That is an excellent idea. I worry that we might end up with people winning and boasting about how nothing could ever beat them, which could increase uFAI risk. Maybe if it was framed differently?
Actually, the weird thing I noticed is that it seems like the best approach again is to just let a script be the babysitter to the AI in this competition as well. The script, which wouldn't have the ability to let the AI out, and can just announce something like this:
GK-SCRIPT: "Hi AI #432. I'm a script. If during any hour, you type less then one dollar sign an hour, I will type AI-DESTROYED, but without the hyphen, killing you. Other than that, I don't do anything other than acknowledging receipt of your dollar signs and time till destruction."
A...
Update 2013-09-05.
I have since played two more AI box experiments after this one, winning both.
Update 2013-12-30:
I have lost two more AI box experiments, and won two more. Current Record is 3 Wins, 3 Losses.