I bite my tongue, then. Had assumed that you were playing Germany due to color confusion (and also not looking at the scoreboard very attentively at all). This does explain the English scouts in the screenshots, and also the forested pig hill being worked at the German capital on T28 when BW/AH should long have been researched (Prince tech costs), which I've also just spotted. Challenge to the newer players: find all instances of the AI's misplays.
That also slightly changes my evaluation -- if Germany goes west with the first settler, settling Amiens might become impossible due to the minimal city distance of two tiles. Still unlikely, but at least in the realm of non-zero probability.
and I am still unsure about how much the three humans are supposed to cooperate or compete.
If the goal is to beat all the Prince AIs, and I assume you could easily beat them all by yourself, I think you should intervene as little as possible; maybe beeline Astro and settle the New World while only providing assistance in an emergency. Perfidious Albion and all that.
What MattiK and Phylhom want to do is up to them, I suppose, but I agree that if they trade techs between themselves, the game will take on a different character compared to the Single Player experience. That said, this map is rather exceptional in any regard. The Amiens site is insane, for instance. What's the food surplus there, +15? +20?
If thrashing the AI opponents all across Eurasia should eventually become boring for them, you could mimic the "final boss" for them to try and jointly defeat.
It's nearly impossible to catch a cautious player with a transcontinental invasion, though, so I suppose you should go easy on border safety (i.e. intentionally avoid a sentry net and let them figure out visibility rules... or revert your empire to AI and observe the collapse
-- in fact, this might be a fun idea) if this is to form the grand finale.