The coopetition theory holds that the overall IR process is an allocation process of power, institution and Ideas. If only from the perspective of idea distribution, it acknowledges its role and importance in international relations, regardless of IP Cognitive School of the unit level, the Foreign Policy Analysis (FPA) or the mainstream IR theory — Constructivism and other schools on the system level. However, neither constructivism, the English school, nor Cognitive School can provide a clear language on the construction process of the international system through ideas. Therefore, it has some special theoretical significance in examining the validity of ideas on IR from the perspective of ideas or ideology history, and in discussing how the coopetition of the idea distribution influences and shapes the renewal and transformation of the international system. Historically, since the beginning of the modern international relations in 1648, the coopetition of statism, conservatism, radicalism, nationalism, liberalism and other ideas, has successively become the dominant concept of four major international systems, the Westphalian system, the Vienna system, the Versailles system, and the Yalta system, all of which dominate the use of power and distribution of institution in the various periods. It's also the process of the establishment of the international system when the main ideas become the dominant positions in the coopetition. As an integral factor, the idea is always an indispensable force to shape and change the international system. Statism was the first to become the dominant idea in Europe. After the Renaissance, Reformation and the Thirty Years' War, dominant European ideas transformed from church supremacy to the supremacy of national interest and sovereignty. Statism took the place of the theocentricism, and the idea of sovereignty was further confirmed and strengthened in the following centuries. The subsequent Enlightenment further promoted the development of liberalism and influenced and promoted the bourgeois revolution in Europe and America. But with the failure of Napoleon in war, liberalism and nationalism—the two subversive forces released by the French Revolution—were then suppressed, and conservatism dominated the Vienna system period. However, conservatism could not prevent the development of liberalism. Extreme nationalism, imperialism, militarism and radicalism directly led to the outbreak of the First World War, and overthrew the old order. In order to avoid further human catastrophes and rebuild peace, U.S. President Woodrow Wilson brought out idealism, which is literally a combination of liberalism and nationalism, shaped and established the Versailles System. With the intensifying coopetition of radicalism and idealism, idealism failed. The combination of nationalism and imperialism produced wild fascism and triggered the Second World War. In general, this period was dominated by radicalism. In World War Ⅱ, US President Franklin D.Roosevelt learned the advantages of socialism and put forward the ″Four Freedoms,″ once again raising the once depressed liberal flag. Until the Yalta system after World War Ⅱ, nationalism finally defeated imperialism, while liberalism succeeded over totalitarianism. With the end of the Cold War, the tide of statism and nationalism began to ebb in the era of post-cold war and globalization. Moreover, socialism as a higher and lofty human ideal and social form will rejuvenate the strong youth and vitality if it can correctly and comprehensively absorb the essence of liberalism, and will eventually become the dominant ideas in shaping the emerging international system after the Cold War. The process of idea coopetition should be part of it. Therefore, correctly grasping the general trend of the world development in the last 500 years and the future of mankind is essential for us to study the changes of the international system.