There is a caveat: if you are an agent who is constructed to live in the world where Omega tossed its coin to come out tails, so that the state space for which your utility function and prior are defined doesn't contain the areas corresponding to the coin coming up heads, you don't need to give up $100. You only give up $100 as a tribute to the part of your morality specified on the counterfactual area of the state space.