Airline revenue management games with simultaneous price and quantity competition

This paper treats airline revenue management under simultaneous price and quantity competition in a network. Within this setting, a competitor's demand is a function of his price as well as the competitor's price and booking limits. We present a model to optimize a competitor's behavior in a network revenue management game. To the best of our knowledge, our model is the first of this type. We also present an approach to compute a possibly approximate Nash equilibrium in the game assuming that the competitors make decisions based on our model. Since the model is non-linear, we compute equilibrium prices and booking limits separately. The procedure's performance is shown in a computational study. When both price competition and quantity competition are taken into account, prices as well as demands tend to increase leading to higher revenues compared to monopolistic prices.