BACI-VI-Bench: A dataset of variational inequality benchmark instances for multi-agent trade-network equilibrium

This article presents BACI-VI-Bench, a processed benchmark dataset and reproducible construction pipeline that transforms CEPII-BACI product-level international trade records into finite-dimensional variational inequality instances for multi-commodity trade-network equilibrium. The source data are CEPII-BACI HS17 bilateral trade files, version V202601, covering annual exporter-importer-product flows from 2017 to 2024. The pipeline filters positive bilateral trade flows, maps six-digit Harmonized System products to commodity sectors, selects leading exporting and importing economies, aggregates values and quantities into structured flow tensors, normalizes observed trade volumes, and calibrates a Nagurney-style benchmark cost-and-price operator. The dataset provides year-level instances of dimension 500 (five commodity sectors, ten exporters, ten importers, one route) and sector-level instances of dimension 100 for five HS commodity groups: Machinery, Minerals, Chemicals, Transport Equipment, and Metals. Each variational inequality instance contains a feasible set, a calibrated operator, observed and normalized flow tensors, exporter and importer identifiers, sector labels, operator parameters, and projection residual diagnostics. The repository includes Python construction and validation scripts, benchmark characterization data for extragradient and self-adaptive inertial solvers, figures, and metadata files enabling reuse with projection, extragradient, self-adaptive variational inequality algorithms, and multi-agent reinforcement learning frameworks. The benchmark dataset was originally developed in the context of a broader study on trade-network equilibrium modeling. Nevertheless, the present data article provides a complete and self-contained description of the dataset, benchmark construction pipeline, instance format, metadata, validation procedures, and reproducibility resources, enabling independent reuse of the benchmark.