Revenue Management Games: Horizontal and Vertical Competition

A well-studied problem in the literature on airline revenue (or yield) management is the optimal allocation of seat inventory among fare classes given a demand distribution for each class. In practice, the seat allocation decisions of one airline affect the passenger demands for seats on other airlines. In this paper we examine the seat inventory control problem under both horizontal competition (two airlines compete for passengers on the same flight leg) and vertical competition (different airlines fly different legs on a multi-leg itinerary). Such vertical competition can be the outcome of a code sharing agreement between airlines, for each airline sells seats on the partner airlines’ flights but the airlines are unwilling, or unable, to coordinate yield management decisions. We provide a quite general sufficient condition under which a pure-strategy Nash equilibrium exists in these 'revenue management games', and we also compare the total number of seats available in each fare class with, and without, competition. Analytical results as well as numerical examples demonstrate that under horizontal competition more seats are protected for higher-fare passengers than when a single airline acts as a monopoly, while under vertical competition the booking limit may be higher, or lower, than the monopoly level, depending upon the demand for connecting flights in each fare class. Finally, we discuss revenue-sharing contracts that coordinate the actions of both airlines.