Linear-Quadratic $N$-person and Mean-Field Games with Ergodic Cost

Martino Bardi · Fabio Simone Priuli

105 citations0/0 files storedSIAM Journal on Control and Optimization

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Stochastic processes and financial applications Game Theory and Applications Adaptive Dynamic Programming Control

Abstract

We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is ergodic. We first study the existence of affine Nash equilibria by means of an associated system of $N$ Hamilton--Jacobi--Bellman (HJB) and $N$ Kolmogorov--Fokker--Planck (KFP) partial differential equations. We give necessary and sufficient conditions for the existence and uniqueness of quadratic-Gaussian solutions in terms of the solvability of suitable algebraic Riccati and Sylvester equations. Under a symmetry condition on the running costs and for nearly identical players, we study the large population limit, $N$ tending to infinity, and find a unique quadratic-Gaussian solution of the pair of mean-field game HJB--KFP equations. Examples of explicit solutions are given, in particular for consensus problems.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 105 citations exist upstream.

References

2007Brownian Motion and Stochastic Calculus 2007Mean field games 1998Dynamic Noncooperative Game Theory, 2nd Edition 2007Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria 2006Jeux à champ moyen. I – Le cas stationnaire 2006Jeux à champ moyen. II – Horizon fini et contrôle optimal 2010Mean Field Games: Numerical Methods 2013$\epsilon$-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents

Cited by

2016Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics 2017Mean field games models of segregation 2015Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control: From Finite Horizon to Infinite Horizon 2016Stationary focusing mean-field games 2018Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints 2018

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.