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Characterization of transport optimizers via graphs and applications to Stackelberg–Cournot–Nash equilibria

Author

Listed:
  • Beatrice Acciaio

    (ETH Zurich)

  • Berenice Anne Neumann

    (Trier University)

Abstract

We introduce graphs associated to transport problems between discrete marginals, that allow to characterize the set of all optimizers given one primal optimizer. In particular, we establish that connectivity of those graphs is a necessary and sufficient condition for uniqueness of the dual optimizers. Moreover, we provide an algorithm that can efficiently compute the dual optimizer that is the limit, as the regularization parameter goes to zero, of the dual entropic optimizers. Our results find an application in a Stackelberg–Cournot–Nash game, for which we obtain existence and characterization of the equilibria.

Suggested Citation

  • Beatrice Acciaio & Berenice Anne Neumann, 2025. "Characterization of transport optimizers via graphs and applications to Stackelberg–Cournot–Nash equilibria," Mathematics and Financial Economics, Springer, volume 19, number 3, September.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:1:d:10.1007_s11579-024-00375-x
    DOI: 10.1007/s11579-024-00375-x
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    References listed on IDEAS

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    9. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
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    More about this item

    Keywords

    Optimal transport; Connected graphs; Entropic regularization; Stackelberg–Cournot–Nash equilibria;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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