A lot of people and documents online say that positive-sum games are "win-wins", where all of the participants are better off. But this isn't true! If A gets $5 and B gets -$2 that's positive sum (the sum is $3) but it's not a win-win (B lost). Positive sum games can be win-wins, but they aren't necessarily games where everybody benefits. I think people tend to over-generalize from the most common case of a win-win.

E.g. some of the claims you see when reading about positive-sum games online:

There's LLM-written text here. Google AI Overview writes:

A positive-sum game is a "win-win" scenario in game theory and economics where participants collaborate to create new value, ensuring all parties can gain or benefit.

[Win-win games are] also called a positive-sum game as it is the opposite of a zero-sum game. – Wikipedia

Here I use "positive-sum game" to refer to resource games that involve allocating resources, not allocating utility. "Positive-sum game" isn't a meaningful thing when referring to utility because the utility of each participant can be individually rescaled, so you can turn any game into one with an arbitrary sum; the sign of the sum doesn't matter.

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