Invariant Distributions in Nonlinear Markov Chains with Aggregators: Theory, Computation, and Applications
研究了未来行为依赖当前状态和状态分布函数的非线性随机系统何时存在唯一不变分布。提出基于单调性的条件、存在性结果和简化子问题的计算方法，适用于战略排队、库存系统、动态经济中的财富分布等，帮助识别和计算稳态。
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.