Game theory and complex systems represent two pivotal and increasingly intersecting fields in contemporary scientific research. While game theory provides a structured mathematical framework for understanding decision-making under conditions of conflict and cooperation, complex systems science offers the tools to analyze the intricate, non-linear interdependencies that characterize the real world—from biological ecosystems to socioeconomic structures. By weaving game theory into the fabric of complex systems, researchers can decipher not only the adaptive strategies of individual agents but also the macroscopic evolutionary trajectories that emerge from their interactions.

This Research Topic, “Game Theory and Evolutionary Dynamics: Unraveling Complex Systems,” was curated to advance our comprehension of how emergent phenomena are born from strategic interactions. We sought to move beyond conventional assumptions of complete rationality, encouraging models that reflect the nuanced realities of limited information, bounded rationality, and dynamic network structures. The resulting collection of five articles offers a diverse yet cohesive exploration of these themes, spanning primate evolution, public health policy, organizational management, and competitive sports.

The contributing articles can be broadly categorized into three thematic areas: evolutionary foundations of cooperation, dynamics of social and organizational adaptation, and strategic optimization in competitive environments.

MacLaren et al. provide a foundational perspective by investigating the Social Brain Hypothesis through the lens of evolutionary game theory. In their article, “Cooperation and the social brain hypothesis in primate social networks,” the authors combine data on primate brain size with theoretical models of cooperation on networks. They utilize a gift-giving game framework to demonstrate that species with larger brain sizes tend to form social network structures that more effectively foster cooperation. This work highlights the critical role of network reciprocity in the evolution of social complexity, offering empirical support for the idea that cognitive capacity and social structure co-evolve to solve collective action problems.

Moving from biological to human social systems, two articles employ dynamical modeling to understand adaptation and policy impact.

In “How do policy tool combinations drive the construction of public health technology R&D alliances?”, Cao et al. construct a tripartite evolutionary game model involving government bodies, pharmaceutical enterprises, and research institutions. Their analysis of supply-side, demand-side, and environmental policy tools reveals that demand-side government procurement is the most effective incentive for fostering alliances. Crucially, they identify non-linear threshold effects, showing that excessive intervention can paradoxically reduce participation—a classic complex system phenomenon where “more is not always better.”

Similarly, Hailu et al. apply advanced mathematical control theory to organizational psychology in “Insight into employees’ perceptions on reform initiatives in public service organizations using fractional order derivatives with optimal control strategies.” By modeling employees as “indifferent,” “resistant,” or “adaptive,” they use fractional calculus to capture the memory effects and dynamics of opinion change. Their application of optimal control theory suggests that targeted training and clear communication are the most effective strategies to minimize resistance, providing a rigorous quantitative basis for change management.

The final two articles explore optimization and performance in competitive physical and virtual arenas.

Gullholm et al. offer a fascinating intersection of sports analytics and game theory in “Diversity is key: fantasy football dream teams under budget constraints.” By analyzing “dream teams” in Fantasy Premier League under various constraints, they find that top-performing teams exhibit a high degree of diversity across multiple variables—a feature not found in randomly assembled teams. This finding suggests a “game theoretic” advantage to diversity, paralleling biological principles where diversity enhances system robustness and evolutionary fitness.

In the realm of physical performance, Marcojos et al. contribute “Modified training drills in improving the dribbling agility of futsal athletes.” While more empirical in nature, this study addresses the “complex physical systems” aspect of the Research Topic. It demonstrates how specific, modified interventions (training drills) can optimize the adaptive capacity (agility) of agents (athletes) operating in highly dynamic environments.

Together, these five articles illustrate the immense versatility of game theory and evolutionary dynamics as analytical lenses. Whether explaining the roots of primate cooperation, optimizing public health alliances, managing organizational resistance, or assembling competitive sports teams, the underlying mathematical principles reveal a common truth: complex systems are driven by the continuous interplay of strategic adaptation and structural constraints. We hope this collection inspires further interdisciplinary research that bridges the gap between theoretical models and real-world complexities.