The resilience of unmanned autonomous swarms (UAS) is critical for their ability to adjust behaviors and maintain essential functions when errors and failures occur. While significant advancements have been made in enhancing UAS resilience, the potential to utilize their inherent self-organizing and self-restructuring capabilities for further improvement remains largely underexplored. In this study, we present a game theory- based reconfiguration framework for UAS, enabling dynamic adjustments to the swarm's network structure through cooperative payoffs. Building on this framework, we propose a UAS resilience metric to quantify the swarm's task performance under continuous disturbances, validated through a case study. Finally, our analysis of the optimal configurations for enhancing UAS resilience-considering payoff matrices, swarm composition, communication range, and network structure-provides actionable insights for UAS design. We find that an optimal agent configuration ratio exists that maximizes UAS resilience, with specific constraints established for this ratio. Additionally, while increasing the communication range improves resilience, the benefits diminish beyond a certain threshold. We also find that network topology significantly impacts UAS resilience, particularly in structures with short global paths, which exhibit greater resilience.