Tariff Responses: A Graph-Theoretic Approach with Industry Dependencies

In response to the growing prevalence of tariffs as instruments of economic policy and strategic competition, this paper introduces a formal mathematical framework for optimizing counter-tariff strategies. We model the global trade ecosystem as a multi-layered, directed, weighted hypergraph, where vertices represent countries, industries, and subindustries, and hyperedges capture complex trade relationships and supply chain dependencies. The proposed framework employs bilevel optimization techniques to maximize strategic impact on target economies while minimizing self-inflicted economic costs. Through integration of graph theory, spectral analysis, and multilevel optimization methods, we develop a rigorous formalism that enables policymakers to identify optimal counter-tariff portfolios under various constraints. Our model explicitly accounts for industrial interdependencies, where export competitiveness depends on imported inputs, thus providing a more realistic representation of global value chains. Case studies applying our model to historical trade disputes demonstrate its capacity to generate superior strategic outcomes compared to conventional approaches. The framework’s axiomatic foundation allows for rapid recalibration in response to shifting economic conditions and policy objectives.