Strategic trade theory has been criticized on the grounds that its predictions are overly sensitive to modeling assumptions. For example, Eaton and Grossman (1986) show that Brander and Spencer's (1985) seminal result – i.e., when firms compete by setting quantities the optimal policy involves governments subsidizing their domestic industries – is reversed if the firms compete by setting prices. Applying recent results in duopoly theory, this paper considers three-stage games in which governments choose subsidies, firms' owners choose incentive schemes for their managers, and then the managers compete in the product market. We show that if firms' owners have sufficient control over their managers' behavior, then the optimal strategic trade policy does not depend on whether firms compete by setting prices or quantities. In a linear-demand model in which managers are compensated based on a linear combination of their own firm's profit plus a (possibly negative) multiple of the rival firm's profit, the optimal policy is to subsidize if goods are substitutes and tax if the goods are complements.
Miller, Nolan, and Amit Pazgal. “Strategic Trade and Delegated Competition.” KSG Faculty Research Working Papers Series RWP02-042, 2002.