I know a little about game theory, zero sum and positive sum games etc. I'm wondering if there is a specific term for a situation where a game is not technically zero sum but which still has similar feel to a zero sum game where cooperation is strictly worse and one person's benefit is generally at the detriment of another.
So for an example imagine a game where both players have an option to either cooperate or compete. If they cooperate each player earns X. If the compete player A earns 2X while player B earns .1X.
This game is not technically zero sum, since in the compete option player A gains more then player B looses leading to a net gain. However, it still feels similar to a zero sum game in that there is never a motivation for cooperation, the incentive is to compete, and one player's benefit always comes at another player's loss.
Is there a commonly agreed upon term for this sort of situation in game theory?