So on the face of it it seems that the only accessible outcomes are:
and it seems like in fact everyone does better to choose "sim" and will do so. This is also fairly clearly the best outcome on most plausible attitudes to simulated copies' utility, though the scenario asks us to suppose that X doesn't care about those.
I'm not sure what the point of this is, though. I'm not seeing anything paradoxical or confusing (except in so far as the very notion of simulated copies of oneself is confusing). It might be more interesting if the simulated copies get more utility when they choose "not sim" rather than less as in the description of the scenario, so that your best action depends on whether you think you're in a simulation or not (and then if you expect to choose "sim", you expect that most copies of you are simulations, in which case maybe you shouldn't choose "sim"; and if you expect to choose "not sim", you expect that you are the only copy, in which case maybe you should choose "sim").
I'm wondering whether perhaps something like that was what pallas intended, and the current version just has "sim" and "not sim" switched at one point...
Thanks for the explanation. I had no idea what was actually going on here.
Person X stands in front of a sophisticated computer playing the decision game Y which allows for the following options: either press the button "sim" or "not sim". If she presses "sim", the computer will simulate X*_1, X*_2, ..., X*_1000 which are a thousand identical copies of X. All of them will face the game Y* which - from the standpoint of each X* - is indistinguishable from Y. But the simulated computers in the games Y* don't run simulations. Additionally, we know that if X presses "sim" she receives a utility of 1, but "not sim" would only lead to 0.9. If X*_i (for i=1,2,3..1000) presses "sim" she receives 0.2, with "not sim" 0.1. For each agent it is true that she does not gain anything from the utility of another agent despite the fact she and the other agents are identical! Since all the agents are identical egoists facing the apparently same situation, all of them will take the same action.
Now the game starts. We face a computer and know all the above. We don't know whether we are X or any of the X*'s, should we now press "sim" or "not sim"?
EDIT: It seems to me that "identical" agents with "independent" utility functions were a clumsy set up for the above question, especially since one can interpret it as a contradiction. Hence, it might be better to switch to identical egoists whereas each agent only cares about her receiving money (linear monetary value function). If X presses "sim" she will be given 10$ (else 9$) in the end of the game; each X* who presses "sim" receives 2$ (else 1$), respectively. Each agent in the game wants to maximize the expected monetary value they themselves will hold in their own hand after the game. So, intrinsically, they don't care how much money the other copies make.
To spice things up: What if the simulation will only happen a year later? Are we then able to "choose" which year it is?