Correspondence: Karl Isler, Swiss International Air Lines Ltd., P.O. Box, 8058 Zurich-Airport, Switzerland. Tel: +41 44 564 8610; Fax: +41 44 564 8699

¹Karl Isler is Head of Operations Research and Strategy at the Revenue Management, Pricing and Distribution department of Swiss International Airlines. He holds a PhD in Theoretical Physics from ETH Zurich. He developed the concepts for the integrated O&D pricing and inventory control strategy used by Swiss Airlines. His main research areas are O&D pricing and control, interface between revenue management and scheduling, schedule reliability and performance measures.

²Henrik Imhof is Head of Yield Management and Pricing at Sixt Autovermietung, www.sixt.de. He holds a PhD in Mathematics from the University of Freiburg i. Br. and has worked in airline revenue management, airline operations and IT.

Received 15 June 2008; Revised 15 June 2008; Published online 29 August 2008.

Abstract

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.