses theoretical advantages and limitations considering methodological, organizational, technical and pedagogical aspects. The contribution of this study comes from an interdisciplinary understanding of EERGs, and a conceptual and design framework intended to inform future design-based and empirical research on EERGs. Full article
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