When Is Bad “bad Enough”? a Framework for Analyzing Benefits of Coordination under Environmental Externalities

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 players own action, “opponent effect” – altering the marginal externality, or “submodular effect” strengthening the games 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.