Computing approximate Nash equilibria in general network revenue management games

•A network revenue management problem under competition is studied.•Booking limits for competing airlines are computed.•A heuristic for computing an approximate Nash equilibrium is introduced.•Payoff values are computed on demand, i.e. there is no need to provide the complete playoff matrix in advan...

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Bibliographic Details
Published in:European journal of operational research 2014-09, Vol.237 (3), p.1008-1020
Main Authors: Grauberger, W., Kimms, A.
Format: Article
Language:English
Subjects:
Algorithmic game theory
Allocations
Approximate Nash equilibria
Approximation
Competition
Computation
Equilibrium
Game theory
Heuristic
Management
Mathematical analysis
Network revenue management
Networks
Resource allocation
Revenue management
Revenues
Studies
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Summary:•A network revenue management problem under competition is studied.•Booking limits for competing airlines are computed.•A heuristic for computing an approximate Nash equilibrium is introduced.•Payoff values are computed on demand, i.e. there is no need to provide the complete playoff matrix in advance. Computing optimal capacity allocations in network revenue management is computationally hard. The problem of computing exact Nash equilibria in non-zero-sum games is computationally hard, too. We present a fast heuristic that, in case it cannot converge to an exact Nash equilibrium, computes an approximation to it in general network revenue management problems under competition. We also investigate the question whether it is worth taking competition into account when making (network) capacity allocation decisions. Computational results show that the payoffs in the approximate equilibria are very close to those in exact ones. Taking competition into account never leads to a lower revenue than ignoring competition, no matter what the competitor does. Since we apply linear continuous models, computation time is very short.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2014.02.045