IDEAS home Printed from
   My bibliography  Save this paper

Optimal Transport and Cournot-Nash Equilibria


  • Blanchet, Adrien
  • Carlier, Guillaume


We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many relevant cases. This enables us to obtain new uniqueness results and a characterisation of equilibria in terms of some partial differential equations, a simple numerical scheme in dimension one as well as an analysis of the inefficiency of equilibria.

Suggested Citation

  • Blanchet, Adrien & Carlier, Guillaume, 2012. "Optimal Transport and Cournot-Nash Equilibria," TSE Working Papers 12-321, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:26030

    Download full text from publisher

    File URL:
    File Function: Full text
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    2. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August.
    3. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    4. Le Breton, Michel & Weber, Shlomo, 2011. "Games of social interactions with local and global externalities," Economics Letters, Elsevier, vol. 111(1), pages 88-90, April.
    5. repec:dau:papers:123456789/6443 is not listed on IDEAS
    6. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," CORE Discussion Papers RP 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Adrien Blanchet & Pascal Mossay & Filippo Santambrogio, 2016. "Existence And Uniqueness Of Equilibrium For A Spatial Model Of Social Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 31-60, February.
    8. Ivar Ekeland, 2010. "Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 275-315, February.
    9. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Blanchet, Adrien & Carlier, Guillaume & Nenna, Luca, 2017. "Computation of Cournot-Nash equilibria by entropic regularization," TSE Working Papers 17-785, Toulouse School of Economics (TSE).
    2. 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).
    3. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Working Papers hal-00967662, HAL.
    4. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2013. "Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria," Papers 1307.1685,
    5. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Papers 1403.7800,
    6. Stefan Steinerberger & Aleh Tsyvinski, 2019. "Tax Mechanisms and Gradient Flows," Papers 1904.13276,
    7. 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).

    More about this item


    Cournot-Nash equilibria; mean-field games; optimal transport; externalities; Monge-Amp`ere equations; convexity along generalised geodesics;

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tse:wpaper:26030. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.