The human nature is not always direct. So, it's not always clear what the stakes are. Sometimes stakeholders communicate them directly, most of the time they don't. The level of communication is indirect; stakes are contained in requirements made to the project, process and products. Requirements are always a clearly defined state that is desired. This is in contrast with stakes, which are generally vague and abstractly formulated (if formulated at all).

An oversimplified example: a stake of a programmer is "to be also involved in way cool new technologies like my brother-in-law", say Java; the corresponding requirement could be that "the system can only be programmed in Java". The requirement can be stated surrounded by other technical arguments, but it's only the stake mentioned that caused it to appear.

So, the project manager has this project, surrounded by requirements he has to take care of. But, remind yourself, they are not the stakes, they are not the crown jewels you may not touch. So you can mess with the requirements? Can you?

Related links
Project Management Communications Bible
Communication Failures between Team Members