Using Linear Programming and Game Theory to Optimize the relation between US and China

This paper develops an optimization model to analyze U.S.–China bilateral trade dynamics and competition in artificial intelligence (AI). First, grounded in WTO tariff limits, we formulate a linear programming model to maximize the combined trade volume and conduct a comprehensive sensitivity analysis on tariff parameters. Second, we integrate zero‑sum and non‑zero‑sum game‑theoretic frameworks to identify the Nash equilibria governing both trade negotiations and technological rivalry. The model is implemented in Python using PuLP and is empirically validated with real‑world tariff data to highlight the policy relevance of the optimal solutions. Our results reveal a high concordance between the zero‑sum game equilibrium and the linear programming optimum under constrained tariff regimes, and demonstrate that equilibrium outcomes remain robust to parameter perturbations when the tariff variation magnitude satisfies t≤3/2. These findings offer policymakers quantitative insights for formulating effective bilateral trade and AI competition strategies.