Is there a better phrase that means "non-zero–sum game?"

Solution 1:

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.

Solution 2:

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)