Coagent networks formalize the concept of arbitrary networks of stochastic agents that collaborate to take actions in a reinforcement learning environment. Prominent examples of coagent networks in action include approaches to hierarchical reinforcement learning (HRL), such as those using options, which attempt to address the exploration exploitation trade-off by introducing abstract actions at different levels by sequencing multiple stochastic networks within the HRL agents. We first provide a unifying perspective on the many diverse examples that fall under coagent networks. We do so by formalizing the rules of execution in a coagent network, enabled by the novel and intuitive idea of execution paths in a coagent network. Motivated by parameter sharing in the hierarchical option-critic architecture, we revisit the coagent network theory and achieve a much shorter proof of the policy gradient theorem using our idea of execution paths, without any assumption on how parameters are shared among coagents. We then generalize our setting and proof to include the scenario where coagents act asynchronously. This new perspective and theorem also lead to more mathematically accurate and performant algorithms than those in the existing literature. Lastly, by running nonstationary RL experiments, we survey the performance and properties of different generalizations of option-critic models.