4x game in space, the player runs an Empire, there is a "rebelion event". I look for a mechanic for it (I especially look for balance).

My quick idea is:

* each planet has "empire/rebel" support stat, but it does not necessarily mean which planet will rebel. When a rebelion starts a center of rebelion is choosen (randomly one of the highest rebel support planets). Then each turn each planet has a chance to switch sides based on both rebel suppot and proximity of other rebel worlds (so, even highly rebelious world will not rebel is it's in the middle of your loyal empire, but even a loyal planet might rebel if it's next/surrounded by other rebel planets (note that a planet rebelling does not mean the "people there wanted it", it does not change the empire/rebel support values, it only indicates who control the planet). Also, a loyal world can become rebelious if the rebel fleet invades it succesfully (in such case your loyal citizens there are kind of "rebels against rebels" and might do some guerilla job).

[note: it's a domino effect mechanic from Twillight Struggle if you played it]

* fleets are more problematic, one concept is each fleet has a commander/admiral that has a loyalty stat, which affects if it will rebel (but then what if all fleets rebel? it's kind of hard to balance...) Alternatively the imperial fleets always stay loyal (lame :D) and rebels get some free fleets (that they were producing secretly in order to start the rebelion) and they fight using these (it's easiest balance wise, but...)

I wonder if it may be useful to break down rebellions into sub-categories based on intrastate conflicts in the real world? Some examples:

• Military Coup
  While the planets remain loyal, some or all of the fleets rebel against your rule, and set out to wrest control of planets from you one by one.
• Populist Revolt
  A group of industrial and/or agrarian worlds revolt against the core worlds. The fleets remain loyal, but guerrilla warfare spreads quickly to nearby worlds.
• Civil War
  A subset of the planets in your empire, along with a matching subset of the fleets, attempt to secede from your empire. If you wish to prevent the secession, your only choice is all-out war.

If this 4X game is multiplayer then I would think about having the 'rebellion' effect all players equally (across that particular game if not all at the same time for all players) otherwise it is a matter of a player loosing simply because of a random factor with major effect.

For single (as well as multi) player games the likelyhood of these rebellions happening if to be a significant part of the games situation (big negative effects) then (pre)countermeasures the player can take is part of the game strategy - with player decisions as to how much resources they commit to the possibility (or to minimize its effects) -- with the usual loopholes 'easiest'/'foolproof' ways having to be designed away (or to burden the player so much that it detracts from other game elements).

I wonder if it may be useful to break down rebellions into sub-categories based on intrastate conflicts in the real world?

For the purpose of the discussion, probably yes. But I won't be able to implement more than one rebelion type (the game is not about rebelion, it's just a part of it, also it would be too troublesome to balance these - doable of course, but again, since the game is not a rebelion simulator it would be prohibitively expensive to implement). So, while we could discuss different rebelions in the end I will need just one generic rebelion mechanic.

Storyline wise I would use some sort of "usurp the throne rebelion", also "Populist Revolt" (assuming they want to become a new government) and Military Coup (since they would want to install military government) are OK (I think these 3 can be treated very similar/identical since they want to conquer the Empire from inside and become the new government).

Civil War (if we mean secession) I want to avoid. I don't want "spawning new empires due do dividing older empires" mechanic, it's not compatible with the rest of the gameplay.

If this 4X game is multiplayer then I would think about having the 'rebellion' effect all players equally

It's strictly singleplayer only.

I don't think rebellion spreads at the scale of planets. Suppose they have interstellar flight or interstellar Internet. Would there be a lot of tourism between close planets? Close in light years. Or trade. I think you need some reason for rebellion like starvation or high prices or mass poverty. Have partial rebellion in cities and that detract from efficiency or productivity. Or population, growth rate.

What penalty do you want players to incur when one of their planets "rebel"?

Do you want them to altogether lose control over that settlement, or do you want them to focus their efforts towards protecting this world?

Should they be economically crippled by this? be unable to retain ownership of their production settlements? or altogether need to murder their own kind?

Siftcoder's approach is interesting because it gives more options as to which way to go, but it could be that your game handles only one, but it needs to be chosen carefully. Remember that you're looking for more depth, not more complexity. Knowing what benefits your general gameplay scheme the best is important and should be described in full. Your OP clearly depicts what happens in terms of expected propagation, but the actual effects are very vague / loosely described.

What penalty do you want players to incur when one of their planets "rebel"?

Do you want them to altogether lose control over that settlement, or do you want them to focus their efforts towards protecting this world?

Should they be economically crippled by this? be unable to retain ownership of their production settlements? or altogether need to murder their own kind?

First of all, planets do not rebel. There is a rebelion that "takes over planets" or that "planets can join the rebelion". The focus is not on planets (like population rebelling) but on a "secret dissident organization that want to get rid of the emperor" or something like that.

Rebelion is not triggered by pop happiness (althrough it might be a factor) but is more like an event (or half event, it might happen earlier/more often if population is unhappy and there are other internal problems).

Mechanically I envision it as a "progress bar", like the strength/support of rebel forces, when it reach a certain point an open rebelion starts. Also you can set in it options before the game starts (like if you want a game when you focus on fighting rebels you can add them frequency/strenght).

The player's goal is to crush the rebelion as fast as possible (retake all planets). Prolonged rebelion is devastating (loss of prestige, which eventually leads to game over), so a stalemate means the player will eventually lose the game.

I'm not sure about "granting some planets freedom and therefore let the seceed" as an option, it is messy and would not play well with the rest of the game (I don't want to simulate "creation of new political entities/empires"), but it would make sense I guess...

Economy - I'm not sure... definitely the Empire should not get any taxes from rebelled planet, but as economy I think maybe the planets still should trade? Not sure.

"murder their own kind" - no, definitely not. It's not the population rebelling, or at least not directly and not only, it's the other factions inside the empire (like Communist "revolution", in history it was never done with the consent of the population, it's just that the population learned to live with it after it happened, but it was organized by various minor communists groups that took over the country and changed the government and the ideology).

So, I don't want the Emperor be seen as the bad guy against whom the population rises, but more like some evil dissidents brainwashing some onocent population and then with some support (partially by evil aliens myabe) they rise to dismantle the Empire, even through majority of citizens do want the empire (or at least don't care and are neutral).

Sounds something like one of the sort of random events you'd see in games like Romance of the Three Kingdoms. I think the idea is that you have things like storms, rebellion, and plagues that occur seemingly at random and as emperor you make a point of trying to prepare for them at a cost of some other element. Something like if you develop a region to have lots of farm land you get lots of food out of the region and population growth but you are prone to greater damage from a storm's flooding. The storm is going to come one day, is it worth the risk now? Are you going to be able to respond when it does?

So I guess the question is, what decisions do you plan on offering your emperor to stem the tide of rebellion's storm? How does it make being an emperor challenging or fun? Or do you just have to make sure to keep a bunch of troops camped on every planet?

(loss of prestige, which eventually leads to game over)

I'd like to hear more about this "prestige" metric. Is that some form of in-game score? What does it direct specifically? Is it responsible for winning/losing condition(s)?

"murder their own kind" - no, definitely not. It's not the population rebelling, or at least not directly and not only, it's the other factions inside the empire (like Communist "revolution", in history it was never done with the consent of the population, it's just that the population learned to live with it after it happened, but it was organized by various minor communists groups that took over the country and changed the government and the ideology).
So, I don't want the Emperor be seen as the bad guy against whom the population rises, but more like some evil dissidents brainwashing some onocent population and then with some support (partially by evil aliens myabe) they rise to dismantle the Empire, even through majority of citizens do want the empire (or at least don't care and are neutral).

But wouldn't quelling this form of rebellion incur population losses?

So I guess the question is, what decisions do you plan on offering your emperor to stem the tide of rebellion's storm? How does it make being an emperor challenging or fun? Or do you just have to make sure to keep a bunch of troops camped on every planet?

OK, let's simplify, you can't prevent rebelion. It will happen on turn 48 and you are to deal with it.

The question is how the rebelion mechanic should work?

I'd like to hear more about this "prestige" metric. Is that some form of in-game score? What does it direct specifically? Is it responsible for winning/losing condition(s)?

Quite trivial. You start with 5 prestige, you get +1 per each acquired planet and -1 for each lost planet (there are also other sources of prestige). When you reach prestige 0 you automaticly are overthrowned and replaced with "a better emperor". You lose prestige when you have negative treasury and per each turn a battle takes on the imperial capital planet (you are supposed to stop all enemies before they even reach the capital) and for each turn of prolonged rebelion (like if longer than 30 turns -1 prestige per additional turn).

But wouldn't quelling this form of rebellion incur population losses?

Yeah, sure, probably. But it's not very relevant. You are to crush the rebels (organization), not their supporters (part of the population).