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A "zero-sum game" is a reasonably well understood phrase, though often incorrectly used as "zero sum gain." The opposite of this is a "non-zero–sum game," which I find rather unwieldy. Is there a better phase than "non-zero–sum game?"

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You used the dash in the wrong place: what you have written is a (non-zero)–sum game, which makes no sense. When you start with a hyphenated word, like zero-sum, than to make another hyphenated compound, this time you use an en dash, making it a non–zero-sum game. I might be tempted to create an open compound, but non doesn’t stand alone. –  tchrist Sep 19 '12 at 2:22
    
@tchrist - copied and pasted from the wiki. The logic applied was (presumably) that the game's collective value (sum) does not balance, thus is non-zero. –  dave Sep 19 '12 at 2:44
    
Yes there is a better phrase, namely a game where there are winners and losers. –  Chris Sep 19 '12 at 6:24
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@Chris - The point of a zero-sum game is that the winner's gains are exactly offset by the loser's losses. If a pizza has 8 slices and you eat one, then someone else losses it. In a fixed budget, if you want to spend $50 on something then you have $50 less to spend on other things. –  dave Sep 19 '12 at 7:14
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3 Answers

up vote 12 down vote accepted

In addition to zero sum games, there are also positive sum games and negative sum games. See this discussion.

Positive-sum outcomes are those in which the sum of winnings and losses is greater than zero.

Negative-sum situations [are those] where the pie is shrinking. In the end, the gains and losses will all add up to less than zero.

Apparently, these are related, but different from win-win games.

Though similar, these terms differ from the terms "win-win, win-lose, and lose-lose" which refer to wins or losses relative to expectations.

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I think not. In game theory there are games where the overall outcomes have a constant sum no matter what the choices of the participants and games which have a variable sum. The former are called zero-sum games as the positive or negative constant should not affect optimal play (even if it sometime does affect real-life behaviour for psychological reasons). The latter are called non-zero-sum games. –  Henry Sep 19 '12 at 7:01
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I wouldn't be too sure a zero sum game is that well-known...

In decision theory, situation where one or more participants' gain (loss) equals the loss (gain) of other participants. Thus, a gain (loss) for one must result in a loss (gain) for one or more others. Also called constant sum game. See also negative sum game and positive sum game.

But putting aside the more "academic" overtones of the above definition, I suppose when it's used in common parlance the focus is on the fact that there's no collective gain. So the opposite is a...

Win-win game (or more often, Win-win negotiation)

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@tchrist: I never typed a single one - all cut and pasted from the links. They're by no means always hyphenated. The popup won't hurt you, and it'll go away forever once you close it. Unlike links to the M-W and OED which are much worse. –  FumbleFingers Sep 19 '12 at 2:27
    
@FumbleFingers - The context that I most hear it is not gaming theory, rather allocating a fixed number of resources. For example: balancing a budget. –  dave Sep 19 '12 at 2:47
    
@dave: Perhaps I didn't express myself well, but that's what I meant by my last paragraph. For example, when you're trying to sort out the corporate budget, every gain for one department must be balanced by a loss for another. No matter what you do, there's no overall gain or loss - you're just shuffling the same fixed amount of money around. –  FumbleFingers Sep 19 '12 at 11:04
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I'm not a gamer, so game theory is all new to me. Clearly positive-sum and negative-sum are not what you are looking for either. I came here seeking that apparently illusive opposite as well.

In my context the win/win vs. win/lose concept are close but too vague for my liking. After reading this thread I have chosen to coin (or unconsciously plagiarize) the phrase "Infinite-Sum game.

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