Ed M. answered 02/23/16
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I think the term imperialism is what you're after here, though I don't believe the element "that deepened their sense of rivalry and mistrust for one another" is necessarily part of its definition, i.e., a nation could adopt an imperialist policy without that causing conflict with other countries doing the same thing, even if that's usually the outcome especially if the imperialistic efforts are concentrated in one geographic area (like the European colonization of Africa during the 19th century).