Comput Optim Appl (2011) 50:287–326 DOI 10.1007/s10589-010-9340-8 Network capacity management under competition Houyuan Jiang · Zhan Pang Received: 22 February 2010 / Published online: 22 July 2010 © Springer Science+Business Media, LLC 2010 Abstract We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model to ad- dress the competitive network revenue management problem. These two models are based on well-known deterministic linear programming and probabilistic nonlinear programming approximations for the non-competitive network capacity management problem. We prove the existence of a Nash equilibrium for both games and investigate the uniqueness of a Nash equilibrium for the Nash game. We provide some further uniqueness and comparative statics analysis when the network is reduced to a single- leg flight structure with two products. The comparative statics analysis reveals some useful insights on how Nash equilibrium booking limits change monotonically in the prices of products. Our numerical results indicate that airlines can generate higher and more stable revenues from a booking scheme that is based on the combination of the partitioned booking-limit policy and the generalized Nash game model. The results also show that this booking scheme is robust irrespective of which booking scheme the competitor takes. Keywords Revenue management · Capacity control · Generalized Nash games · Existence · Uniqueness This paper is dedicated to Professor Liqun Qi on the occasion of his 65th birthday. H. Jiang ( ) Judge Business School, University of Cambridge, Trumpington Street, Cambridge CB2 1AG, UK e-mail: h.jiang@jbs.cam.ac.uk Z. Pang Management School, Lancaster University, Lancaster LA1 4YX, UK e-mail: z.pang@lancaster.ac.uk