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<p>This article focuses on two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enables us to prove the existence of solutions (<i>u</i>,&#xa0;<i>m</i>) of the system, where <i>u</i> is a viscosity solution of the discounted Hamilton-Jacobi equation and <i>m</i> is a projected minimizing measure satisfying the continuity equation in the sense of distributions. The second is the vanishing discount problems for both the discounted mean field games system and its discretized system. The methods we use primarily derive from weak KAM theory. Moreover, we provide an example demonstrating the non-uniqueness of solutions to the discounted mean field games system.</p>

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Discretization and vanishing discount problems for first-order mean field games

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Renato Iturriaga,
  • Cristian Mendico,
  • Kaizhi Wang,
  • Yuchen Xu

摘要

This article focuses on two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enables us to prove the existence of solutions (u, m) of the system, where u is a viscosity solution of the discounted Hamilton-Jacobi equation and m is a projected minimizing measure satisfying the continuity equation in the sense of distributions. The second is the vanishing discount problems for both the discounted mean field games system and its discretized system. The methods we use primarily derive from weak KAM theory. Moreover, we provide an example demonstrating the non-uniqueness of solutions to the discounted mean field games system.