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Earthquakes cause irreparable damages to the built environment, which has led bridge engineers to develop structural control systems to mitigate damage and improve vibration reduction in real-time. Among control systems, base isolation is one of the most commonly used passive control strategies for seismic protection of civil structures. Yet, it lacks real-time adaptability, has lower energy dissipation, and poor performance during near-fault earthquakes. To overcome these limitations, a hybrid control system comprised of semi-active magneto-rheological (MR) dampers and passive base isolation bearings is installed at the deck and piers for vibration reduction of highway bridge structures. This paper, inspired by evolutionary game theory and artificial intelligence, proposes data-driven replicator dynamic control algorithms to distribute the command voltage to the current driver of the semi-active MR dampers. It incorporates a load balancing strategy to reallocate additional resources. To achieve a high-performance design of the game-theory-inspired controllers, a patented neural dynamic model is used to optimize the control parameters. The evaluation of the proposed methodology uses a benchmark control problem based on the 91/5 highway bridge in Southern California subjected to near-field earthquake accelerograms. The performance of five different proposed controllers is compared with conventional Lyapunov and fuzzy logic control algorithms using 21 performance criteria. Results show the load balancing capability of the proposed control algorithms to mitigate the vibrations experienced by the bridge structure and further increase the durability of semi-active devices. The novelty of the methodology impacts how game-theory controllers make control decisions among multiple devices in engineering problems. • Five data-driven control algorithms inspired by evolutionary game theory. • Load balancing strategy for reallocation of available resources. • Patented neural dynamic model optimizes the nonlinear design control parameters. • Methodology increases the lifespan and reliability of semi-active devices. • Advanced vibration mitigation of highway bridge structures subjected to earthquake loading. [ABSTRACT FROM AUTHOR]