I'd be down for this.
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And good luck taking any form of action. They don't own the genre. They have no say in how Epic designed the mode for Fortnite.
If Bluehole want to waste their own time and money going after the company that not only supplies them the game engine but at the same time tarnishing their own reputation then go for it. The case would be laughed out of court in an instant.
If anything Epic have the high ground here because they could just stop them using Unreal 4. Game companies have been building games that are inspired by others for ages. It's perfectly normal that Fortnite would create a game mode inspired by a game that right now is a success.
And you've never seen companies take digs at each other in advertising? Rift did it towards WoW and Sega and Nintendo absolutely went after each other in the 90s in fun ways.