BNR: Looking to play against... Yourself? Well, it looks like Catch-22 is the right game for you.
AppSpy: The name encapsulates the gameplay of this high score zen puzzler beautifully.

Touch Arcade: Mango Down's Catch-22 [$0.99] is a mesmerizing, one-button arcade game that has you constantly facing your toughest opponent: yourself. The goal is to increase your score by gathering the orange orbs and avoiding the oncoming ball. Each round you survive increases the multiplier and the amount of orbs to collect. Once you gather all the visible orbs, you "switch" players, and the jumps you make become the path of your enemy-self. This alternating dance plays out until the two balls crash.

GameZebo writes:
Catch-22 has me mesmerized, and I can’t figure out why. Part twitch arcade title, part puzzle, part Impressionist painting, it’s caught somewhere between addictive and otherworldly. In fact, it’s the kind of experience I don’t even want to ruin by attempting to pigeonhole it into a rating, and a simplified list of pros and cons. I wish there was a phrase to describe this kind of predicament.