Book excerpt: We explore the interplay of market structure and government trade policy in the context of a heterogenous goods duopoly model (allowing for goods to be substitutes or complements) wherein governments simultaneously and noncooperatively choose whether or not to provide subsidies for their firms and then firms noncooperatively choose output levels, either sequentially (i.e., in a Stackelberg leader-follower model) or simultaneously (i.e., in a Cournot-Nash model). We focus on competition in quantities but also provide results when firms compete in prices. In both the quantity and price models we further allow for endogenous market structure by considering two game forms wherein one of the firms, a potential leader, can choose to lead or not lead (play Cournot). We find that government trade policy and market structure can interact. First, the trade regime can alter traditional firm preferences over sequential versus simultaneous play. Second, different market structures can influence governments' preferences about free trade versus subsidies. Further, if one of the firms is a potential leader, allowing for endogenous market structure generates equilibrium outcomes that sometime reinforce, and sometimes counter, received results in the extant strategic trade literature. For example, when firms compete in quantities, endogenous market structure results in Cournot-Nash competition, but competition in prices results in a leader-follower structure.