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During the Cold War, although the primary conflict was between Moscow and Washington, there were several nations which attempted to stand out on their own. The PRC is the most notable example of this, and French attempts to galvanize an Europe independent of American hegemony also deserves a mention.

Your challenge thus is to create a Cold War scenario wherein the United States, the Soviet Union, a European power (or a somewhat-unified Europe, or multiple European powers), and China (Nationalist, Communist, maybe even two Chinas) all vie for power and influence, although not on equal footing.
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