I have one minor question about this problem, would I be allowed to say, offer omega $50 instead of the $100 he asked for in exchange for $5000 and the promise that, if it had occured that the coin landed head, it would give me $5000 and ask me for $50, which he (going to refer to all sentinents as he, that way I don't have to waste time typing figuring out whether the person I'm talking about is he,she, or it.) would know to do since Omega would simulate the me when the tail landed tails, and thus the simulated me would offer him this proposition. Which should not be too difficult to accept, given that the cost to Omega is basically zero across all possibilities, unless part of the point of the exercise was to mess with me.
In the event that he rejects this offer, I'm going to give him $100, and then mug him. (Assuming of course that the probability is not 0 that I succeed in the mugging, if he were to say kill me in response to the mugging, I'd simply have the copy that succeeded in mugging him force him to use some of his powers to resurrect my less fortunate copies. Assuming of course that that power is part of his omnipotence, else I wouldn't mug him, no point in betting my life in something that does not generate more of my life (given that if I succeeded I can have him make all copies of me immortal. Of course, if he had this power, there's a might be a chance that his retaliation might have been to simply wipe out all copies of me in all existances, in that case, the probability of success should be computed as a negative value, given I CAN fail more times then I try.) In the case I succeed in the mugging, I'd get at least my $100 back, and the cases I fail, I doubt I'd care about $100.
In the case that neither of the above are possible, I would not give him the $100, given that the diminishing returns of increasing amounts of money might well make the $10000 less utility than 2x instances of $100. (The 2x instances of $100 scale linearly, where each increasing $100 in the $10000 diminishes in value. As in, each instance of $100 would be worth just as much as a prior instance of $100 since it's being distributed among different copies of me, so diminishing returns does not kick in, whereas the $10000 all goes to one instance. It should be obvious that I prefer $50 to 50% chance of $100)
Of course, due to the above, there's a fourth possiblity, one where the iteration of me being offered the choice is being very much affected by the diminishing returns on the value of money. In that case, I would give $100 to omega, since this action would partially smooth out the differing amounts of wealth among multiple copies of me across worlds. Or rather, diminish the number of me who are "poorer," since the copies that are in need of money do not give up $100, but will recieve some regardless, unless that doesn't work out because Omega simulates the exact version, including current finiancial assets, which rather nullifies his capabilities as an interdimentional arbitrageur among copies of me. But at that point, the diminishing returns on money should be such that each additional $100 should be roughly equal in value, since diminishing returns ALSO suffer from diminishing returns, with increasing amounts of diminishing returns diminishing less returns.
In short, the options are, I offer him $50 for a constant $5000 across all outcomes of the coin flip, and he accepts, I give him $100 then I mug him, I do not give him $100 if diminishing returns is not yet itself affected by much by diminishing returns, or I give him $100 if it is.