Why did the U.S.A. make the Taft-Katsura Agreement with Japan?The purpose of this study is to research this question thoroughly. My research consists of three parts: Parts one and two are the game theory of the Taft-Katsura Agreement through the Hague Convention (1899). Part three is the theory practice of the Taft-Katsura Agreement through the Arbitration Treaty between the U.S.A and Japan (1905)during the Russo-Japanese War, 1904-1905. The Hague Convention is the result of the First Hague Peace Conference. The Hague Convention is designed for the peaceful settlement of disputes between nations by “good offices”, mediation,and arbitration. The good offices and mediation of the Hague Convention practice putting arbitration into action in case of war. If, therefore,the Korean Peninsula is on the brink of war, the powers of the Hague Convention can intervene based on the values and policies of the Hague Convention. This idea stands on the grounds that the Hague Convention is the game theory and the theory practice of the Taft-Katsura Agreement. What effect does the Hague Convention have on Taft-Katsura Agreement? The fact that a lawsuit cannot be raised. The Hague Convention prescribed three cases: the first is about the independence of nations, the second is about honor and the third is about vital interests. Among these, the vital interest theory is applicable to the Korean Peninsula. The politics of imperialism changed the vital interests article in theory into the protectorate in practice. Theodore Roosevelt played a major role in this change. The politics of imperialism changed the vital interest theory into playing a major role in developing the protectorate within imperialism. He thought that Korea was the “impotence” nation which could not keep the self-preservation among the international peace community of nations. Roosevelt saw that Korea could harm international peace with the Korean Emperor’s plan to restore stolen independence by bringing the Korean Question forward at the Hague Arbitral Court. On the eve of the Russo-Japanese action, Roosevelt concluded that the Korean right of access to the Hague court must be “deprived for world peace”, and it should be transferred to Japan. In other words, the concluded treaty between Korea and powers in 1882-1884 must be withdrawn, and Korea was not admitted to the Arbitration treaty system. Theodore Roosevelt said that this plot was in accord with the Imperial Japanese plan for expansion to Korea and Manchuria. If the theory of the vital interest in the Hague convention was to be realized, two steps should be followed. One is that the two countries conclude the Arbitration Treaty including the clause of vital interests. The other is that the two countries conclude the Protectorate Agreement including the clause of vital interests. The former is the Arbitration Treaty between the U.S.A and Japan,January, 1905. The latter is Taft-Katsura Agreement, July, 1905. In conclusion, the Hague Convention produced the Arbitration Treaty and the Arbitration Treaty produced the Taft-Katsura Agreement.