Revenue Management Games

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 the literature thus far, passenger demand is an exogenous parameter. However, 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 with two fare classes and two airlines under competition. Each airline chooses an optimal booking limit for the lower-fare class while taking into account the overflow of passengers from its competitor. We show that under certain conditions this 'revenue management game' has a pure-strategy Nash equilibrium, and for special cases we show that the equilibrium is unique. We also compare the total number of seats available in each fare class with, and without, competition. Analytical results for one special case as well as numerical examples demonstrate that, all else equal, under competition more seats are protected for higher-fare passengers than when a single airline acts as a monopoly or when airlines form an alliance to maximize overall profits.