what are the pros & cons of military alliance vs vassals vs empire

[Dweller Beyond the Threshold]

So 3 forms of coalition with/between AIs
- military alliance: common enemies, but no shares of income, no tribute. Your ally may seek peace with your common enemy.
- vassal: you get part of their income, you can force them to war against the enemy, vassal has little autonomy
- join empire: never really understood the point of this. What's the advantage of doing this over the other two?

[GamerCH]

You can annex their settlements in an empire.

[Dweller Beyond the Threshold]

Originally posted by Ivanka 46th:

You can annex their settlements in an empire.

Thanks, is that the only advantage? If so that's kinda useless for me right now... since I'm the one actually giving my ally territories that I find are hard to defend and make the AI rule them for me instead.

[GamerCH]

In an empire you can also kick others out, annex them in one go, distribute money.

I don't know too much about it.

[nullpo]

Military alliance: most non binding, member can ask help in war and can declare alliance war where every member join. No economic advantage

Vassalage: economic benefit for master in return for vassal protected by master. Master can ask vassal for help in war and they must accept

Empire:all member (including emperor) submit a percentage of their income, then emperor distribute the income to all member. Back then it's 80 percent so emperor always lose money by forming empire with weak state, but they change it now to i think 60 or 40 percent so emperor can afford forming empire with smaller state. Emperor can annex county of other member and only emperor can invite member. War is seperate for each member but can ask help.

[Geroiko]

Some general downsides is that as you progress from nothing to coalition, coalition to military alliance, military alliance to empire, it gradually becomes more difficult for the AI to accept to join such a diplomatic relation as there are more negative modifiers for the AI associated with joining more advanced diplomatic relations. You are also getting indirectly more hated by the enemies of your allies for signing deals with them, so in due time, you will end up getting declared war on for allying with their enemies (keep in mind that this applies to any diplomacy, not just coalitions and stuff, even trade suffices for them to start hating you gradually).

Empire's strong point compared to coalition and military alliance is that the other members / subjects in your empire are paying a tribute to you, so you are making easy money. Downside, as mentioned above, is that it's way way harder to convince AI to join it, and also this is a diplomatic option that becomes available way way later in the game once you become one of the 3 kingdoms, so it's out of the question for the biggest part of the game compared to the other two options.

Vassals is the budget version of empire that is available from early in the campaign. The main downside is that vassals tend to be weak and due to that they are declared war by numerous other factions, so you will have to choose to either defend them (which results in you being more respectable / honourable, i.e. better diplomatic standing), or reject to defend your vassal which leads to their independence and potentially you becoming treacherous which lowers your diplomatic standing.

Practically speaking, vassals are more valuable than anything else because of the money you get from them which can propel your economy early on. If they are in close proximity and you give them some land, then they can become valuable militarily too, but that will depend on the personality of the leader (i.e. if it is a leader with pacifist or defensive personality, don't expect much). Another benefit of giving your vassals land you conquer is that you lower the corruption in your faction's commanderies, because corruption increases with the more land you directly own. If you are not planning to develop certain commanderies, it's way more beneficial to sell them to your vassal for gold per turn, because keep in mind that your vassals pay you tribute based on their economy, so the larger they are the more money you make off them. Also it's not optimal to develop poor and under-developed commanderies from scratch (unless it's your starting commandery or the ones you can capture in your first few turns), because the amount of turns it will take to develop them and make a return on investment is going to be not cost-effective unless you drag your campaign for too long.

Overall, only thing you should consider with vassals is proximity (for the most part opt to vassalize factions close to you, not that far away dude that you cannot trade land with or utilise as meat-shield) and your willingness to be dragged into wars to defend your vassal in exchange for the money you make out of them.

[Dweller Beyond the Threshold]

I see, thanks for the detailed explanations everyone. I'm still not quite sure given my situation, if empire would be helpful.
I'm playing as Liu Bei, it's 215 and I have 2/4 of the land with two imperial capitals, Cao Cao (the other emperor) has 1.5/4, and Yuan Shu (my ally) has 0.5/4. Yuan Shu is sitting between us and his war efforts against Cao Cao is pretty essential for me as he draws a lot of Wei armies away and occasionally also manages to take a few cities or two from Wei.
However, the little **** sued for peace with Wei during a very critical stage of the war which allowed Wei to direct few massive armies back against me. I want Yuan to go back to war but he doesn't want to. He also refuses to be my vassal (-2.5 only though) even though our affinity is at 400+ because I give him a lot of the lands I conquered that are hard to defend.
So right now the only option is keeping the alliance or moving to empire (which he wants), but even after seeing those answers, it doesn't seem forming an empire will help my situation since the wars and peace are separate.
Is there any way I can make Yuan Shu my vassal? I want to know how the points in favor/against a proposal are calculated and can be increased (I already give him lots of money and food per turn)