By taking/not taking its offer, you are only controlling the conditions under which Omega appears
And by assuming you are a certain sort of agent (which you incorrectly call money-maximizing), you set those conditions to your own disadvantage! An agent which just flips a coin to decide whether to accept or refuse the £10 will have a bigger expected payoff than you. So surely a rational entity can do better.
And by assuming you are a certain sort of agent (which you incorrectly call money-maximizing), you set those conditions to your own disadvantage!
You are setting the conditions for appearance of Omega. The best conditions for Omega to appear are those where you take its money, since it's good for nothing else.
By refusing the £10, you maximize the amount of money that the agents who see Omega get, by moving Omega around. It's similar to trying to become a lottery winner by selling to existing lottery winners the same dietary supplement you take, since thi...
This is a variant built on Gary Drescher's xor problem for timeless decision theory.
You get an envelope from your good friend Alpha, and are about to open it, when Omega appears in a puff of logic.
Being completely trustworthy as usual (don't you just hate that?), he explains that Alpha flipped a coin (or looked at the parity of a sufficiently high digit of pi), to decide whether to put £1000 000 in your envelope, or put nothing.
He, Omega, knows what Alpha decided, has also predicted your own actions, and you know these facts. He hands you a £10 note and says:
"(I predicted that you will refuse this £10) if and only if (there is £1000 000 in Alpha's envelope)."
What to do?
EDIT: to clarify, Alpha will send you the envelope anyway, and Omega may choose to appear or not appear as he and his logic deem fit. Nor is Omega stating a mathematical theorem: that one can deduce from the first premise the truth of the second. He is using XNOR, but using 'if and only if' seems a more understandable formulation. You get to keep the envelope whatever happens, in case that wasn't clear.