•Game model improves NIR, analyzing port and flag states and shipowners’ strategies.•First-time reputation rewards and punishments add shipowner payoffs and flag states.•It is important to differentiate flag state performance when punishing or rewarding.•Shipowners care less about their reputations and more about their profits. Port state control is regarded as the “last safety net” for maintaining maritime safety and environmental pollution prevention standards for foreign ships calling at or anchoring off international ports. Owing to limited resources, port states select and inspect ships that are more likely to be substandard under their inspection regimes and then record and publish the performance of shipowners and flag states. To encourage ships to comply with standards during subsequent inspections and improve new inspection regimes, we develop a game model analysing the strategies of port states, flag states, and shipowners. We then confirm the Nash equilibrium of the pure and mixed strategies. Subsequently, we investigate the influence of different reward and punishment conditions on flag states and shipowners and generate the following three results: first, differentiating flag state performance is crucial for port states to provide appropriate punishments or rewards to improve ship safety; second, reputation rewards have stronger impacts than reputation punishments for flag states; and third, reputation rewards or punishments from port states have little influence on shipowners’ strategies, since shipowners are much more concerned about their profits.