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Cournot-Nash equilibrium and optimal transport in a dynamic setting

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  • Beatrice Acciaio
  • Julio Backhoff-Veraguas
  • Junchao Jia

Abstract

We consider a large population dynamic game in discrete time. The peculiarity of the game is that players are characterized by time-evolving types, and so reasonably their actions should not anticipate the future values of their types. When interactions between players are of mean-field kind, we relate Nash equilibria for such games to an asymptotic notion of dynamic Cournot-Nash equilibria. Inspired by the works of Blanchet and Carlier for the static situation, we interpret dynamic Cournot-Nash equilibria in the light of causal optimal transport theory. Further specializing to games of potential type, we establish existence, uniqueness and characterization of equilibria. Moreover we develop, for the first time, a numerical scheme for causal optimal transport, which is then leveraged in order to compute dynamic Cournot-Nash equilibria. This is illustrated in a detailed case study of a congestion game.

Suggested Citation

  • Beatrice Acciaio & Julio Backhoff-Veraguas & Junchao Jia, 2020. "Cournot-Nash equilibrium and optimal transport in a dynamic setting," Papers 2002.08786, arXiv.org, revised Nov 2020.
    • Handle: RePEc:arx:papers:2002.08786
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    References listed on IDEAS

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    1. Blanchet, Adrien & Carlier, Guillaume, 2014. "From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem," TSE Working Papers 14-490, Toulouse School of Economics (TSE).
    2. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    3. Daniel Lacker & Kavita Ramanan, 2019. "Rare Nash Equilibria and the Price of Anarchy in Large Static Games," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 400-422, May.
    4. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
    5. Adrien Blanchet & Guillaume Carlier, 2016. "Optimal Transport and Cournot-Nash Equilibria," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 125-145, February.
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    Cited by:

    1. Daniel Krv{s}ek & Gudmund Pammer, 2024. "General duality and dual attainment for adapted transport," Papers 2401.11958, arXiv.org.

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