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Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case

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  • Blanchet, Adrien
  • Carlier, Guillaume

Abstract

This article is devoted to various methods (optimal transport, fixed-point, ordi- nary differential equations) to obtain existence and/or uniqueness of Cournot-Nash equilibria for games with a continuum of players with both attractive and repulsive effects. We mainly address separable situations but for which the game does not have a potential, contrary to the variational framework of [3]. We also present several nu- merical simulations which illustrate the applicability of our approach to compute Cournot-Nash equilibria.

Suggested Citation

  • Blanchet, Adrien & Carlier, Guillaume, 2014. "Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case," TSE Working Papers 14-491, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:28214
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    References listed on IDEAS

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    1. Blanchet, Adrien & Carlier, Guillaume, 2012. "Optimal Transport and Cournot-Nash Equilibria," TSE Working Papers 12-321, Toulouse School of Economics (TSE).
    2. 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 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.
    2. Julio Backhoff-Veraguas & Xin Zhang, 2023. "Dynamic Cournot-Nash equilibrium: the non-potential case," Mathematics and Financial Economics, Springer, volume 17, number 1, March.

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    More about this item

    Keywords

    Continuum of players; Cournot-Nash equilibria; optimal transport; best-reply iteration; congestion; non-symmetric interactions;
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