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Competition with high number of agents and a major one

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  • In the framework of mean field game theory, a new optimization problem is presented by adding an additional player, called the principal. After introducing a proper payoff for the principal, continuity and existence of minimum is proved. Some considerations about uniqueness and possible ways of continuing the analysis of this problem are given.
    Mathematics Subject Classification: Primary: 35Q91, 35Q70; Secondary: 91A13.

    Citation:

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  • [1]

    Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta, Meand field games: Numerical methods for the planning problem, SIAM J. Control Optim., 50 (2012), 77-109.doi: 10.1137/100790069.

    [2]

    M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems and Control: Foundations and Applications. Birkhauser Boston Inc., Boston, MA, 1997.doi: 10.1007/978-0-8176-4755-1.

    [3]

    T. BorgersAn introduction to the Theory of Mechanism Design, 2015. doi: 10.1093/acprof:oso/9780199734023.001.0001.

    [4]

    P. CardaliaguetNotes on Mean Field Games, 2012.

    [5]

    H. Gintis, Game Theory Evolving, Princeton University Press, 2009.

    [6]

    O. Guéant, J. M. Lasry and P. L. Lions, Mean field games and applications, 2009.

    [7]

    M. Lasry and P. L. Lions, Jeux à champ moyen. I. Le cas stationaire, C. R. Math.Acad. Sci. Paris, 343 (2006), 619-625.doi: 10.1016/j.crma.2006.09.019.

    [8]

    M. Lasry and P. L. Lions, Jeux à champ moyen. II. Horizon fini et controle optimal, C. R. Math.Acad. Sci. Paris, 343 (2006), 679-684.doi: 10.1016/j.crma.2006.09.018.

    [9]

    J. M. Lasry and P. L. Lions, Mean field games, Japanese Journal of Mathematics, 2 (2007), 229-260.doi: 10.1007/s11537-007-0657-8.

    [10]

    J. M. Lasry and P. L. LionsCours du College de France, 2009.

    [11]

    S. Perkins and D. S. Leslie, Stochastic fictitious play with continuous action sets, Journal of Economic Theory, 152 (2014), 179-213.doi: 10.1016/j.jet.2014.04.008.

    [12]

    A. Porretta, Weak solutions to Fokker Planck equations and mean field games, Archive for Rational Mechanics and Analysis, 216 (2015), 1-62.doi: 10.1007/s00205-014-0799-9.

    [13]

    D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer Verlag, 1979.

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