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This paper addresses the problem of determining when coordination is beneficial. I describe a negative externality game containing a "worsening parameter" and develop a framework linearizing this parameter for tractable examination. The worsening parameter can be classified according to "own effect" -- changing the marginal utility of a player's own action, "opponent effect" -- altering the marginal externality, or "submodular effect" – strengthening the game's submodularity. Using this framework, I examine the sufficient conditions for parameter changes to move non-cooperative and cooperative solutions in opposite directions. In a symmetric game, an increase in own effect will increase the distance between utility and action level of the non-cooperative and cooperative solutions. In a non-symmetric game, there are sufficient conditions on the second derivatives which give this pattern as well. I argue that situations behaving in this manner have more benefit to coordination through the increased range in actions.
