Interesting take!
But surely if Rice only wants Arsenal, and Arsenal know this as clearly as is being suggested, they would just sit tight on their current offer and wait it out until West Ham’s resolve weakens as time to find a replacement starts to run out.
There’s absolutely no benefit whatsoever from Rice’s perspective to force his new club into needlessly overpaying for him (a move I’m sure they’d be absolutely delighted with him for!), as that will limit how much they can then offer him in turn on wages/bonus, etc.
Going to the trouble of lying to City to pretend he wants to join us, and seriously pissing his new club off by making them overpay for him, seems like an absolutely bizarre way to go about getting his dream move!