Bratz maker Isaac Larian wants to merge his MGA with Mattel. Barbie isn't interested

California toy mogul Isaac Larian has spent more than a decade battling his company’s bitter rival Mattel Inc.

Now, he wants to run it, and guess what? The struggling Barbie-doll maker is having none of it.

Last month, Larian made an unsolicited offer to merge his MGA Entertainment Inc. with his...