It seems unfortunate that “zero sum” is the term of art. Utility functions are only meaningful up to (positive) scalar multiplication and a constant. So, zero-sum games can be constant-sum if we add a constant to someone’s utility function, or ever variable sum if we multiply one of the player’s utility functions by a constant. “adversarial games” or “(purely) competitive games” or something like that would be more descriptive.
It seems unfortunate that “zero sum” is the term of art. Utility functions are only meaningful up to (positive) scalar multiplication and a constant. So, zero-sum games can be constant-sum if we add a constant to someone’s utility function, or ever variable sum if we multiply one of the player’s utility functions by a constant. “adversarial games” or “(purely) competitive games” or something like that would be more descriptive.