An effect of consumer's earlier decision to purchase a discount ticket

In this article, we consider how effect consumer's earlier decision to purchase a discount ticket will have on the competition, price and timetable, between airlines. We focus on a relationship between consumer's purchasing behavior and a competition between airlines. We consider that a consumer can purchase a ticket two times, i.e. ex-ante and ex-post, corresponding to this timing, airlines also can set their prices of tickets. The main conclusion highlighted by this article is that, in a subgame perfect equilibrium, each airline's expected profit is unique and timetable is socially optimal regardless to a consumer's purchasing behavior.