I think my answer would be “I would have agreed, had you asked me when the coin chances were .5 and .5. Now that they’re 1 and 0, I have no reason to agree.”
Seriously, why stick with an agreement you never made? Besides, if Omega can predict me this well he knows how the coin will come up and how I’ll react. Why then, should I try to act otherwise. Somehow, I think I just don’t get it.
And if Omega comes up to me and says “I was going to kill you if you gave me $100. But since I’ve worked out that you won’t, I’ll leave you alone.” then I’ll be damn glad I wouldn’t agree.
This really does seem like pointless speculation.
Of course, I live in a world where there is no being like Omega that I know of. If I knew otherwise, and knew something of their properties, I might govern myself differently.