Verification of Local Equilibrium Stability through Evolutionary Game Data Simulation

<p>This research was conducted in the MATLAB environment, employing evolutionary game data simulation to verify the local stability of equilibrium points. Specifically, we utilized evolutionary game theory to analyze strategic interactions under different conditions and developed MATLAB simulation programs to replicate evolutionary game processes. The implementation involved creating population dynamics models using differential equations (e.g., replicator dynamics) and tracking strategy evolution through iterative computation. Key functions included payoff matrix calculations, strategy update rules, and stability analysis algorithms. Through systematic analysis of simulation data, we demonstrated that equilibrium points maintain local stability under varying parameter conditions, providing crucial insights and support for further game theory research. The simulation framework incorporated sensitivity analysis to test robustness and convergence properties. In future studies, we plan to investigate additional factors influencing game behavior, such as network structures and mutation rates, and validate theoretical findings through extended simulation experiments with enhanced visualization capabilities.</p>