A game theoretic model for airline revenue management and competitive pricing

We consider a revenue management (RM) model with two competing airlines offering one flight leg each and using fenceless fare structures. We use a simple utility model to derive the buying probabilities dependent on the fares in the market. In the first part, we simulate the competitive dynamics when the two airlines derive an elasticity forecast from the observation of their own bookings and use an exact optimisation algorithm for the monopoly problem. In the second part, we describe a game theory formulation of the problem and analyse the Nash equilibria, assuming complete information. We show that for continuous fares the game has a unique pure strategy, subgame perfect equilibrium. The results of both the simulation and the Nash equilibrium show that for larger capacities, prices will spiral down to the lowest level and that the revenue is substantially lower compared to a monopoly or cooperative situation. This is typical for one–shot games and we argue that a better model of reality would be a repeated game. For RM practitioners this means that dynamic pricing cannot be automated completely and that long–term strategies have to be supplemented by the pricing analyst.