I think that’s a weird take. A cooperation game typically has actions where you lose, but others gain more (whatever actions others take). Prisoner’s Dilemmas and public goods games are simple examples. The only wrinkle is “what counts as more” if you take seriously the idea that utility is non-comparable across persons. But a weaker criterion is just “everyone would be better off if everyone cooperated”, which again the PD and public goods games satisfy.
I think that’s a weird take. A cooperation game typically has actions where you lose, but others gain more (whatever actions others take). Prisoner’s Dilemmas and public goods games are simple examples. The only wrinkle is “what counts as more” if you take seriously the idea that utility is non-comparable across persons. But a weaker criterion is just “everyone would be better off if everyone cooperated”, which again the PD and public goods games satisfy.