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Computation of Cournot-Nash equilibria by entropic regularization

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  • Blanchet, Adrien
  • Carlier, Guillaume
  • Nenna, Luca

Abstract

We consider a class of games with continuum of players where equilibria can be obtained by the minimization of a certain functional related to optimal transport as emphasized in [7]. We then use the powerful entropic regularization technique to approximate the problem and solve it numerically in various cases. We also consider the extension to some models with several populations of players.

Suggested Citation

  • 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).
    • Handle: RePEc:tse:wpaper:31576
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    References listed on IDEAS

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    1. 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.
    2. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    3. Adrien Blanchet & Guillaume Carlier, 2016. "Optimal Transport and Cournot-Nash Equilibria," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 125-145, February.
    4. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    6. 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).
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    Cited by:

    1. Omar Besbes & Francisco Castro & Ilan Lobel, 2021. "Surge Pricing and Its Spatial Supply Response," Management Science, INFORMS, vol. 67(3), pages 1350-1367, March.
    2. 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.

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    Keywords

    Optimal transport; entropic regularization; Cournot-Nash equilibria;
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