Biography
In a hereditary monarchy, every so often the throne is inherited by someone completely out of their gourd. Maybe it's the fault of that lead-lined plumbing, or those mercury-laced medicinal elixirs, or maybe it's genetic (in which case you're in some deep trouble). Whatever the cause, the sovereign is still given the full power and support of the state despite their obvious insanity, with inevitably disastrous consequences.
The Caligula will usually be wildly irrational, violently moody, extremely debauched, utterly intolerant of being told anything they don’t want to hear, and probably afflicted with a god complex. In short, they will be a Psychopathic Manchild with the power of life or death over everyone whom they can reach. They may be a sexual deviant, or they might take pleasure in the pain and suffering they cause. They may indulge in renaming cities or even the entire country after themself or throwing out increasingly ridiculous decrees with brutal punishments in store for anyone who breaks them. Whatever form the madness takes, one thing is certain: to do anything the Caligula finds displeasing is to inevitably be dragged off to a grisly death or worse. Of course, any number of things might trigger their rage, and they might even decide on a whim to punish those who have not done anything at all. And while all of this is going on, the land over which the Caligula rules is rapidly going down the drain due to their neglect. Here, in particular, they have a decided advantage over most other crackpots when it comes to messing things up: they can start wars. Be it for the perceived personal glory or their obsession with perceived enemies, the Caligula's country will probably be in a constant state of war.
Never ever ever try With Due Respect on a Caligula — many of them do not take criticism well, if at all.
Due to their continuing close proximity to the Caligula, members of the court (decadent or otherwise) will be the primary targets of their fits of rage. Nobody within reach is safe from them, whether they be nobles, servants, bureaucrats, foreign ambassadors, or even members of their own family. The Caligula is very definitely a Bad Boss. With any luck, thanks to The Starscream and/or La Résistance, a conspiracy will eventually develop to remove the crazy sovereign from his post... permanently.
This is not limited to sovereign heads of state. The Caligula can be anyone wielding great power within an organization while being completely nuts.
Named for what is probably history's best-known whack-job, Roman emperor Gaius Julius Caesar Augustus Germanicus, better known as Caligula (Little Boots, his childhood nickname, because he was the army's mascot and wore tiny version of a legionnaire's boots; it was probably adorable); remembered for talking to statues, locking granaries, declaring war on the god Neptune (and "winning", then commanding his soldiers to collect seashells as war-prizes), making his horse a consul (admittedly, this one may have simply been a gesture of spite towards the senate), and boning his sisters. (Though the veracity of some of these claims is in question, the reputation persists. See here for all the details.)
In terms of the ranks of Authority Tropes, the tropes that are equal are The Good Chancellor, Evil Chancellor, Standard Royal Court, and Decadent Court. The next step down is The Brigadier. The next steps up are The Evil Prince, Prince Charming, Prince Charmless, Sheltered Aristocrat, Warrior Prince, The Wise Prince, and all Princess Tropes.
Compare:
Evil Overlord, who is similarly malicious, though not necessarily insane.
The Generalissimo, an often-mad military dictator who forced their way into power.
President Evil, just as brutal and malevolent, but voted into power.
Royal Brat, who might be just as despicable due to immaturity rather than insanity.
Royally Screwed Up, where pervasive insanity runs in the monarch's family.
Small-Town Tyrant, the rural version of this.
Trumplica, as more negative examples often amount to modernized takes on this.
Tyrant Takes the Helm, where the Reasonable Authority Figure gets replaced by, well, a tyrant.
Contrast:
Psycho Supporter, who has the same personality traits but is usually on the opposite end of the authority hierarchy.
The Wonka, another type of mad authority figure whose madness makes him more competent as opposed to more destructive.