An airline seat allocation game

We examine a seat allocation game between two airlines for flights with two fares with dependent random demands. The strategic variable of this game is each airline's booking limit for the low fare. We have shown that there exists an equilibrium booking strategy such that both airlines will protect the same number of seats for the full fare and the total number of seats available for the discount fare under competition is smaller than the total number of seats that would be available if the two airlines collude. A numerical example is used to illustrate the equilibrium solutions and to examine the impact of the capacity shares and the level of dependency between random demands.