It seems that my communication attempt failed badly last time, so let me try again. The "standard" approach to indexicals is to treat indexical uncertainty the same as any other kind of uncertainty. You compute a probability of being at each location, and then maximize expected utility. I tried to point out in this post that because decisions made at each location can interact non-linearly, this doesn't work.

You transformed my example into a game theory example, and the paradox disappeared, because game theory does take into account interactions between different players. Notice that in your game theory example, the computation that arrives at the solution looks nothing like an expected utility maximization involving probabilities of being at different locations. The probability of being at a location doesn't enter into the decision algorithm at all, so do such probabilities mean anything?