Integrating static and dynamic game theory with complex networks: Enhancing strategy dynamics through adaptive update rules

Understanding the dynamics of strategic interactions in real-world systems is crucial across various fields, from economics to biology. This research is motivated by the need to bridge the gap between game theory models and the complex structures of real-world networks, particularly scale-free networks with their robust, hub-dominated topology. This study explores the integration of evolutionary game dynamics within complex networks under various update rules to identify which game-theoretic model—static or dynamic, with complete or incomplete information—most closely resembles real-world scenarios. Focusing on evolutionary games such as the Prisoner's Dilemma, Signaling Game, Auction Game, and the Ultimatum Game, and examining the degree distribution exponent γ to determine the best match to scale-free properties. The findings of this study reveals that the analysis of cooperation levels across various game types and network structures reveals that strategic interactions significantly influence the efficiency of reaching Nash equilibrium. Higher cooperation levels are observed in structured networks, while stochastic best response strategies show consistent timeframes to equilibrium. These findings highlight the critical role of network topology and strategy in fostering cooperative behavior, providing insights into how network topology influences the evolution of strategies and offering a robust framework for future studies on applying game theory to real-world network dynamics.