I don’t understand your notion of context here. I’m understanding pairwise comparisons as standard decision theory—you are comparing the expected values of two lotteries, nothing more. Is the context about psychology somehow? If so, that might be interesting, but adds a layer of complexity this sort of methodology cannot be expected to handle.
Players may have different utility functions, but that might be reasonable to ignore when modelling all of this. In any case, every intervention Ai will have its own, unique, expected utility from each player p, hence xpij=E[Up(Ai)]/E[Up(Aj)]=1/xpji. (This is ignoring noise in the estimates, but that is pretty easy to handle.)
I don’t understand your notion of context here. I’m understanding pairwise comparisons as standard decision theory—you are comparing the expected values of two lotteries, nothing more. Is the context about psychology somehow? If so, that might be interesting, but adds a layer of complexity this sort of methodology cannot be expected to handle.
Players may have different utility functions, but that might be reasonable to ignore when modelling all of this. In any case, every intervention Ai will have its own, unique, expected utility from each player p, hence xpij=E[Up(Ai)]/E[Up(Aj)]=1/xpji. (This is ignoring noise in the estimates, but that is pretty easy to handle.)