Mean-field-type games on airline networks and airport queues: Braess paradox, its negation, and crowd effect

In this paper we study the performance of hub-based airline networks. We design, model and analyze the interactions using mean-field-type game theory. We identify three types of interactions between within the game: interaction between passengers, passengers-airlines, and interaction between airlines. The key mean-field terms are the traffic flow (or frequency of flights), number of people at the same slot per flight/airline. In absence of congestion, there is a dominating strategy for a designer to adopt the Hub network leading a negation of Braess Paradox. However, when the frequency of flights increases due to demand, the Hub network is no longer superior and all the links will be used, leading to an Enhanced Hub Network. At an Enhanced Hub network, higher prices (could be congestion-dependent) are charged to passengers taking the longer direct flights compared to the ones who transit via the Hub. We show that the resulting Stackelberg mean-field-type game with multiple leaders and multiple followers has an equilibrium and the equilibrium payoffs are compared in both type of networks. An analogy with communication networks is established with hybrid small base stations (femto, pico) and macro base stations. The small cell base stations help to work with low-power regime and save some energy. However, the femto cell network alone does not cover the entire area and does not dominate the market. It is shared with the enhanced macro cell.