{"ID":22920847,"CreatedAt":"2026-09-17T01:02:08.507062015Z","UpdatedAt":"2026-09-17T08:01:51.988411856Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.17584","arxiv_id":"2609.17584","title":"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.","short_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 fin...","url_abs":"https://arxiv.org/abs/2609.17584","url_pdf":"https://arxiv.org/pdf/2609.17584v1","authors":"[\"Jing Dong\",\"Bar Light\",\"Xin Tong\"]","published":"2026-09-10T08:07:49Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"math.PR\"]","methods":"[]","has_code":false}