# Stochastic Comparative Statics in Markov Decision Processes

arXiv: https://arxiv.org/abs/1904.05481 · HTML: https://mlsanity.com/paper/1904.05481/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [Operator-Theoretic Foundations and Policy Gradient Methods for General MDPs with Unbounded Costs](https://mlsanity.com/paper/2603.17875/) (2026)

## Abstract (arXiv)

In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes as a function of the dynamic optimization parameters in the context of Markov decision processes. We call this analysis stochastic comparative statics. We derive both comparative statics results and stochastic comparative statics results showing how the current and future optimal decisions change in response to changes in the single-period payoff function, the discount factor, the initial state of the system, and the transition probability function. We apply our results to various models from the economics and operations research literature, including investment theory, dynamic pricing models, controlled random walks, and comparisons of stationary distributions.