In a “zero-sum” situation, one person’s gain requires someone else’s loss. If three people are equally sharing a six-slice pizza, each person would have two slices. If one person gets three slices, someone else would only get one slice.

The sum of the changes — a gain of one slice for one person, a loss of one slice for the other — is zero.

Growing hair, to pick an odd example, is not a “zero-sum” problem. Your ability to grow more hair does not depend on someone else losing theirs.

This is often applied in economics to make the point that prosperity for one does not necessarily mean losses for another, if the economy in general is growing.

A zero sum game is where for every winner there is a corresponding loser.

That expression (Not a Zero Sum) means that in a particular conflict both sides can emerge happy (like cutting a donut in half so each person gets some or letting someone read the Sunday paper Sports section while you read the Entertainment section).

It is not for situations where you have two apples and agree to share. It is more for situations where you have an apple and I have an apple but you want both apples. No good will can come out of that.

Think of a custody battle over a child or some other situation where there is a clear winner and a clear loser and both really care about the outcome.

Zero Sum Problem

In game theory, zero-sum describes a situation in which a participant’s gain or loss is exactly balanced by the losses or gains of the other participant(s). It is so named because when the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Chess and Go are examples of a zero-sum game: it is impossible for both players to win. Zero-sum can be thought of more generally as constant sum where the benefits and losses to all players sum to the same value. Cutting a cake is zero- or constant-sum because taking a larger piece reduces the amount of cake available for others. In contrast, non-zero-sum describes a situation in which the interacting parties’ aggregate gains and losses is either less than or more than zero.

I think you have it. A zero-sum problem in game theory is where any gains by one participant has to met by equivalent losses by another participant. If you add in the goodwill you recieve as a value of half an apple (just as an example). Then you gave me two apples which makes me +2 in apples, and you’re only -1.5 in apples counting the goodwill I give you.

Our gains and losses don’t balance out to zero, and thus “it’s not a zero-sum problem”

The term comes from game theory. Imagine that you and a friend are playing a game. Each of you has two choices in the game, “fight” or “don’t fight.” If you both choose “don’t fight,” you each win one point. If you both choose “fight,” you each lose two points. If one person chooses “fight” and the other chooses “don’t fight,” the fighter receives two points and the nonfighter loses two points. The points may vary with the game. The players learn to cooperate and not fight, because you win points continually; however, there is a big reward for suddenly fighting while the other person isn’t. If you fight too often, the other person fights, too, and there is a big penalty.

Finally, to your question. In a situation where several persons are in a position to receive rewards, there is a “zero sum problem” if whatever is won by one person must be lost by another. The alternatives to “zero sum” are “win-win” and “lose-lose” situations.

In mathematics, “zero-sum problem” means a problem where the answer is zero.

In usages like negotiation and politics, “zero-sum problem” refers to a problem where no matter how you resolve it, someone will win and someone else will lose. When you combine the benefits and costs for everyone, it comes out roughly even: “zero-sum.”

To say “it’s not a zero-sum problem,” then, means that there IS a way to resolve a situation so that **everyone** benefits, instead of having some people come out as winners and some as losers.