The theoretical and quantitative analysis of trade wars is grounded in a relatively narrow treatment of optimal tariff theory and non-cooperative Nash equilibria. The lynchpin of this analytical framework is the assumption that trade policymakers are rational and have a simple well-established objective function to optimize. We argue that the preferred specification of this objective function ignores inequality at its peril. Working with a numerical model, we show that including equity (a primary focus of the earlier literature) as a determinant of social welfare can substantially change the noncooperative Nash outcome. In addition, when policy-makers do not meet the core assumption of rationality on trade policy, the economic outcomes of trade wars may also be very different from what estimates grounded in optimal tariff theory would suggest.