Complex systems exhibit strategic interactions in which risk propagation is influenced by networked relationships. This study presents a network–agent model within sports contexts, demonstrating how Nash equilibria emerge from bounded rationality. Using scale-free networks where nodes represent sports agents, we simulate evolutionary game dynamics under varying protection and learning parameters. The model reveals four distinct equilibria: coexistence with sufficient protection, system-wide failure under low protection, partial coexistence with limited protection, and robust protection with minimal failure. The balance between social learning and strategic adaptation crucially determines system behavior; low values produce fragmented strategic clusters, whereas high values drive convergence toward uniform protection strategies. Nash equilibria naturally emerge when competitive outcomes coexist with cooperative protection behaviors, offering practical insights for sports practitioners on prevention strategies, knowledge transfer, and the emergence of complementary specialized roles within teams.