No. Not "new business". "A" new business. It's a sweetheart deal for one company in particular subsidized by the taxpayers. They're not reducing their citywide tax rate to attract Amazon, they're just giving a handout directly to Amazon.

What you're describing is nothing close to the reality. It's the prisoner's dilemma. Cities that participate in this scheme take turns screwing each other over in an attempt to get a minor benefit themselves, but compared to the scenario where nobody played the game to begin with, they all lose.