- After several posters pointed out that things were actually going surprisingly well for King Robert, an In-Joke developed regarding Robert's skill as a manipulator. This eventually grew, in true ASOIAF fashion, into a full-fledged theory. Though some refuse to accept it, the evidence does seem to suggest that King Robert is a political guru; not someone people usually describe as such, this theory grew around the fact that things are actually very much going Robert's way despite the fact that he should by all rights be fucking everything up. Much of this is true not just for this quest, but even in canon. Obviously, many of the supposed indications of his poor rule are in fact examples of his genius, and proof that he's the King Westeros deserves, just not the one it needs right now.
- Petyr Baelish - Robert is very aware that Petyr Baelish is corrupt scum, but he's corrupt scum that serves a very useful purpose to the King. By constantly borrowing gold and causing chaos, he keeps anyone House from growing strong enough to challenge him even in a post-Targaryen Westeros, where neither dragons nor inertia are around to ensure the regions remain united. King Robert is also the only one corrupt enough to allow him to have a free hand in order to enrich himself, which means Petyr is actually forced to remain relatively loyal to King Robert himself since Robert's death could potentially lead to a less corrupt government.
- Tywin Lannister - Robert has Petyr borrow from Tywin as a part of his ultra-secret plan to weaken the Lannister family. Are the Lannisters investing in an industry? In agriculture? In an infrastructure? NAH, Robert the chessmaster is siphoning off their gold for a useless return called "Influence" that is something that can be turned off and reversed at any moment. If he were to stop the corruption and stop borrowing, it could lead to a Westerland economic boom as Tywin Lannister invests that money in his own region and builds up the mother of all economic bases, unmolested thanks to this time of peace. This is also another reason why he keeps Petyr, he needs the corruption in order to ensure he has an excuse to continue to destroy the Westerlands in the long-run. Gold mines - unlike infrastructure that could be built with them - will run out, and this will arguably keep his dynasty safer in the long-run than letting Tywin sit in Casterly Rock and open up a bank or something.
- Jon Arryn - Jon is vaguely aware of Robert's chessmaster plans but considers the charade of mindless hedonism useful. By pretending he is the only competent one in the capital, any assassination attempt on Robert will probably target him first. He nobly takes the hit for both of them since Robert is like a son to him. It also gives them an early warning system since if someone targets him politically or physically, Robert knows that said person is hostile to his regime.
- Ned Stark - Ned recognizes the superior mental might of his bro in the South. He was purposely kept out of King's Landing because Robert and him decided that they needed a large garrison force in the North that could sweep in at any time to help out in the case of a counter-coup. If Ned Stark was in the south, he might get captured and it would lead to the North being paralyzed since they wouldn't know whether to march or not, since Stark's kids are still too young to lead.
- Renly and Stannis - Deep down Robert loves these two but pretends to be uninterested in either of them. This makes both of them less at risk to assassination attempts since Robert's enemies think they have no influence on him. He kept Stannis in Dragonstone because Stannis is his favorite, and when it comes down to it control of the Royal Navy is wayyy more important than whatever it is a Master of Laws does in a society that barely has the concept of rule by law. He also needed Stannis to dispense some JusticeTM against the extremely pro-Targaryen populace in the region. He also put Renly in Storm's End because it makes it look like Robert is generous, when in truth he's in control of two regions (Crownlands and Stormlands). Stannis also isn't gay and Renly is... So no heir to stop his plan of creating an enlarged Crownlands which will create a secure base for his heir.
- Cersei Lannister and the Incest Babies - Robert is aware of Cersei's incest and allows it since it is all part of the plan. He knew that even real kids with Cersei would be tainted by association/their mother's teachings, so he instead decided to rely on his bastards to continue his legacy, preventing succession crisis by not having any trueborn children so that whoever he legitimizes is the uncontested heir after the Lannisters are dealt with. While Tywin would, of course, reject Robert's statements, nobody else would. The Rebel Alliance would ensure the Vale, North, and Riverlands came to the King's aid, while Robert's heir would be the perfect age to marry to Margaery Tyrell, which Mace would jump at since his daughter would be the Queen. Dorne may not like Robert, but they would leap at the chance to strike at the Lannisters. This would set the Stormlands, Reach, Dorne, Crownlands, Riverlands, Vale, and North against the Westerlands.
- Even his general hedonism and apparent mismanagement of Westeros feeds into this. It means that when he chooses his heir, everybody will be so relieved to have a much more stable alternative that they wouldn't dream of questioning his choice. Thus, the stability of his heir's reign will be secured at the cost of his reputation.
- His actions regarding Jon in this quest work within this framework as well. By publicly knighting Jon, he associates himself with this rising knight and earns quite a bit of his gratitude...despite the fact that doing so cost him absolutely nothing. Jon would have been knighted anyways by the Blackfish. Jon in turn has killed a Westerland-born Kingsguard (reducing Lannister influence at court and effectively gaining the King whatever he traded that position for free of cost), and executed the Mountain in a Trial of Seven - further harming Tywin. Robert has deftly managed to associate Jon's rising fortunes to the crown, all with minimal effort and is in the perfect position to profit from the reduced Lannister power to further his own schemes.
WMG / A Dragon of the North