The 1954 update to the doctrine of containment, announced by Secretary of State John Foster Dulles, that declared a Soviet attack on any American ally would be countered by a nuclear attack on the Soviet Union, was called "brinksmanship" by its critics and this by supporters?

Massive retaliation.

Explanation:

The American and Soviet Union leader were over zealously interested in diplomacy of Latin America, Asia, and Africa which prompted the Cold War.

In the 1950s, America and soviet observed the globe as a backdrop where their high stakes contest of imaginations and authority muscle flexing were being waged. As a result, these officials often projected a global Cold War framework upon local events and discounted the agency and ideas of the actual participants.

The result of this war had different influx of effects to the citizens if the American and Soviet, also to the different parts of the other continents that did not partake.

The result and outcomes of the Cold War extended into the domestic lives, where civil rights advocates, union leaders, and any others who espoused messages that were critical of the United States and its political leaders were accused of disloyalty.