You mean a game with no end, where you're just continually playing? No... No nothing like that exists in the fashion you mean (esp. with the 'coming and going as you please).

But arguably you could make a game where no one ever agrees to draw. It could potentially continue indefinitely. (i.e through stalemate lines and stubborn players)

Why play if there is no chance to win. And if no winners then no losers. It would be a waste of time. Its really not diplomacy either. It reminds me of an online game called imaginations where you ruled an imaginary nation. Not my cup of tea.

They tried a pacifist variant once over on the other site. I got in six hundred and sixty six kinds of trouble for moving and showing how fucked up the idea was.

We played an "Extreme Personalities" game here 'for entertainment value only'. We used the Known World 901 variant and had a moderator alot 'extreme personalities' at random for everyone from the list below. The idea was just to get wild and crazy with your character and see what develops. Spain, for example, was awarded Pirate Pete, a character who "swears all the time, builds at least one fleet when he can during the builds phase, and doesn't move to any inland SC's or territories. Tends to raid coastal SC's and sees no issues moving on." And Spain was frickin hilarious (about 10x as funny as Johnny Depp in Pirates), though many players were pretty good, including a few who had very little to work with, like the player who "always screws up his orders." We played for quite a while. A few people did get eliminated, or eliminate themselves, and then we finally called a draw.

EXTREME PERSONALITY LIST

1. Wanna-rule-the-world dictator.
2. Believes non-existent players are about to attack him and others.
3. Tries to seize a totally obscure part of the board without regard to normal gameplay.
4. Believes they're a major religious figure - Jesus/Buddha/Mohammad/your own cult etc.
5. Think you're the megalomaniac historical figure of the country you represent - Hitler, Napoleon, insert name of relevant crazy person who's run that country before (Discussion on if we draw that, should one be forced to fight like that person too? I mean it's all fine and dandy if someone's pretending to be Hitler, but if they then make an alliance with France, where's the "crazy" part you know? So Hitler would form an A/I/G (or attempt to) etc.).
6. Think you're a famous entertainer - you pick who it could be, past or present, e.g., Elvis, Lady Gaga, member of the Village People, etc. (suggested that you could be the whole group of the Village People, etc.).
7. Vendetta - makes up a reason to hate a particular country and weaves it into a story. Tries to get the rest of the board to help them gain their objective. Kinda goes with the fixated on a specific part of the map idea.
8. Paranoid - This person doesn't really trust anyone and will stab/protect from stabs that either don't exist, or wouldn't make sense to go through with because everyone's "out to get them".
9. Extremist Group - Your crazy extremist group has grabbed control of the government. Think Westboro Baptist Church if you're a christian nation, or Al Qaeda if you're Turkey. Or it could be as silly as PETA or Greenpeace seizing a nation's leaders.
10. Self-Loather - The character actually hates his country/loves another country more, e.g., he's English but wants to be French: he emulates another player, their culture, etc., and does everything he can to support that country. How does he deal with a stab? Who knows? That's the fun part of being crazy.
11. Grossly incompetent character who always f^cks up. Basically you'd put in your orders the way you planned, but would then have to deliberately go back and screw up one of the orders. e.g.:

France (the f^ck up) wants to:

A Marseilles -> Spain
A Paris -> Burgandy
F Brest -> MAO

Has to (randomly?) screw up an order so F Brest->Picardy instead. Basically you have to choose the stupidest move possible (maybe there's a stupider move than that as you could easily pick up Belgium that way, perhaps he just holds?
12. The Bully - someone who feels he's bigger/ stronger then he really is, boasts and makes more 'aggressive only' moves.
13. The Pacifist - doesn't start any wars, but fights whoever hits him first (I think this could work, but its not really crazy as such).
14. A person who just randomly supports others with no indications of alliances or trade offs, that will at least keep the game moving (discussion on two personalities: always lies and always tells the truth. But as this may get picked up on relatively quickly, another alternative would be the overly helpful character - overly pleasing and helping others out all the time even if it makes no sense, e.g., let's say France has a fleet in Belgium and helps out England by supporting an attack from NTS to German Holland while a French fleet in EC supports a German fleet in Denmark attacking NTS.
15. Mr. Prissy – although not so game-changing crazy like the others. Unless we stipulate that Mr. Prissy must ALWAYS be guided by the person who is loudest and most intimidating towards them (thereby making Mr. Prissy feel scared and afraid of that person), it shouldn't be a personality.
16. Giver-Upper - immediately when he loses a SC, he abandons the front and moves on.
17. Color Man - a person who would rather spend moves coloring more territories in their color than capturing SC's. Obsesses over "neutral" non-SC territories, such as North Africa, Syria, Finland, Bohemia, Clyde, etc.
18. Pirate Pete - swears all the time, builds at least one fleet when he can during the builds phase, doesn’t move to any inland SCs or territories: must stay on the coast. Tends to raid coastal SC’s and sees no issues, moving on.
19. Military Man - builds armies no matter what (sorry England), speaks in clipped military-like tones and behaves like he’s in the army.
20. Moocher - builds alliances based on food, not by different deals which are being made (e.g., France allying with Italy or England for a fine dinner or a tea break with French bread). Can substitute something else for payment here.
21. Nuke Inventor - always tries to convince his allies that he will develop nukes in the near future. He constantly keeps explaining what his scientists are doing and the physics of a nuclear weapon.
22. The Horse Trader - basically bandied together and strikes deals to swap territories with players. Lives for the deal.
23. Barking Mad - takes on the persona of an animal. You can still speak human language but you take everything from your chosen animal perspective. Open to discussion if you can swap and change animals during the game. Alternatively you could only speak in your species' native tongue, e.g., you bark, woof, and pee everywhere the whole game. Could be interesting in diplomatic conversations.
24. The Mirror - in 1901 you behave totally rationally like a normal Dip player, then in 1902 (grab dice or do some kind of random allocation of the other players) and then take on the same traits as that randomly selected player. 1903 rolls by, roll the dice to see who you'll randomly be next turn. This way you have to do your best to imitate the style/personality you think that player has.
25. Irrational Lover/Hater - randomly select a player in 1901 and go to war with them with full bravado (even if you're England and you just drew turkey). Then in 1902, you randomly go to war with another player while sucking up to the guy you just attacked the previous turn. Serious craziness if you get the same player back-to-back with messages swapping between love & hate.
26. The Revolutionary - speaks in nothing but propaganda and rants about "liberating" the oppressed masses.
27. Captain Convoy - tries organizing the most complex multi-national convoys the world has ever seen, delivering countries' armies to the furthest possible destination just because he can!
28. The straight faced liar - nothing he ever says is true (I thought this one might be good).

sounds awesome. Anyone want to play a game like this?

I'd like a game of this.

I mean extreme personalities.

In the perpetual game I'm imagining, the goal would be to rule the world -- or own all the supply centers. At any time, a new player can enter the game with 3 units that are able to exist without a supply center, until 3 supply centers are captured. Then the first three supply centers captured become the home supply centers going forward.

Wouldn't that be basically impossible? In order to rule the world, or own all the supply centers, you'd have to have units attacking those supply centers that you don't own. In order to do that, you have to leave supply centers undefended elsewhere since you need units to support your attacks. Therefore, at any given time, people could join in and just take 3 of your undefended supply centers. The only way anyone could ever win is if no one wants to join and the game just gets played with the remaining people (although, even in that situation, if you eliminate someone, they can just join back in and take your undefended SCs so it's basically impossible to win).

I guess I just don't see the point since without a realistic way to win, why play?

Right, extreme personalities was fun. We called a draw because iirc Russia CDed and we couldn't find a replacement. NMR rules dictated we get a replacement so well...

In a perpetual game there is no "winner" because the game never ends. There is only the most powerful player on the board, which everyone is striving to become. There is bragging rights, "I am the King of the World! Ruler of the Board! I dare anyone to try and take my throne!"

I get that...except it's super easy for anyone to "take my throne". If three people join the game at the same time, and drop 3 units each near undefended SCs of mine (per your idea that anyone can join at any time and have 3 units that need no support and would presumably be able to be dropped just about anywhere) then I'm toast. And it'll just be a cycle. Eliminate me, and I'll just pop back up near your undefended SCs and take them.

Extreme personalities sounds hilarious.

You want to play a perpetual game of Diplomacy? My recommendation is find a girl you love (preferably a gamer) and negotiate your bliss until death do you part. That means no caving in and condeding if you hit a rough spot...no solo's allowed. It's a challenge, and the rewards are vast.

"Preferably a gamer"
Ahh the rare and very elusive beautiful gamer girl. I hear they exist but so far it seems they do so only in fairy tales.

The extreme personalities would be fun.

Tomohaha - my wife was always tolerant of my gaming, but I converted her to a full gamer. played WoW back in teh day together for years, and she and my daughters are both strategy board gamers. It's awesome. (And yes...she's hot, too....krellin hit the gold mine!)

I'd love to play another round of Extreme Personalities, but I really can't spare the time until my World Diplomacy game winds up, and that's still around two months away. But don't let that stop any of you. However, if a game of this does end up starting after September, I'm in.