Designing an Adaptive Robust and Evolutionary-Game Framework for Minimum Shipment Quotas in Capacity-Constrained Freight Markets
Minimum shipment quota regulations ensure that socially critical commodities are not excluded from capacity-constrained freight markets by profit-driven allocation. Existing models of such regulation are deterministic and static, assuming perfect market knowledge and instantaneous convergence to a rational equilibrium. This paper relaxes both assumptions through a framework combining adaptive robust optimization, multi-objective optimization, and evolutionary game theory. A robust optimization model first characterizes the regulator's quota-setting problem under uncertain commodity availability, trading social welfare against enforcement cost to generate a Pareto frontier of quota policies. This frontier then defines the regulator's strategy space in a three-population evolutionary game in which the regulator, suppliers, and carrier co-evolve under replicator dynamics, so that the prevailing policy emerges from the interaction of the three players. The framework is calibrated to a Canadian rail freight case study that covers crude oil, corn, barley, and oat. Quota regulation raises social welfare from 65.0 to 288.2 million CAD, at an enforcement cost of about 2% of the gain. Two findings carry particular policy weight: capacity shortfalls fall entirely on unprotected commodities the carrier ships voluntarily, sparing both the highest-margin and the protected products; and a fall in transport cost can end the regulation while the exclusion it was designed to correct persists, because the margin observable before bidding diverges from the margin prevailing once suppliers adapt.