## 2 Literature Review  
Transport systems with a centralized decision-making process use the Stackelberg approach to optimize traffic flow distribution. The authors of [25] analyzed intermodal water-rail-road transport using the Stackelberg approach and an iterative algorithm. The optimization of an enterprise in the rail transport industry is presented in [26], using a two-tier approach to [PERSON]'s game theory based on efficiency maximization. The Nash equilibrium is used to optimize decentralized systems [5]. The authors of [27] suggested a cellular transmission model to find an optimal balance of the traffic flow density of a highway network in a highway network. In [28], the authors analyzed a transport system through decomposing it into local subsystems managed independently. Such subsystems often cooperate or function under conditions of mutual competition. Using both the Nash equilibrium equation and the Stackelberg approach as a numerical example, this paper proves that locally determined travel prices can be both advantageous and disadvantageous for traffic users within the entire transport system, depending on the structure of the road network and movement routes. However, in the case of parallel intercity networks [29], it was demonstrated that the application of the Stackelberg approach contributes to improving the cost efficiency of a transport process relative to the solutions obtained with the Nash equilibrium. An important element in studies of the optimization of traffic flow distribution in the transport network is determining the relationship between the value of objective functions obtained with the Nash equilibrium and the Stackelberg approach. The quotient of the objective function value for both approaches was defined as the \"Price of Anarchy\" (PoA) [30; 31; 32; 33; 34]. The authors of [35] present research on road traffic in London, Boston, and New York. The maximum PoA values for the analyzed agglomerations were 1.24-1.28,which translates into a percentage difference in the range of 24-28%. In turn, the authors of [36] analysed the road network in Singapore, followed by determining the PoA values on individual calendar days within the study period (April 2012). The results fell within the range of 1.0-2.4. Optimization of a single criterion transport process based on the time or cost criterion often leads to a reduction in adverse impacts on the environment [37; 38; 39]. The publication [40], based on the example of a perishable product distribution network, demonstrated that achieving an optimal solution for the transport time criterion could lead to a reduction in fuel consumption and CO\({}_{2}\) emissions into the atmosphere, while the authors of [41], using an example of supply chains in France, demonstrated a strong correlation between logistics costs and CO\({}_{2}\) emissions using only road transport. [PERSON] et al. [42] developed a graph convolution neural network to forecast traffic flow in urban transport networks. [PERSON] et al. [43], however, developed a long-term spatial-temporal graph convolutional fusion network model (LSTFGCN), which was validated on factual data from the Caltrans performance measurement system. In [44], a deep learning approach is presented to model traffic congestion. Using traffic data from Google Maps, a hybrid support vector machine Xception was validated. The model achieved an accuracy of 97.16%. [PERSON] et al. [45] developed a model based on Self-Organising Feature Mapping (SOFM) to categorise urban areas according to road congestion. They conducted their study using the example of the road network in the urban area of Guiyang city. [PERSON] et al. [46] proposed an approach based on Ant Colony Optimisation and Genetic Algorithm (GA) to optimise traffic light management at a road junction. In turn, [PERSON] and [PERSON] [47] developed a model based on Bayesian optimisation (BO) and Gaussian process (GP), which they used to optimise the management of the traffic signal road network in New York.