Invariant Distributions in Nonlinear Markov Chains with Aggregators: Theory, Computation, and Applications

Unique Steady States Without Contraction in Nonlinear Stochastic Models

Many models in operations and economics describe systems whose future behavior depends not only on the current state but also on a function of the current distribution of states. In “Invariant Distributions in Nonlinear Markov Chains with Aggregators: Theory, Computation, and Applications,” Bar Light studies when such systems have a unique invariant distribution. The paper develops flexible monotonicity-based conditions that can be tailored to different models to establish uniqueness. It also shows that standard contraction arguments may fail in natural settings with strategic behavior, aggregate feedback, or interacting agents. The paper provides existence results and a simple computational method that finds an invariant distribution by solving easier subproblems. The framework applies to strategic queues, inventory systems, nonlinear equations, and wealth distributions in dynamic economies, helping identify and compute unique steady states in stochastic systems where aggregate conditions shape individual dynamics.