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Optimal transport and Cournot-Nash equilibria


  • Adrien Blanchet

    () (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT1 - Université Toulouse 1 Capitole - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Guillaume Carlier

    () (MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)


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

  • Adrien Blanchet & Guillaume Carlier, 2012. "Optimal transport and Cournot-Nash equilibria," Working Papers hal-00712488, HAL.
  • Handle: RePEc:hal:wpaper:hal-00712488
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    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. 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.
    5. 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.
    6. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    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. 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


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

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