Price of Airline Frequency Competition

Frequency competition influences capacity allocation decisions in airline markets and has important implications to airline profitability and airport congestion. Market share of a competing airline is a function of its frequency share and the relationship between the two is pivotal for understanding the impacts of frequency competition on airline business. Based on the most commonly accepted form of this relationship, we propose a game-theoretic model of airline frequency competition. We characterize the conditions for existence and uniqueness of a Nash equilibrium for the 2-player case. We analyze two different myopic learning dynamics for the non-equilibrium situations and prove their convergence to Nash equilibrium under mild conditions. For the N-player game between identical players, we characterize all the pure strategy equilibria and identify the worst-case equilibrium, i.e. the equilibrium with maximum total cost. We provide an expression for the measure of inefficiency, similar to the price of anarchy, which is the ratio of the total cost of the worst-case equilibrium to the total cost of the cost minimizing solution and investigate its dependence on different parameters of the game.