What do you call a situation in which any resource you gain is a loss of resource for someone else?

Zero-Sum Game

Explanation:

In Game Theory, the zero sum occurs when the gain obtained by one participant is equivalent to the loss suffered by the other participant, so that the final result is always the same. Thus, each participant maximizes its result at the expense of the other.

The same principle applies to situations where there are several participants. An example of a zero-sum game is poker: a player's gain is the sum of the losses of the others.

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