  We propose a deep learning framework, DL-opt, designed to efficiently solve
for optimal policies in quantifiable general equilibrium trade models. DL-opt
integrates (i) a nested fixed point (NFXP) formulation of the optimization
problem, (ii) automatic implicit differentiation to enhance gradient descent
for solving unilateral optimal policies, and (iii) a best-response dynamics
approach for finding Nash equilibria. Utilizing DL-opt, we solve for
non-cooperative tariffs and industrial subsidies across 7 economies and 44
sectors, incorporating sectoral external economies of scale. Our quantitative
analysis reveals significant sectoral heterogeneity in Nash policies: Nash
industrial subsidies increase with scale elasticities, whereas Nash tariffs
decrease with trade elasticities. Moreover, we show that global dual
competition, involving both tariffs and industrial subsidies, results in lower
tariffs and higher welfare outcomes compared to a global tariff war. These
findings highlight the importance of considering sectoral heterogeneity and
policy combinations in understanding global economic competition.
