Recent geopolitical conflicts in Ukraine and Taiwan urge the democratic world to take prompt actions to defend democracy, to promote humanity and to prevent hot wars. Taking the geopolitical crisis into the perspective of game theory, International Order is a game played by the democratic world and the authoritarian regimes. Argumentation Mechanism Design in Answer Set Programming offers an automatic, flexible, programmable tool to lead the game towards desirable outcomes by modifying the game rules. This study abstracts International Order Reshaping as a Mechanism Design problem, tries and compares two approaches of mapping games into Answer Set Programming, then conducts an Argumentation Mechanism Design case study. Focused on International Order Reshaping, the case study re-designs the games with “Battle of Sexes” model, maps the games into Dung’s Argumentation Frameworks, then encodes the Game-Based Argumentation Frameworks into Answer Set Programming, where Argumentation Mechanism Design solutions can be automatically enumerated. The case study also promotes two methods to increase the interpretability of Argumentation Mechanism Design solutions—assigning compulsory attack relations and limiting the complexity of attack relation set. Results demonstrate support for Argumentation Mechanism Design in Answer Set Programming as an effective tool of automatically solving complex real-world issues. Code-generated Argumentation Mechanism Design solutions are interpretable as practical suggestions for International Order Reshaping.