LQ mean-field games on hybrid manifold graphs admit FBPDE Nash limits with high-probability tracking error O((log N)^{-1/2}) sparse and O(N^{-γ(p,s)}) dense.
Nonlinear graphon mean-field systems
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abstract
We address a system of weakly interacting particles where the heterogenous connections among the particles are described by a graph sequence and the number of particles grows to infinity. Our results extend the existing law of large numbers and propagation of chaos results to the case where the interaction between one particle and its neighbors is expressed as a nonlinear function of the local empirical measure. In the limit of the number of particles which tends to infinity, if the graph sequence converges to a graphon, then we show that the limit system is described by an infinite collection of processes and can be seen as a process in a suitable $L^2$ space constructed via a Fubini extension. The proof is built on decoupling techniques and careful estimates of the Wasserstein distance.
representative citing papers
In a linear-quadratic model with network spillovers, the continuum-limit contract approximates the finite-N optimum with error of order 1/N and remains stable to perturbations of the interaction function.
citing papers explorer
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Linear-Quadratic Mean Field Games with Hybrid Local-Global Interactions on Manifolds
LQ mean-field games on hybrid manifold graphs admit FBPDE Nash limits with high-probability tracking error O((log N)^{-1/2}) sparse and O(N^{-γ(p,s)}) dense.
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Contracting a crowd of heterogeneous agents
In a linear-quadratic model with network spillovers, the continuum-limit contract approximates the finite-N optimum with error of order 1/N and remains stable to perturbations of the interaction function.