Computing Stationary Equilibria in Measure-Dependent Markov Systems
Abstract
Many stochastic systems in operations and economics exhibit feedback between their long-run state distribution and the transition law governing their dynamics. In this paper, we develop a computational framework for stationary equilibria in such measure-dependent Markov systems when this feedback operates through a finite-dimensional aggregate. We show that the original stationary-equilibrium problem can be reduced to a finite-dimensional self-consistency equation, separating steady-state analysis of the underlying Markov system from equilibrium computation. We use properties of the resulting self-consistency map to guide the choice among fixed-point iteration, relaxed fixed-point iteration, and minimization of the fixed-point residual. The last approach requires derivatives of the self-consistency map, which are typically unavailable in closed form. We therefore develop finite-time infinitesimal perturbation analysis estimators for these derivatives, with error bounds that separate Monte Carlo error from finite-time bias. We illustrate the framework through a strategic G/G/c queue and an opinion-dynamics model, showing how different structural properties lead naturally to different equilibrium-computation methods.
Related
- Computing Multi-Slot First-Price Pacing Equilibria at Scale via Entropic Smoothing
- Computing Equilibria in Integer Programming Games with Shared Constraints
- A Fast and High-Accuracy Finite-Time Sliding-Mode Algorithm for Computing Local Stackelberg Equilibria in Nonlinear Bilevel Games
- Computing Equilibria in Simulation-Based Insurance Markets with Discontinuous Demand
- The Laplace transform of the stationary measure of the open KPZ equation in the shock region
BibTeX
@misc{dong2026computing,
title = {{Computing Stationary Equilibria in Measure-Dependent Markov Systems}},
author = {Jing Dong and Bar Light and Xin Tong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17584},
eprint = {2609.17584},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17584},
}
RIS
TY - UNPB
TI - Computing Stationary Equilibria in Measure-Dependent Markov Systems
AU - Jing Dong
AU - Bar Light
AU - Xin Tong
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.17584
UR - https://arxiv.org/abs/2609.17584
AB - Many stochastic systems in operations and economics exhibit feedback between their long-run state distribution and the transition law governing their dynamics. In this paper, we develop a computational framework for stationary equilibria in such measure-dependent Markov systems when this feedback operates through a finite-dimensional aggregate. We show that the original stationary-equilibrium problem can be reduced to a finite-dimensional self-consistency equation, separating steady-state analysis of the underlying Markov system from equilibrium computation. We use properties of the resulting self-consistency map to guide the choice among fixed-point iteration, relaxed fixed-point iteration, and minimization of the fixed-point residual. The last approach requires derivatives of the self-consistency map, which are typically unavailable in closed form. We therefore develop finite-time infinitesimal perturbation analysis estimators for these derivatives, with error bounds that separate Monte Carlo error from finite-time bias. We illustrate the framework through a strategic G/G/c queue and an opinion-dynamics model, showing how different structural properties lead naturally to different equilibrium-computation methods.
ER -