I realise I'm coming to this a little late, but I'm a little unclear about this case. This is my understanding:
When you ask me if I should give Omega the $100, I commit to "yes" because I am the agent who might meet Omega one day, and since I am in fact at the time before the coin has been flipped right now, by the usual expected value calculations the rational choice is to decide to.
So does that mean that if I commit now (eg: by giving myself a monetary incentive to give the $100), and my friend John meets Omega tomorrow who has flipped the coin and it has landed tails, I should tell him that the rational choice is to not give the $100, since he is deciding after the coin toss.
Would anyone be so kind as to tell me if that seems right?