The emperor is sitting on a throne and there is an audience. You have a pool of "money" and "people". Various officials come to you and ask for resources, you decide (one by one) if to grant it or not. The trick is you don't know who will come next and how important the next request might be, so you can't determine perfectly how much mony you can still spend safely (maybe the last one will come with an info about an invasion?)
Military (fleet and land imperial infantry regiments) could be as "tokens". You don't move them on any map but "assign/borrow" to certain task (upon request). For example an official come in and says they might have detected aliens near planet X and request scout ships squadron. You would have 3 options regarding how many ships to send (if any), and then all the assigned ships will be locked (unavailable) for X days.
That really doesn't make much sense. The last person in line brining news of an invasion would likely have badgered someone with the important news, and a group of high level officials would have pushed their way to the front of the line. If they were late and came at the end anyway, then the emperor would simply whistle get everyone's attention again and say "Well, sorry chaps, all your stuff is canceled, found something more important."
May I suggest reading Dune: House Atreides (1999), Dune: House Harkonnen (2000), and Dune: House Corrino (2001)? They deal with high politics in a space empire, and may give some ideas of what can actually be done.