Soon, a game will be developed to rival Angry Birds, cleverly dubbed Bust My Balls.
Off the top of my head:
Player one has a tiny ball on their screen, the size of which they can barely see. Upon turning it on, it creates a new ball of which is numbered, in this case it is number 1. Number 1 ball leaves the screens to travel eventually appearing on somebody else's screen who has their own ball showing. The goal is to get a visiting numbered ball to hit your ball so that it can grow in size.
The larger your ball is, the better the odds of having it make contact with a visiting ball. The closer the people are who simply have the app on their smartphones, the more numbers balls will enter your domain.
You're only allowed to send out one ball per day, unless... (still thinking on this)
Since numbered 1 is the first and will be in the wild the longest, it would most likely make the most contacts. Each time it does such, it travels faster through the system, interacting with more users. This does not mean it travels faster across your screen. It's always at the same pace allowing you time to make contact with it. It can only be on one screen at a time.
A website can be created to show what numbered balls you have made contact with, alone with keeping a tally.
Just figured it out: As you level up, you'll be able to send out more numbered balls per day. You also gain points as your created balls make contact.
Further thinking: Assign one satoshi to each created numbered ball. Design the game so that it is very easy to play, but there's a monetary reward each time your created balls make contact. The more balls you create, the potentially more money you can earn, albeit it's only satoshis--at first.
Somebody will have to create and maintain the BallChain to keep track of the contacts/transactions.