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Full Idea
The minimax theorem says that there is always a rational solution to a precisely defined conflict between two people whose interests are completely opposite.
Gist of Idea
The minimax theorem says a perfect game of opposed people always has a rational solution
Source
William Poundstone (Prisoner's Dilemma [1992], 03 'Minimax')
Book Ref
Poundstone,William: 'Prisoner's Dilemma' [OUP 1992], p.62
A Reaction
This is Von Neumann's founding theorem of game theory. It concerns maximising minimums, and minimising maximums. Crucially, I would say that it virtually never occurs that two people have completely opposite interests. There is a common good.