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One-Dimensional Stationary Mean-Field Games with Local Coupling

Author

Listed:
  • Diogo A. Gomes

    (King Abdullah University of Science and Technology (KAUST))

  • Levon Nurbekyan

    (King Abdullah University of Science and Technology (KAUST))

  • Mariana Prazeres

    (King Abdullah University of Science and Technology (KAUST))

Abstract

A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.

Suggested Citation

  • Diogo A. Gomes & Levon Nurbekyan & Mariana Prazeres, 2018. "One-Dimensional Stationary Mean-Field Games with Local Coupling," Dynamic Games and Applications, Springer, vol. 8(2), pages 315-351, June.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:2:d:10.1007_s13235-017-0223-9
    DOI: 10.1007/s13235-017-0223-9
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    References listed on IDEAS

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    1. Alessio Porretta, 2014. "On the Planning Problem for the Mean Field Games System," Dynamic Games and Applications, Springer, vol. 4(2), pages 231-256, June.
    2. P. Cardaliaguet, 2013. "Long Time Average of First Order Mean Field Games and Weak KAM Theory," Dynamic Games and Applications, Springer, vol. 3(4), pages 473-488, December.
    3. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
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    Cited by:

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    2. Diogo Aguiar Gomes & Ricardo de Lima Ribeiro, 2021. "Stationary mean-field games with logistic effects," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-34, February.

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