game of thrones - Why use a fancy and easily recognizable dagger?

In a previous question it was established Who actually sent the assassin to kill Bran, however, I fail to understand why would the culprit choose a very expensive and easily recognizable dagger and give it to the assassin, when any blade, no matter how cheap it is, would do fine as long as it can cut through flesh.

Even if Joffrey wanted to set up his uncle Tyrion from whom he stole the dagger, the trail left by this evidence would still lead to his house (well, actually, his mother's house, but you know what I mean).

The only reasonable explanation is that no one considered a failure as an option and a backup plan was never created. Was this supposed to show how careless and reckless the culprit is?

Answer

I've been rereading the series, and fortunately came across this section just yesterday (book 3, A Storm of Swords. Viewpoint of Tyrion, about page 550 of 786 in the version I have):

The blade Joff chose was nice and plain. No goldwork, no jewels in the hilt, no silver inlay on the blade. King Robert never wore it, had likely forgotten he owned it. Yet the Valyrian steel was deadly sharp... sharp enough to slice through skin, flesh, and muscle in one quick stroke. I am no stranger to Valyrian steel. But he had been, hadn’t he? Else he would never have been so foolish as to pick Littlefinger’s knife.

_{A Storm of Swords, Tyrion VIII}

So, it's a combination of two things:

1. Joffery didn't know what Valyrian steel was at that time


2. The hilt of the dagger looked ordinary enough to the uneducated eye

I don't give Joffery enough credit to weave another layer of cunning into this - I highly doubt he ever aimed to implicate someone else, just get away with a remarkably simple scheme.