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Computing approximate Nash equilibria in general network revenue management games

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  • Grauberger, W.
  • Kimms, A.

Abstract

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.

Suggested Citation

  • Grauberger, W. & Kimms, A., 2014. "Computing approximate Nash equilibria in general network revenue management games," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1008-1020.
    • Handle: RePEc:eee:ejores:v:237:y:2014:i:3:p:1008-1020
    DOI: 10.1016/j.ejor.2014.02.045
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    Cited by:

    1. Grauberger, Waldemar & Kimms, Alf, 2016. "Revenue management under horizontal and vertical competition within airline alliances," Omega, Elsevier, vol. 59(PB), pages 228-237.
    2. Löschenbrand, Markus, 2020. "Finding multiple Nash equilibria via machine learning-supported Gröbner bases," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1178-1189.
    3. Wang, Chun-Han & Zhang, Wenzhu & Dai, Yue & Lee, Yu-Ching, 2022. "Frequency competition among airlines on coordinated airports network," European Journal of Operational Research, Elsevier, vol. 297(2), pages 484-495.
    4. W. Grauberger & A. Kimms, 2018. "Computing pure Nash equilibria in network revenue management games," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 481-516, March.
    5. Zhao, Xuan & Atkins, Derek & Hu, Ming & Zhang, Wensi, 2017. "Revenue management under joint pricing and capacity allocation competition," European Journal of Operational Research, Elsevier, vol. 257(3), pages 957-970.

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