Catspaw assassin

"You're not s'pposed to be here; no one's s'pposed to be here. It's a mercy; he's dead already."

- The Catspaw to Catelyn Stark before attempting to kill Bran The catspaw assassin is a minor character in the first season. He is played by guest star Lalor Roddy and only appears in "The Kingsroad." He is never named, but is referred to as such in casting announcements and the script, a reference to a catspaw being someone unwittingly used to further another person's agenda.

Season 1
The catspaw assassin was paid to kill Bran Stark while he is in a coma in Winterfell, following his fall. The assassin arranges for a fire to start in the castle, reasoning it will draw people away from Bran's room. This diversion succeeds in persuading Robb Stark to leave the room, but Catelyn remains behind. When the assassin goes into Bran's room to kill him, he finds Catelyn there. They struggle and he injures Catelyn's hand, but is then attacked by Bran's direwolf, Summer, who tears his throat out.

The assassin carried an elaborate dagger with a dragonbone hilt and a Valyrian steel blade. Catelyn resolves to carry the blade to her husband in King's Landing to investigate further. Petyr "Littlefinger" Baelish falsely claims that the dagger belongs to Tyrion Lannister. This leads Catelyn to take Tyrion prisoner when she chances across him at the Inn at the Crossroads. Her actions spark a conflict between House Stark and House Lannister. Tyrion acquits himself of the crime via trial by combat at the Eyrie.

In the books
In the A Song of Ice and Fire novels, the assassin is never named.

In A Clash of Kings, Catelyn found out that Littlefinger lied to her about the dagger only after she interrogated Jaime Lannister. Jaime bluntly admitted that he pushed Bran from the window in attempt to kill him, but claimed that neither he nor Cersei nor Tyrion had anything to do with the assassin; both Tyrion and Jaime pointed out the key flaw in Littlefinger's story- Tyrion couldn't have won the dagger in a gambling bet because he never betted against Jaime in such circumstances. When asked about the dagger, Jaime remembered that Littlefinger bet and lost it - to Robert, not to Tyrion. Catelyn realized Jaime was telling her the truth, for he had nothing to gain by lying about the assassin and the dagger after admitting that he pushed Bran. Jaime admits that he and Cersei considered having Bran killed, but given the fact Catelyn was in his bed chamber at all times and the room was guarded, it would have meant murdering their way through half of Winterfell's population to reach Bran, and they concluded there was no need when it seemed more likely that Bran would die of his injuries from the fall.

During a casual conversation at King's Landing, Tyrion made a comment about Littlefinger's elegant suit and handsome knife. Littlefinger drew his knife, glanced at it casually, as if he had never seen it before and said “Valyrian steel, and a dragonbone hilt. A trifle plain, though. It’s yours, if you would like it”. Noticing the mischief in his eyes, Tyrion realized that Littlefinger was teasing him insolently about the assassin's dagger, without saying anything explicit.

Tyrion suffered a lot as a result of Littlefinger's lie: he was humiliated, kidnapped, beaten, locked in a sky cell and nearly killed three times (on the way to the Eyrie, at the Eyrie and on the way back) - and yet he never attempted to settle the score with Littlefinger, either openly or secretly (as he did with a singer who tried to blackmail him), even after being taunted about it. It is unclear why Tyrion let Littlefinger get away with that, in contrast to the unofficial motto of his house (though Tyrion does note that at the time, Littlefinger is still too useful to House Lannister to kill him out of hand simply for revenge, though Tyrion's own train of thought infers that he will gladly have Littlefinger killed for the grief he caused Tyrion once his usefulness is at an end).

In A Storm of Swords, Tyrion and Jaime independently deduce that it was Joffrey who sent the assassin:
 * After Joffrey uses his new sword to cut the book Tyrion gave him at his wedding, he says "I am no stranger to Valyrian steel". That strange comment makes Tyrion realize it was him (discounting the only two other possible culprits, because Jaime was too proud to have another do his killing for him, while Cersei was too cunning to use a knife that could be traced back to her). Tyrion remembers overhearing Joffrey jesting with the Hound in Winterfell about killing wolves: "Send a dog to kill a wolf". Even Joffrey was not so foolish as to command the Hound to slay a son of Eddard Stark, as Clegane would have informed Cersei. Instead he found his catspaw among the unsavory lot of freeriders, merchants, and camp followers who had attached themselves to the King's party as they made their way north. Since even Joffrey was not stupid enough to use his own dagger, he went poking among his father's weapons. No doubt some diligent servant had made certain that the King's weapons went with him, in case he should desire any of them. The only thing Tyrion cannot figure out is Joffrey's motive. Recalling a nasty quarrel between Joffrey and Robb, Tyrion asks Sansa if there was any ill feeling between Bran and Joffrey, but her answer is negative. He guesses then it was mere cruelty of Joffrey. Another possibility is that Joffrey grew incensed when Tyrion slapped him and ordered him to offer his sympathies to Eddard and Catelyn about Bran's injury (simply for the sake of decorum); in his warped mind, Joffrey felt so insulted at being commanded to express sympathy to Bran's parents that he may have wanted to sooth his wounded pride by having an unconscious seven year old boy assassinated.
 * Jaime tells Cersei that Catelyn suspected him of sending the assassin to kill Bran. Cersei recalls Robert saying of Bran: "We kill our horses when they break a leg, and our dogs when they go blind, but we are too weak to give the same mercy to crippled children" in the presence of their children, including Joffrey. Jaime figures out it was Joffrey, as a child hungry for a pat on the head from his father.

Although there is no direct evidence that definitively proves that Joffrey was the one who sent the assassin, it is very likely Tyrion and Jaime are correct about pinning the assassination attempt on him. When Jaime finally engineers Tyrion's escape from the dungeons, during their conversation through the secret tunnels of the Red Keep, Tyrion becomes annoyed and asks Jaime if he knew that his son tried to kill Bran Stark. Jaime grudgingly admits that he had thought he might have.

Littlefinger had no role in convincing Joffrey to attempt this (as he was south in King's Landing at the time), but this proved to be another example of how Baelish thrives on chaos, thinking quickly to turn events to his benefit. He had already set in motion his plan to trick the Starks and Lannisters into fighting each other, by convincing Lysa Arryn to poison her own husband and also write a secret letter to Catelyn claiming that the Lannisters did it. When Catelyn inquired about the knife, Littlefinger knew that he'd lost it to Robert, and must have realized someone in the royal entourage had taken it, but quickly decided to blame Tyrion as the culprit. He possibly chose Tyrion to blame because Cersei and Jaime were already back in the capital city, surrounded by their own guards, while Tyrion was still traveling in the North and would be more vulnerable to Stark reprisal.

It is unknown why the TV series never reveals that it was Joffrey who sent the assassin; Joffrey receives the Valyrian steel sword Widow's Wail as a wedding gift, as he did in the books, but no mention is made of the assassination attempt on Bran back in Season 1. It is possible that the reason is the same for not revealing the truth about Tysha in "The Children": the producers grew afraid that casual viewers wouldn't remember that this happened in early Season 1 - even though this was one of the escalating events which sparked the entire Stark-Lannister conflict.