Abstract
In the airline market, companies compete on the right to use a limited number of airport slots at specific times to increase their own market share and squeeze out the others. This ongoing airport slot competition, which is also closely related to the airline frequency competition, is an important part of the business strategy of airline companies. We establish a departure-airport-based equilibrium programming model, which computes the exact flight-frequency equilibrium solution to analyze the profitability of airlines. The profits of all airlines are affected by the frequencies of flights that are adjusted simultaneously by all airlines. Under the Nash equilibrium solution, no airline can increase profits by unilaterally changing the flight frequency. We derive the equilibrium formula from the Karush-Kuhn-Tucker (KKT) condition, a necessary and sufficient optimality condition of the profits maximizing problem for individual airlines. Then, we concatenated the KKT conditions of all airlines and formed the equilibrium programming model, which means that the optimality for all airlines is simultaneously held. The real-data numerical studies for two different scenarios, aimed at satisfying the market demand and restricting the total number of flights, both indicate that the airlines should concentrate and fly more frequently along higher lucrative routes. The equilibrium programming model is scalable for setting a game from between airlines to between alliances and from one airport to a network containing multiple airports. Finally, we conducted an empirical equilibrium analysis for different scales of the competition. Keywords: airline competition, slot competition, slot reduction, game theory, Nash Equilibrium, takeoff slots