The title essentially says it all. I am asking since I came across the following statement: “Zero-sum games are also known as games of pure conflict”. This seemed to imply that zero-sum and pure conflict are synonyms, which confuses me since I figured that all constant-sum games should be games of pure conflict, by definition. So, are all constant-sum games games of pure conflict or are there some constant sum games that do not follow this rule?
For most purposes, there is no difference between (two-player) zero-sum and constant-sum games. One usually assumes in game theory that players maximize expected utility. Payoff functions are von Neumann-Morgenstern utility functions. One does not change the preferences induced by such a payoff function if one adds or subtracts a constant. One can, therefore, transform every constant-sum game into a zero-sum game without changing preferences and behavior.