I'm going to go a bit off-piste with this entry, and indulge some of my own thoughts before I continue on the main thread of this series and what I know of Réné Girard's thinking. I take complete responsibility for what's in this entry, so if it's complete bollocks, don't blame Girard!
Competition is, by its nature, in search of a resolution. It must either be won or abandoned. If the point of a competition is to win it, then how do you win so definitively that you nullify any opportunity for rivalry to return? If you achieve your desire, even if this desire has no further desire on the other side of it (uncommon) you continually compete to retain it; to prove, eternally, that you are the most deserving. Using the example from yesterday of a romantic relationship, marriage is only the end of the story in Disney movies. The same goes for other thresholds of achievement.
There are two ways to put a complete stop to mimetic rivalry: first, relinquish your desire. The cuckolded husband in 'El curioso impertanente' commits suicide, the ultimate concession of defeat. The other is to prove your absolute dominance of the desire by destroying the object of that desire.
This last is a common feature in Romantic literature, especially tragedies. The mimetic rivalry becomes so consuming that in order to best all one's rivals, one destroys the very thing that you were rivals for. My sterling example of this is Rogozhin in Dostoevsky's
The Idiot: his desire for Nastasya, who has drawn most of the men in the book into a mimetic rivalry for her, is so completely overpowering that (spoiler) he ends up murdering her. Othello's murder of Desdemona is much the same: it doesn't matter that the rivalry which obsessed him was fabricated by Iago, once that seed was planted, they were on their way to tragedy. Many such 'crimes of passion' arise from this compulsion to assert one's dominion over the object of desire, from sudden slaying to the slow death of emotional abuse.
The destructive resolution of mimetic rivalry explains a phenomenon in fan culture, too, I think, which has been called 'breaking all the toys.' Russell T. Davies was often criticised for this when he was showrunning
Doctor Who and then
Torchwood, when he would write the canon into a closed box by killing off the cast or some other such finality. In some fandoms the competition between fans gets so intense that the fans become rivals of the creators, trying to prove that theirs is the greater love, greater even than the love that brought the thing into being. This seems especially common in pre-existing properties where the current creators are continuing a franchise started by someone else, and are therefore merely a sort of elevated fan. If these creators are not careful, they can get sucked into the fan rivalry. I think Davies' moves were his power play in that game: he asserted his dominance over those who desired a show by writing it into a position where no one else could get their grubby hands on it, even if it meant destroying it. The image of a toddler breaking the toys he doesn't want to share strips bare the role of mimetic rivalry in this behaviour.

On a global level, the United States and Soviet Union were so entrenched in their mimetic rivalry that they amassed enough firepower to annihilate the world they wanted to possess. Luckily for all of us it never came to that (or, at least, we have backed away from that precipice), but for a while we were well on our way to the ultimate breaking of the toys.
Admitting defeat or destroying the object of desire are internal resolutions for the mimetic rivalry – the dynamic is entirely contained amongst the players, including its ending. This makes sense in a narrative, where you need to wrap things up within the characters and timeline you've established. In reality, internal resolutions are generally best avoided: most of us would rather not commit murder, or admit defeat. Therefore the anxieties stirred up by mimetic rivalry are transferred externally, and that will get us back on the Yellow Brick Road tomorrow.
Chapter 9: Transference