Bridging transport economics and traffic models: multi-decision-maker toll equilibration with a calibrated metamodel in full-scale networks

Designing road pricing in multi-decision-maker scenarios is computationally demanding, particularly when using full-scale traffic models. This paper presents a novel metamodel-based equilibration (MBE) scheme that leverages a fast game-theoretical metamodel to compute optimal/equilibrium tolls for an underlying setup of full-scale traffic models. MBE follows an iterative calibration–equilibration cycle: the metamodel is calibrated using full-scale outputs, game-theoretical equilibrium is computed by the metamodel, and the resulting tolls are passed back to the full-scale model, until a desirable outcome is identified. Unlike conventional surrogate approaches that approximate a single objective function, the metamodel in MBE approximates the entire transport system, thereby shifting the computational burden of toll equilibration to the metamodel, and enabling efficient analysis in multi-decision-maker settings. Applied to a real-world network with variable demand, MBE outperforms Bayesian Optimization for single-decision-maker problems and, for the first time, computes Nash and Stackelberg equilibria for multi-decision-maker problems in a full-scale traffic model.