Alternative solution: Offer Omega $1,100,000,000,000 to put nothing in the boxes.

Love it. But, no, that would be caught by Alpha's monitoring before things came to that point.

I was looking for an elegant way to say "These are the only possible options, ignore any change that there will be any other result (such as $1,000,000 in box B.". I was trying to give a context where the rules made sense. In terms of reputation being exchangeable for money, that represents both Alpha and Omega being immensely embarrassed among the AI society at screwing up the basic physical setup and invalidating their own contest. It is sort of a side issue. :-)