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.

翻译：我们提出了一个深度学习框架DL-opt，旨在高效求解可量化一般均衡贸易模型中的最优政策。DL-opt整合了以下三个要素：(i) 优化问题的嵌套不动点(NFXP)表述，(ii) 用于增强求解单边最优政策的梯度下降过程的自动隐函数微分方法，以及(iii) 用于寻找纳什均衡的最优响应动态方法。利用DL-opt，我们在包含7个经济体和44个部门、并纳入部门外部规模经济的模型中，求解了非合作关税与产业补贴。我们的量化分析揭示了纳什政策中存在显著的部门异质性：纳什产业补贴随规模弹性增加而增加，而纳什关税则随贸易弹性增加而下降。此外，我们表明，与全球关税战相比，同时涉及关税和产业补贴的全球双重竞争会导致更低的关税和更高的福利结果。这些发现凸显了在理解全球经济竞争时，考虑部门异质性和政策组合的重要性。