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Suppose there are two important factors to a beneficial objective. Bigger values of both factors lead to higher achievement in the objective. However when one of the two factors increases, the other has to decrease. There is a point at which the optimality is achieved. What would be the best word to describe this kind of duality, and accurately capture the abstract concept of achieving optimality through compromise?

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trade-off

a situation in which you must choose between or balance two things that are opposite or cannot be had at the same time

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Balance suggests an optimal state where one factor does not dominate the other. Balance is both a noun and a verb.

Equilibrium is another possibility, but can only be used as a noun.

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  • Balance and equilibirum indicate that a stable status is maintanined, but they don't convey the concept that an optimal objective is achieved.
    – user1600
    Oct 4, 2014 at 12:27
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It sounds like a zero-sum game. As described in Wikipedia, that is

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which a participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero-sum game if all participants value each unit of cake equally (see marginal utility).

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