Network Capacity Management Competition

We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model for such a capacity competition problem over a network. These two models are based on well-known deterministic linear programming and probabilistic nonlinear programming approximations for the non-competitive network capacity management problem. We prove the existence of a Nash equilibrium for both games and provide conditions to ensure the uniqueness of the Nash game. Our numerical results indicate that airlines can generate higher and more stable revenues from a booking scheme that is based on the combination of the partitioned booking-limit policy and the generalized Nash game model. The results also show that this booking scheme is robust irrespective of which booking scheme the competitor takes.