FFA can be played in a variety of modes.
Here are some examples:
1. Hunger Game style
Alliances are made before the game starts and are highly political in nature.
Teammates will have to betray eachother eventually so that there is only 1 remaining victor, but they are likely to remain allied as long as there are still other alliances out there.
I doubt many players would like FFA in Zero-K to be like that.
2. Ingame alliances with different private channels for communication
Currently, players can whisper to specific players with the ingame chat so this is a decent way to form alliances. However, it is kind of a hidden feature and I bet most players doesn't know how to use it.
Voice chat can give an advantage here as it is much easier to communicate while giving inputs to the game, but on the other hand, it can be harder to lie using voicechat rather than just text.
Zero-K used to have a cease-fire function that makes temporary allies not shoot automatically at eachother. I wish this feature was in Zero-K again. It makes the alliances much clearer and distinct.
3. Ingame alliances with only public communication.
There is no whisper function and if voice chat is used, every player has to be in the same voicechannel.
4. Lone wolf FFA.
Alliances are prohibited and kept by a code of honor/gentlemens agreement.
All forms of communication would likely be banned or considered extraneous.
Common sense strategies:
Attacking the most skilled player first and then attacking the players with the strongest position is a way to defeat the odds and give lower skilled players a chance to win. If you can't handle being teamed up on, you should never play any type of diplomatic FFA game.
If you want to maximize your chances of winning, you should never surrender in an FFA as long as you have a builder and there are more than 2 sides left.
The innate +2m +2e income that you get can be enough to get you back in the game as long as you have a con and if you can stay under the radar for long enough, you might be able to have a comeback if your opponent keeps fighting eachother.
If you trust opponents and they all agree that one player is by far the strongest, you can surrender if you want to save some time. However, if you do not trust your opponents to tell the truth or communication is non-existent, you should never surrender if you want to maximize your chances of winning.
Like with a Poker hand, how you play your hands affects your opponents strategies and how they view you throughout the game.
We might wish that each FFA game is a new fresh start, but human psychology will persist and even if you yourself can leave all old baggage behind, many can not.
Being a cockroach:
Persisting and continuing to fight have several advantages in the FFA metagame. Even if your chances of a comeback is slim to none, fighting on against the odds means players will be more scared to attack you in the future if they are not sure they can wipe you out completely. If they might get drawn into a prolonged fight, even if they managed to cripple you with a nuke for example, they have to give much more time to capture your territory which leaves them open to be backstabbed for longer.
Skilled players in Zero-K should have little trouble finishing you off if you have next to nothing left, but trying to scout the whole map for where you are and hunting you down might be costly and require a lot of attention that the player would rather use on fighting the other opponents.
However, I would not recommend trying to prolong the game if there is only you and 1 other opponent left, and it is clear to you that you will lose. You might to be able to bore your opponent to leaving and if they aren't that skilled, they might not know how to properly scout the whole map and find your cloaked units. This is likely to make people less willing to play FFA with you in the future.
Single game vendettas:
How you pursue vendettas during a single game should be consider in logical fashion and not pure anger.
If you are known to start vendettas over any slight transgression, your opponents starting next to you will see you as a higher threat and know they have to take you out before you take them out.
I would say the right time for a vendetta is when you are a dealt a crippling blow. By staying in the game and trying to do your best to tie up resources and hamper your opponents progress, your opponent will know that defeating you isn't easy and just crippling you isn't enough, but that your opponents advantage have to be so big that they can take out you swiftly before they attack you.
Border disputes over mexes can easily escalate into a vendetta if you are not careful where you are continually trading blows over a longer period of time. Consider using diplomacy and chat to resolve border conflicts but also try to keep track of your opponents strength to know how much your opponent can retaliate.
If you know your opponent is unlikely to use diplomacy to resolve border disputes, consider approaching them carefully and maybe let them have a few mexes, or on the opposite, be ready to to escalate the fight quickly so that you can retaliate in one swift blow and take them out of the game.
However, if you continually fold because your opponent is in a stronger position than you, try to convince other players that your opponent is growing out of control and to team against that opponent.
I wouldn't recommend keeping a vendetta across several games. If your nemesis knows you are coming for them, they will be prepared for your attack and it will likely cripple both of you as you try to defeat eachother while the rest of the players eco and grow their strength.
Robbing players of the win:
It is tempting to rob others of their win in FFA. However, most players find it unfun if you are just prolonging the game in a 1v1 situation and even if they leave out of boredom and you win, isn't it just a pyrrhic where none of you really enjoyed winning or valued the win itself?
Leaving while still having a strong position is also a way to cheapen the win for serious FFA players. They might dislike you for it and avoid playing FFA with you in the future. Consider how casual the players attitude is before you leave a FFA game and if you have time to actually sit out a long FFA game.
Lying and deceit:
Most people dislike being lied to even if it is a game mode or game specifically designed for it.
If you escalate your lying to a level beyond of what all of your opponents are doing, you might be targeted just because you are considered a liar. The other players might even hold a certain unspoken standard of telling the truth that you are not supposed to cross. They might hold a grudge against you in future games if you go beyond this standard.
However, more skilled FFA players are likely to have progressed their level of deceit more so that they are comfortable lying and backstabbing, and will not hold a grudge against you for being deceitful.
People are generally more comfortable telling lies through text than voice, and if you get too good at deceiving players while sounding sincere, it might even bleed off to all the future communication you share with them outside the game.
Choosing your opponents
Some FFA games are lost before they even start. If all your opponents are of the same skill level while your rating is much higher than theirs and they abide by the rule of always taking out the greatest threat first, they might make sure to eliminate you before they fight eachother. Consider waiting to play with them until more high skilled players join so you aren't singled out as easily, or just consider this game as a practice of how to be as strong of a cockroach that you can be.
If you are uncomfortable with the level of lying that some players do, consider not playing with them or try to get similar minded people to see through their lies so that they don't fall for their deceit.