Game theory meets complex systems: five studies unravel strategic adaptation

Game theory and complex systems science are two of the most powerful analytical frameworks in modern research, and their intersection is producing insights that reach far beyond the mathematics departments where they were born. Game theory offers a structured way to model decision-making under conditions of conflict and cooperation, while complex systems science supplies the tools to analyze the non-linear interdependencies that characterize everything from biological ecosystems to socioeconomic structures. When researchers weave strategic interaction into the fabric of complex systems, they can decipher not only the adaptive strategies of individual agents but also the macroscopic evolutionary trajectories that emerge from those interactions. A new collection of studies, published as a Research Topic in Frontiers in Complex Systems, sets out to do exactly that, and the results span an astonishing range of domains: primate evolution, public health policy, organizational management, and competitive sports.

The editorial behind the collection, authored by Chengyi Tu of Zhejiang Sci-Tech University and Hongzhong Deng of the National University of Defense Technology, was curated to advance our comprehension of how emergent phenomena are born from strategic interactions. Crucially, the editors sought to move beyond the conventional assumption of complete rationality that has long dominated classical game theory. Instead, they encouraged models that reflect the nuanced realities of limited information, bounded rationality, and dynamic network structures. The resulting compilation of five articles offers a diverse yet cohesive exploration of these themes, and the underlying mathematical principles reveal a common truth: complex systems are driven by the continuous interplay of strategic adaptation and structural constraints.

The contributions can be grouped into three thematic areas: the evolutionary foundations of cooperation, the dynamics of social and organizational adaptation, and strategic optimization in competitive environments. Each area tackles the same fundamental question from a different angle—how do macroscopic patterns emerge from microscopic behaviors when agents interact strategically? The answer, it turns out, involves network reciprocity, threshold effects, memory dynamics, and diversity, concepts that recur across biology, sociology, and economics with remarkable consistency.

In the first thematic area, Nicholas MacLaren and colleagues 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. The finding suggests that the evolution of large brains in primates was not merely about individual intelligence but about the ability to navigate social networks in ways that sustain cooperation.

Moving from biological to human social systems, two articles employ dynamical modeling to understand adaptation and policy impact. In the first, Cao and colleagues construct a tripartite evolutionary game model involving government bodies, pharmaceutical enterprises, and research institutions to examine how policy tool combinations drive the construction of public health technology R&D alliances. 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. This finding has profound implications for policymakers who might assume that increasing subsidies or regulations will always increase collaboration.

In the second article on social adaptation, Hailu and colleagues apply advanced mathematical control theory to organizational psychology. By modeling employees as indifferent, resistant, or adaptive to reform initiatives in public service organizations, they use fractional order derivatives 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 use of fractional calculus is particularly noteworthy because it allows the model to incorporate historical dependencies—how past experiences shape current attitudes—which is essential for understanding how organizational culture evolves over time.

The final two articles explore optimization and performance in competitive physical and virtual arenas. Gullholm and colleagues offer a fascinating intersection of sports analytics and game theory in their study of 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. The implication is that diversity is not merely a social virtue but a strategic advantage in competitive environments.

In the realm of physical performance, Marcojos and colleagues contribute a study on 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 can optimize the adaptive capacity of agents operating in highly dynamic environments. The study is a reminder that the principles of strategic adaptation apply not only to cognitive and social systems but also to the physical systems that underpin human performance.

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. The editors hope this collection inspires further interdisciplinary research that bridges the gap between theoretical models and real-world complexities, and the breadth of the contributions suggests that this bridge is already being crossed in ways that could reshape how we understand everything from the evolution of the social brain to the design of effective public policy.

Subject of Research: Game theory and evolutionary dynamics in complex systems

Article Title: Editorial: Game theory and evolutionary dynamics: unraveling complex systems

Article References: Tu, C., & Deng, H. (2026). Editorial: Game theory and evolutionary dynamics: unraveling complex systems. Frontiers in Complex Systems, 4, Article 1794474. https://doi.org/10.3389/fcpxs.2026.1794474

Image Credits: AI Generated

DOI: 10.3389/fcpxs.2026.1794474

Keywords: game theory, evolutionary dynamics, complex systems, cooperation, network reciprocity, bounded rationality, public health policy, organizational change, sports analytics, Frontiers in Complex Systems, Editorial, Game