A semi-discrete approximation for first-order stationary mean field games

2021/11/23 by Renato Iturriaga, Iturriaga, Renato, Kaizhi Wang +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Quantum chaos and dynamical systems #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2111.11972

openalex publication_date 2021/11/23 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28

Abstract

We provide an approximation scheme for first-order stationary mean field games with a separable Hamiltonian. First, we discretize Hamilton-Jacobi equations by discretizing in time, and then prove the existence of minimizing holonomic measures for mean field games. At last, we obtain two sequences of solutions \u_i\ of discrete Hamilton-Jacobi equations and minimizing holonomic measures \m_i\ for mean field games and show that (u_i,m_i) converges to a solution of the stationary mean field games.

Citations

• Action minimizing invariant measures for positive definite Lagrangian systems

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