Communism verses Free Society, each armed with Atomic Weapons, neither side willing to back down.
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Rivalry between the French and the Dutch in North America lead to increased Indian warfare. The rivalry pushed the Indians to secure more furs and items for trade and more warfare broke out over competition.
The cold war
The confrontational stand-off between the United States and the Soviet Union.
Most likely this would be called a stalemate.
The Space Race between the United States and the Soviet Union grew out of the Cold War. The rivalry between these two super powers led to major technological advances and achievements at the time.