It is well-known that linear quadratic regulators (LQR) enjoy guaranteed stability margins, whereas linear quadratic Gaussian regulators (LQG) do not. In this letter, we consider systems and compensators defined over directed acyclic graphs. In particular, there are multiple decision-makers, each with access to a different part of the global state. In this setting, the optimal LQR compensator is dynamic and is similar to a classical LQG compensator; its state can be interpreted as a filter that predicts unobserved parts of the plant state. We show that when sub-controller input costs are decoupled (but there is possible coupling between sub-controller state costs), the decentralized LQR compensator enjoys similar guaranteed stability margins to classical LQR. However, these guarantees disappear when cost coupling is introduced.