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The noncooperative transportation problem and linear generalized Nash games

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  • Stein, Oliver
  • Sudermann-Merx, Nathan

Abstract

We extend the classical transportation problem from linear optimization and introduce several competing forwarders. This results in a noncooperative game which is commonly known as linear generalized Nash equilibrium problem. We show the existence of Nash equilibria and present numerical methods for their efficient computation. Furthermore, we discuss several equilibrium selection concepts that are applicable to this particular Nash game.

Suggested Citation

  • Stein, Oliver & Sudermann-Merx, Nathan, 2018. "The noncooperative transportation problem and linear generalized Nash games," European Journal of Operational Research, Elsevier, vol. 266(2), pages 543-553.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:543-553
    DOI: 10.1016/j.ejor.2017.10.001
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    Cited by:

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    2. Rahman Khorramfar & Osman Y. Özaltın & Karl G. Kempf & Reha Uzsoy, 2022. "Managing Product Transitions: A Bilevel Programming Approach," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2828-2844, September.
    3. Didier Aussel & Anton Svensson, 2019. "Towards Tractable Constraint Qualifications for Parametric Optimisation Problems and Applications to Generalised Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 404-416, July.
    4. Sagratella, Simone & Schmidt, Marcel & Sudermann-Merx, Nathan, 2020. "The noncooperative fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 373-382.
    5. Migot, Tangi & Cojocaru, Monica-G., 2020. "A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1136-1147.

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